Free coding interview prep with runnable Python solutions. Practice two sum, linked lists, binary trees, dynamic programming, graph algorithms, sliding window, and more. Filter by topic, company (Amazon, Google, Meta, Microsoft), and level (SWE1, SWE2, SWE3). Every question includes multiple solutions with time and space complexity analysis and an interactive Python editor powered by Pyodide. Reverse a string in Python using two-pointer O(n) and slice approaches. Common Amazon and Google new grad interview question. Topics: strings Companies: amazon, google Level: new-grad Two Pointers: Convert to a list, swap characters from both ends moving inward until the pointers meet. Slice: Use Python slice notation s[::-1] to create a reversed copy in one expression. Count vowels in a string using Python set lookup and generator expressions. Easy Amazon interview question for new grads. Topics: strings Companies: amazon Level: new-grad Set Lookup: Iterate over each character and check membership in a vowel set for O(1) per lookup. Check if a string is a palindrome in Python using two-pointer and slice approaches. Common Amazon and Microsoft interview question. Topics: strings, two-pointers Companies: amazon, microsoft Level: new-grad Two Pointers: Clean the string to only alphanumeric lowercase chars, then use two pointers from both ends. Slice Compare: Clean the string then compare it against its reverse using slice notation. Solve FizzBuzz in Python with a clean string concatenation approach. Classic interview question at Amazon, Google, and Meta. Topics: strings, lists Companies: amazon, google, meta Level: new-grad String Concatenation: Build the token by concatenating "Fizz" and "Buzz" conditionally, falling back to str(i). Find duplicates in a list using hash map counting and two-set O(n) approaches. Common Amazon and Google interview question. Topics: lists, hash-map Companies: amazon, google Level: new-grad, swe2 Hash Map Count: Count occurrences with a dict, then return keys whose count exceeds 1. Two Sets: Track a "seen" set and a "duplicates" set — add to duplicates when a number is already seen. Flatten an arbitrarily nested list in Python using recursion and iterative stack. Common Google and Meta interview question. Topics: lists, recursion Companies: google, meta Level: swe2 Recursive: Recursively extend result for sub-lists, append directly for integers. Stack depth = nesting depth d. Iterative Stack: Use an explicit stack (reversed items) to process elements without recursion limits. Filter and transform a list using Python list comprehensions. Easy Amazon new grad interview question. Topics: lists, comprehensions Companies: amazon Level: new-grad List Comprehension: A single list comprehension with an if clause selects evens and squares them in one expression. Build a word frequency counter in Python using Counter and dict. Common Amazon, Google, Microsoft interview question. Topics: dicts, strings Companies: amazon, google, microsoft Level: new-grad collections.Counter: Normalize to lowercase, split on whitespace, and count with collections.Counter. Implement a Stack class in Python using a list with O(1) push, pop, and peek. Common Amazon and Bloomberg OOP interview question. Topics: stack, oop Companies: amazon, bloomberg Level: new-grad, swe2 List-Backed Stack: Use a Python list with append() for push and pop() from the end — both O(1) amortized. Implement a Queue in Python using collections.deque for O(1) enqueue and dequeue. Common Amazon and Google interview question. Topics: queue, deque Companies: amazon, google Level: new-grad Deque-Backed Queue: Use collections.deque with append() to enqueue at right and popleft() to dequeue from left. Design a BankAccount class in Python with deposit, withdraw, and balance. Common Amazon and Microsoft OOP interview question. Topics: oop Companies: amazon, microsoft Level: new-grad Basic OOP: Store balance as a private attribute, validate withdrawals, raise ValueError for overdrafts. Implement a @timer decorator in Python using functools.wraps and perf_counter. Common Google and Meta SWE2 interview question. Topics: decorators Companies: google, meta Level: swe2 functools.wraps Decorator: Wrap the call with perf_counter before and after, print the delta, return the original result. functools.wraps preserves __name__ and __doc__. Implement an infinite Fibonacci generator in Python using yield. Common Amazon and Google interview question on generators. Topics: generators Companies: amazon, google Level: new-grad, swe2 Generator Function: Use yield to produce one value at a time while maintaining two running variables. Implement a custom context manager in Python with __enter__ and __exit__ for safe file handling. Common Google SWE2 interview question. Topics: oop, exceptions Companies: google Level: swe2 Context Manager Class: __enter__ opens and returns the file; __exit__ closes it and optionally suppresses FileNotFoundError. Filter even numbers using lambda+filter and list comprehension in Python. Easy Amazon new grad interview question. Topics: comprehensions, lists Companies: amazon Level: new-grad List Comprehension: A list comprehension with modulo filter — readable and Pythonic. Lambda + filter(): Pass a lambda to built-in filter() and convert to list — functional programming style. Validate email addresses in Python using regular expressions and re.fullmatch. Common Amazon and Google SWE2 interview question. Topics: regex, strings Companies: amazon, google Level: swe2 Regex Fullmatch: Use re.fullmatch with a pattern covering local part, @, domain segments, and TLD with minimum 2 chars. Format a receipt with aligned columns using Python f-strings. Easy Amazon new grad interview question on string formatting. Topics: strings Companies: amazon Level: new-grad f-String Formatting: Use f-strings with alignment specifiers to build aligned columns, then append subtotal, tax, and total. Read a file and count lines with exception handling in Python. Common Amazon and Microsoft new grad interview question. Topics: exceptions Companies: amazon, microsoft Level: new-grad try/except File Read: try/except wrapping a with-statement. Generator expression counts lines without loading the whole file. Design custom exception hierarchies in Python for payment processing. Common Google and Meta SWE2 OOP interview question. Topics: exceptions, oop Companies: google, meta Level: swe2 Exception Hierarchy: Subclass PaymentError for each specific error type, storing context as attributes and building descriptive messages in __init__. Implement a generic type-hinted Stack using TypeVar and Generic in Python. Common Google and Microsoft SWE2 interview question. Topics: typing, stack, oop Companies: google, microsoft Level: swe2 Generic Stack: Use TypeVar and Generic to parameterize the Stack class, providing type-safe operations with full annotations. Use zip and enumerate together in Python to iterate multiple lists with index. Common Amazon new grad interview question. Topics: lists Companies: amazon Level: new-grad enumerate + zip: Combine enumerate and zip to iterate with index, name, and score in a single loop. Understand and fix the Python mutable default argument bug. Common Google and Meta SWE2 interview question on Python gotchas. Topics: lists Companies: google, meta Level: swe2 None Default Pattern: Use None as default and assign a new list inside the body — creates a fresh list per call instead of sharing one object. Master *args and **kwargs in Python. Common Amazon and Google new grad interview question on variadic functions. Topics: oop Companies: amazon, google Level: new-grad *args and **kwargs: *args captures positional args as a tuple; **kwargs as a dict. Use functools.reduce for the product. Implement a closure-based counter factory in Python using nonlocal. Common Google and Meta SWE2 interview question on closures. Topics: oop Companies: google, meta Level: swe2 Closure with nonlocal: Use nonlocal to allow the inner function to mutate the enclosing scope count variable. Implement a shape hierarchy with inheritance and method overriding in Python. Common Amazon and Microsoft SWE2 interview question. Topics: oop Companies: amazon, microsoft Level: swe2 Inheritance with Override: Base class raises NotImplementedError; each subclass overrides area() with its own formula. Use Python abc to define abstract classes and enforce interfaces. Common Google SWE2 OOP interview question. Topics: oop Companies: google Level: swe2 ABC with abstractmethod: abc.ABC + @abstractmethod enforces the interface. Python raises TypeError at instantiation if any abstract method is missing. Implement a custom iterator in Python using __iter__ and __next__. Common Google and Meta SWE2 interview question. Topics: oop, generators Companies: google, meta Level: swe2 Iterator Protocol: __iter__ resets and returns self; __next__ yields and decrements, raising StopIteration when done. Use @property and @setter in Python for a Temperature class with validation. Common Amazon and Google SWE2 interview question. Topics: oop, decorators Companies: amazon, google Level: swe2 @property with Validation: Store Celsius internally; expose both as properties converting on the fly. Celsius setter validates against absolute zero. Use collections.namedtuple for a Point and compute Euclidean distance. Easy Amazon new grad Python interview question. Topics: oop, typing Companies: amazon Level: new-grad namedtuple + math.sqrt: Named tuple gives readable .x .y access; standard Euclidean formula computes distance. Use Python dataclasses to build a Student Registry with filtering and sorting. Common Google and Microsoft SWE2 interview question. Topics: oop, typing Companies: google, microsoft Level: swe2 dataclass + Registry: @dataclass generates boilerplate; __post_init__ validates; Registry methods filter and sort. Solve Two Sum in O(n) with a hash map and O(n^2) brute force. Classic Amazon, Google, Meta, Microsoft interview question. Topics: array, hash-map Companies: amazon, google, meta, microsoft Level: new-grad, swe2 Optimal - Hash Map: One pass: for each element x, check if complement (target-x) is in the map. If yes return indices, else store x->index. Brute Force: Check every pair (i,j) where i<j and return the pair that sums to target. Maximize stock profit in O(n) with a greedy scan. Classic Amazon, Google, Meta interview question with full Python solution. Topics: array, greedy Companies: amazon, google, meta Level: new-grad, swe2 Greedy: Track min_price and max_profit in one pass. At each price, update min or compute profit. Detect duplicates in an array in O(n) using a Python set. Easy Amazon and Google interview question. Topics: array, hash-map Companies: amazon, google Level: new-grad Set Length: If len(nums) != len(set(nums)), a duplicate exists. Early-Exit Set: Iterate and return True as soon as a repeated element is found. Compute product except self in O(n) without division using prefix and suffix passes. Top Amazon, Google, Meta interview question. Topics: array, prefix-sum Companies: amazon, google, meta, microsoft Level: swe2 Prefix & Suffix Pass: First pass builds prefix products into result. Second pass multiplies by running suffix product from right. Solve Maximum Subarray in O(n) with Kadane's algorithm. Classic Amazon, Google, Microsoft, Bloomberg interview question. Topics: array, dynamic-programming Companies: amazon, google, microsoft, bloomberg Level: new-grad, swe2 Kadane's Algorithm: Maintain running sum; reset to current element if running sum goes negative. Track global max. Find maximum product subarray tracking both max and min products in O(n). Amazon and Google SWE2/SWE3 interview question. Topics: array, dynamic-programming Companies: amazon, google Level: swe2, swe3 Track Max and Min: Track both max and min products ending at each position because a negative product can become the largest when multiplied by another negative. Find minimum in a rotated sorted array in O(log n) with binary search. Common Amazon, Google, Microsoft interview question. Topics: array, binary-search Companies: amazon, google, microsoft Level: swe2 Binary Search: Compare mid with right: if mid > right, minimum is in the right half; otherwise minimum is in the left half (including mid). Search a rotated sorted array in O(log n) with modified binary search. Common Amazon, Google, Meta SWE2/SWE3 question. Topics: array, binary-search Companies: amazon, google, meta Level: swe2, swe3 Modified Binary Search: At each step, one half is always sorted. Check if target lies in the sorted half; if so search there, otherwise search the other half. Find all unique triplets summing to zero in O(n^2) with sort + two pointers. Classic Amazon, Google, Meta, Bloomberg interview question. Topics: array, two-pointers, sorting Companies: amazon, google, meta, microsoft, bloomberg Level: swe2, swe3 Sort + Two Pointers: Sort the array. Fix element i, then use two pointers l=i+1 and r=n-1 to find pairs that sum to -nums[i]. Skip duplicates. Maximize water container area in O(n) using two pointers. Common Amazon, Google, Meta medium interview question. Topics: array, two-pointers, greedy Companies: amazon, google, meta Level: swe2 Two Pointers: Start with left=0 and right=n-1. Area = min(h[l],h[r]) * (r-l). Move the shorter pointer inward; this is the only way to possibly increase area. Check if two strings are anagrams using Counter or sorting. Easy Amazon, Google, Microsoft interview question. Topics: strings, hash-map, sorting Companies: amazon, google, microsoft Level: new-grad, swe2 Counter Comparison: Count character frequencies with Counter and compare — O(1) space since alphabet is fixed size. Sort: Sort both strings and compare — simple and correct, but slower. Group anagrams using sorted key hash map in O(n*k log k). Common Amazon, Google, Meta, Microsoft interview question. Topics: strings, hash-map, sorting Companies: amazon, google, meta, microsoft Level: swe2 Sorted Key HashMap: Sort each string to get a canonical key; group strings with the same key using defaultdict. Find the longest common prefix in a string array in O(S). Easy Amazon, Google, Microsoft interview question. Topics: strings Companies: amazon, google, microsoft Level: new-grad Horizontal Scan: Take first string as prefix. Shrink it until every other string starts with it. Validate bracket strings with a stack in O(n). Classic Amazon, Google, Meta, Microsoft, Bloomberg interview question. Topics: strings, stack Companies: amazon, google, meta, microsoft, bloomberg Level: new-grad, swe2 Stack: Push opening brackets. For each closing bracket, pop from stack and check if it matches. Return True iff stack is empty at end. Reverse word order in a string using split, reverse, join in O(n). Common Amazon and Microsoft SWE2 interview question. Topics: strings, two-pointers Companies: amazon, microsoft Level: swe2 Split, Reverse, Join: split() tokenizes (handles extra spaces), reversed() reverses, join() reassembles with single space. Run-length encode a string in O(n) with two pointers. Common Amazon, Microsoft, Bloomberg SWE2 interview question. Topics: strings, two-pointers Companies: amazon, microsoft, bloomberg Level: swe2 Two Pointer RLE: Walk the string counting consecutive identical characters; append char and count to result; return shorter of compressed vs original. Rotate an array in-place in O(n) O(1) space using three reverses. Common Amazon, Google, Microsoft interview question. Topics: array, two-pointers Companies: amazon, google, microsoft Level: swe2 Three Reverses: Reverse whole array, reverse first k elements, reverse remaining n-k elements. Find the missing number in O(n) O(1) using Gauss sum or XOR trick. Common Amazon, Google, Microsoft new grad interview question. Topics: array, bit-manipulation Companies: amazon, google, microsoft Level: new-grad Math / Gauss Sum: Expected sum of 0..n is n*(n+1)//2. Missing = expected - actual sum. XOR: XOR every index (0..n) with every value. Paired values cancel; only the missing number remains. Find the single non-duplicate element in O(n) O(1) using the XOR trick. Common Amazon, Google, Meta easy interview question. Topics: array, bit-manipulation Companies: amazon, google, meta Level: new-grad XOR: XOR all elements together. Duplicate pairs cancel (a ^ a = 0). What remains is the single number. Move zeros to the end in-place in O(n) O(1) with two pointers. Easy Amazon and Google interview question. Topics: array, two-pointers Companies: amazon, google Level: new-grad Two Pointers: Use an insert_pos pointer. Copy non-zero elements to insert_pos. Fill the rest with zeros. Merge overlapping intervals in O(n log n) by sorting and scanning. Classic Amazon, Google, Meta, Bloomberg interview question. Topics: array, sorting Companies: amazon, google, meta, microsoft, bloomberg Level: swe2, swe3 Sort + Scan: Sort by start. Extend last merged interval if current overlaps, else append new interval. Insert and merge a new interval in O(n) with three-phase approach. Common Google and LinkedIn SWE2 interview question. Topics: array Companies: google, linkedin Level: swe2 Three-Phase Merge: Collect all intervals ending before new starts, then merge overlapping ones, then append the rest. Traverse a matrix in spiral order using boundary simulation. Common Amazon, Google, Microsoft, Bloomberg interview question. Topics: matrix Companies: amazon, google, microsoft, bloomberg Level: swe2 Boundary Simulation: Maintain top/bottom/left/right boundaries. Traverse right, down, left, up in turn, shrinking bounds each time. Set matrix rows and columns to zero in O(m*n) O(1) space using first row/col as markers. Amazon, Google, Microsoft interview question. Topics: matrix Companies: amazon, google, microsoft Level: swe2 O(1) Space Using First Row/Col: Use the first row and first column as markers for which rows/cols need zeroing. Handle the first row/col separately. Find longest substring without repeating chars in O(n) with sliding window. Top Amazon, Google, Meta, Bloomberg interview question. Topics: strings, sliding-window, hash-map Companies: amazon, google, meta, microsoft, bloomberg Level: swe2 Sliding Window + Set: Expand right pointer. When duplicate found, shrink from left until removed. Track max window size. Optimized Hash Map: Store char->last index. On duplicate, jump left pointer directly to last_index+1 instead of stepping one at a time. Find minimum window substring in O(|s|+|t|) with sliding window and frequency maps. Hard Amazon, Google, Meta SWE3 question. Topics: strings, sliding-window, hash-map Companies: amazon, google, meta Level: swe3, senior Sliding Window with Counts: Use two hash maps: required counts from t and current window counts. Track "have" vs "need" to know when window is valid. Expand right, shrink left when valid. Find all anagram positions in a string using fixed sliding window in O(n). Common Amazon and Google SWE2 interview question. Topics: strings, sliding-window, hash-map Companies: amazon, google Level: swe2 Fixed Sliding Window: Use a fixed-size window of len(p). Maintain frequency counts and a "matches" counter to check validity in O(1). Count subarrays summing to k in O(n) with prefix sum and hash map. Common Amazon, Google, Meta SWE2/SWE3 question. Topics: array, prefix-sum, hash-map Companies: amazon, google, meta Level: swe2, swe3 Prefix Sum + HashMap: At each position, compute prefix sum. If prefix_sum - k exists in the map, those subarrays sum to k. Store prefix sums with their counts. Compute trapped rainwater in O(n) O(1) with two pointers. Hard Amazon, Google, Meta, Bloomberg senior interview question. Topics: array, two-pointers, stack Companies: amazon, google, meta, microsoft, bloomberg Level: swe3, senior Two Pointers: Two pointers from both ends. Water at any position = min(left_max, right_max) - height. Process the side with smaller max; that side determines the water level. Solve Jump Game in O(n) with greedy tracking of farthest reachable index. Common Amazon, Google, Meta, Microsoft interview question. Topics: array, greedy, dynamic-programming Companies: amazon, google, meta, microsoft Level: swe2 Greedy: Track farthest reachable index. If current position exceeds it, we are stuck. Otherwise update farthest. Reverse a singly linked list in O(n) iteratively (O(1) space) and recursively. Classic Amazon, Google, Meta, Microsoft interview question. Topics: linked-list, recursion Companies: amazon, google, meta, microsoft Level: new-grad, swe2 Iterative: Walk with three pointers; redirect each node's next to prev. O(1) extra space. Recursive: Recurse to the tail; on the way back reverse each link. Detect a cycle in a linked list in O(n) O(1) using Floyd's tortoise and hare. Classic Amazon, Google, Meta, Microsoft interview question. Topics: linked-list, two-pointers Companies: amazon, google, meta, microsoft Level: new-grad, swe2 Floyd's Tortoise and Hare: Slow pointer moves 1 step, fast moves 2. If they ever point to the same node, a cycle exists. Find the middle of a linked list in O(n) O(1) with slow/fast pointers. Common Amazon and Microsoft new grad interview question. Topics: linked-list, two-pointers Companies: amazon, microsoft Level: new-grad Slow/Fast Pointers: Move slow by 1 and fast by 2. When fast reaches end, slow is at middle. Merge two sorted linked lists in O(m+n) iteratively and recursively. Classic Amazon, Google, Meta, Microsoft, Bloomberg interview question. Topics: linked-list, recursion Companies: amazon, google, meta, microsoft, bloomberg Level: new-grad, swe2 Iterative with Dummy: Use a dummy head. At each step append the smaller of list1/list2 heads. Append remaining. Remove nth node from end in one pass using two pointers. Common Amazon, Google, Microsoft SWE2 interview question. Topics: linked-list, two-pointers Companies: amazon, google, microsoft Level: swe2 Two Pointers One Pass: Advance fast pointer n+1 steps ahead. Then move both until fast is None. Slow is just before the node to delete. Check if a linked list is palindrome in O(n) O(1) by reversing the second half. Common Amazon, Google, Meta interview question. Topics: linked-list, two-pointers, stack Companies: amazon, google, meta Level: new-grad, swe2 Reverse Half: Find middle with slow/fast, reverse second half, compare both halves, then restore. Find linked list intersection in O(m+n) O(1) with two-pointer switch trick. Common Amazon and Microsoft interview question. Topics: linked-list, two-pointers, hash-map Companies: amazon, microsoft Level: new-grad Two Pointer Switch: Each pointer traverses both lists. After m+n steps they either meet at intersection or both reach None together. Remove duplicates from a sorted linked list in O(n) O(1). Easy Amazon and Google new grad interview question. Topics: linked-list Companies: amazon, google Level: new-grad Single Pass: Walk the list; skip nodes whose value equals the current node's value. Insert a node into a sorted circular linked list handling all edge cases. Common Google and Amazon SWE2 interview question. Topics: linked-list, circular-linked-list Companies: google, amazon Level: swe2 Three-Case Insert: Traverse and handle: (1) insert between curr and curr.next when curr <= val <= next, (2) at boundary when curr is max and val is outside range, (3) full loop means all equal. Delete a node without head reference in O(1) by copying next value. Easy Amazon, Microsoft, Bloomberg interview question. Topics: linked-list Companies: amazon, microsoft, bloomberg Level: new-grad Copy and Skip: Copy next node's value into the current node, then bypass the next node. Add two numbers represented as reversed linked lists in O(max(m,n)). Classic Amazon, Google, Meta, Bloomberg interview question. Topics: linked-list, math Companies: amazon, google, meta, microsoft, bloomberg Level: swe2 Digit-by-Digit Simulation: Walk both lists simultaneously, add digits with carry. Continue while either list or carry is non-zero. Reverse linked list nodes in k-groups recursively. Hard Amazon, Google, Microsoft SWE3/Senior interview question. Topics: linked-list, recursion Companies: amazon, google, microsoft Level: swe3, senior Recursive: Check k nodes exist. If yes, reverse them and recurse on the rest. If not, return as-is. Deep copy a linked list with random pointers using hash map in O(n). Common Amazon, Google, Microsoft SWE2/SWE3 interview question. Topics: linked-list, hash-map Companies: amazon, google, microsoft Level: swe2, swe3 Hash Map Two Pass: First pass: create a copy of each node and store in a map. Second pass: set next and random pointers using the map. Implement LRU Cache in O(1) with doubly linked list and hash map. Classic Amazon, Google, Meta, Bloomberg SWE2/SWE3 interview question. Topics: linked-list, doubly-linked-list, hash-map Companies: amazon, google, meta, microsoft, bloomberg Level: swe2, swe3 Doubly Linked List + Hash Map: Use a doubly linked list (most recent at head, LRU at tail) and a hash map. On access/update, move node to head. On capacity overflow, evict tail. Sort a linked list in O(n log n) using merge sort. Common Amazon and Google SWE2/SWE3 interview question. Topics: linked-list, sorting, divide-and-conquer Companies: amazon, google Level: swe2, swe3 Top-Down Merge Sort: Find middle with slow/fast, split, recursively sort both halves, merge. O(log n) recursion stack. Reorder a linked list in O(n) O(1) by finding middle, reversing, and merging. Common Amazon and Google SWE2 interview question. Topics: linked-list, two-pointers Companies: amazon, google Level: swe2 Find Middle + Reverse + Merge: Find middle with slow/fast, reverse second half, then interleave first and reversed second halves. Swap adjacent linked list nodes in O(n) O(1) iteratively. Common Amazon, Google, Microsoft SWE2 interview question. Topics: linked-list, recursion Companies: amazon, google, microsoft Level: swe2 Iterative: Use a dummy head. At each iteration, swap the two nodes after prev pointer, then advance prev by 2. Partition a linked list around value x in O(n) O(1) using two sub-lists. Common Amazon and Bloomberg SWE2 interview question. Topics: linked-list, two-pointers Companies: amazon, bloomberg Level: swe2 Two-Partition Lists: Build two sub-lists: one for nodes < x, one for nodes >= x. Merge them at the end. Flatten a multilevel doubly linked list in O(n) by splicing child lists. Common Amazon and Google SWE2 interview question. Topics: linked-list, doubly-linked-list, dfs Companies: amazon, google Level: swe2 Iterative DFS: Walk the list. When a node has a child, find the tail of the child list, splice it between current and current.next, then set child to None. Rotate a linked list right by k places in O(n) O(1). Common Amazon, Google, Microsoft SWE2 interview question. Topics: linked-list, two-pointers Companies: amazon, google, microsoft Level: swe2 Find Length + Rotate: Find length and tail, make circular, then find new tail at length-k%length-1 and break the circle. Inorder traversal of a binary tree recursively and iteratively with a stack. Common Amazon, Google, Microsoft interview question. Topics: binary-tree, dfs, stack, recursion Companies: amazon, google, microsoft Level: new-grad, swe2 Recursive: Recursively visit left subtree, then root, then right subtree. Iterative Stack: Use an explicit stack: push left nodes until null, then pop and record, then process right subtree. Level order traversal of a binary tree using BFS in O(n). Classic Amazon, Google, Meta, Bloomberg interview question. Topics: binary-tree, bfs Companies: amazon, google, meta, microsoft, bloomberg Level: swe2 BFS with Queue: Use a deque for BFS. At start of each iteration, snapshot the queue length to process exactly one level. Find the maximum depth of a binary tree with recursive DFS in O(n). Easy Amazon, Google, Meta, Microsoft interview question. Topics: binary-tree, dfs, bfs, recursion Companies: amazon, google, meta, microsoft Level: new-grad Recursive DFS: Depth is 0 for null; 1 + max of left and right depths otherwise. Check if a binary tree is symmetric with recursive mirror comparison. Easy Amazon, Google, Microsoft interview question. Topics: binary-tree, dfs, bfs, recursion Companies: amazon, google, microsoft Level: new-grad, swe2 Recursive Mirror Check: A tree is symmetric if its left and right subtrees are mirrors. Mirror check: left.val == right.val AND mirrors(left.left, right.right) AND mirrors(left.right, right.left). Invert a binary tree recursively in O(n). Easy Amazon, Google, Meta interview question. Topics: binary-tree, dfs, bfs, recursion Companies: amazon, google, meta Level: new-grad Recursive: Swap left and right at current node, then recursively invert each subtree. Find the diameter of a binary tree in O(n) with post-order DFS. Easy Amazon, Google, Meta interview question. Topics: binary-tree, dfs Companies: amazon, google, meta Level: new-grad, swe2 DFS with Global Max: Post-order DFS: at each node, diameter candidate = left_height + right_height. Return height to parent. Track global max. Check if a root-to-leaf path sums to target in O(n) with recursive DFS. Easy Amazon and Microsoft new grad interview question. Topics: binary-tree, dfs, recursion Companies: amazon, microsoft Level: new-grad Recursive DFS: At each node subtract its value from target. At a leaf, return True if remaining == 0. Find LCA in a BST in O(h) using BST ordering property. Classic Amazon, Google, Meta, Bloomberg SWE2 interview question. Topics: binary-tree, bst, dfs Companies: amazon, google, meta, microsoft, bloomberg Level: swe2 BST Property: Use BST ordering: if both p,q < root go left; if both > root go right; else current root is LCA. Validate a BST in O(n) by passing min/max bounds through DFS. Classic Amazon, Google, Meta, Bloomberg interview question. Topics: binary-tree, bst, dfs Companies: amazon, google, meta, microsoft, bloomberg Level: swe2 DFS with Bounds: Pass min and max bounds to each recursive call. A node must satisfy min < node.val < max. Find kth smallest in BST in O(H+k) with iterative inorder traversal. Common Amazon, Google, Bloomberg SWE2 interview question. Topics: binary-tree, bst, dfs Companies: amazon, google, bloomberg Level: swe2 Iterative Inorder: Use iterative inorder traversal. Decrement k each time we process a node; return when k hits 0. Convert sorted array to height-balanced BST in O(n) with divide and conquer. Common Amazon and Google SWE2 interview question. Topics: binary-tree, bst, divide-and-conquer Companies: amazon, google Level: swe2 Divide & Conquer: Always pick the middle element as root. Recursively build left subtree from left half and right from right half. Find maximum path sum in a binary tree in O(n) with post-order DFS. Hard Amazon, Google, Meta, Microsoft SWE3/Senior interview question. Topics: binary-tree, dfs Companies: amazon, google, meta, microsoft Level: swe3, senior Post-Order DFS: At each node compute: local_max = node.val + max(0,left) + max(0,right). Update global max. Return node.val + max(0, best_one_side) to parent. Serialize and deserialize a binary tree with BFS in O(n). Hard Amazon, Google, Meta, LinkedIn SWE3/Senior interview question. Topics: binary-tree, bfs, dfs Companies: amazon, google, meta, microsoft, linkedin Level: swe3, senior BFS Level-Order: Serialize with BFS, storing null for missing children. Deserialize by replaying BFS order from the tokens. Get the right side view of a binary tree using BFS in O(n). Common Amazon, Google, Meta SWE2 interview question. Topics: binary-tree, bfs, dfs Companies: amazon, google, meta Level: swe2 BFS Last Node Per Level: BFS level-order; append the last node's value from each level to the result. Sum all root-to-leaf path numbers in O(n) with DFS. Common Amazon and Google SWE2 interview question. Topics: binary-tree, dfs Companies: amazon, google Level: swe2 DFS with Accumulated Sum: Pass current accumulated number (curr * 10 + node.val) down the DFS. At a leaf, return the accumulated value. Check if a tree is a subtree of another in O(m*n) with DFS and same-tree comparison. Common Amazon and Google SWE2 question. Topics: binary-tree, dfs Companies: amazon, google Level: swe2 DFS with Same-Tree Check: At each node in root, check if it matches subRoot with an is_same helper. Return True if any match found. Check if a binary tree is height-balanced in O(n) with post-order DFS and -1 sentinel. Common Amazon, Google, Microsoft interview question. Topics: binary-tree, dfs Companies: amazon, google, microsoft Level: new-grad, swe2 Post-Order DFS: Compute height in post-order. Return -1 as a sentinel for "unbalanced" so we can short-circuit early. Implement a Trie with insert, search, and startsWith in O(m) per operation. Common Amazon, Google, Meta, Microsoft SWE2/SWE3 question. Topics: trie, oop Companies: amazon, google, meta, microsoft Level: swe2, swe3 Dict-Based Trie: Each node stores a dict of children and a is_end flag. Insert/search/startsWith traverse character by character. Flatten a binary tree to linked list in-place in O(n) O(1). Common Amazon, Google, Microsoft SWE2 interview question. Topics: binary-tree, dfs, linked-list Companies: amazon, google, microsoft Level: swe2 Morris-like In-Place: For each node with a left child, find the rightmost node of the left subtree, connect it to right child, move left subtree to right, set left to null. Construct a binary tree from preorder and inorder traversals in O(n) with hash map. Common Amazon, Google, Bloomberg SWE2/SWE3 question. Topics: binary-tree, dfs, hash-map Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Recursive with HashMap: preorder[0] is root. Use a hash map to find its position in inorder in O(1). Left subtree has inorder[:pos] elements, right has inorder[pos+1:]. Count islands in a 2D grid using DFS or BFS in O(m*n). Top Amazon, Google, Microsoft interview question with complete Python solution. Topics: graph, bfs, dfs, matrix Companies: amazon, google, microsoft, bloomberg, meta Level: swe2, swe3 DFS: For each unvisited land cell, run DFS marking the island visited by setting "1" to "0". Count DFS initiations. BFS: For each unvisited land cell, BFS to mark the whole island. Count BFS initiations. Deep copy a graph using DFS or BFS with hash map in O(V+E). Common Amazon, Google, Meta interview question with Python solution. Topics: graph, dfs, bfs, hash-table Companies: amazon, google, meta, microsoft Level: swe2, swe3 DFS with Hash Map: Dictionary maps originals to clones. Recursively clone each neighbor, using the map to avoid duplicates. BFS with Hash Map: BFS from start. Clone each node once into a hash map. Link cloned neighbors during traversal. Detect cycle in directed graph with DFS or Kahn's BFS topological sort in O(V+E). Amazon, Google, Bloomberg interview question. Topics: graph, topological-sort, dfs, bfs Companies: amazon, google, microsoft, bloomberg, uber Level: swe2, swe3 DFS Cycle Detection: 3-state DFS: 0=unvisited, 1=visiting, 2=done. If we re-visit a visiting node, there is a cycle. Kahn's BFS Topological Sort: Count in-degrees. Enqueue zero-in-degree nodes. Process BFS decrementing neighbor in-degrees. If all processed, no cycle. Find cells where water flows to both oceans using multi-source BFS in O(m*n). Google, Amazon interview question with Python solution. Topics: graph, bfs, dfs, matrix Companies: amazon, google, bloomberg Level: swe3, senior Multi-Source BFS: BFS from all Pacific border cells and all Atlantic border cells separately. Result is the intersection of both reachable sets. Solve Word Ladder with BFS or bidirectional BFS. Amazon, Google, Bloomberg hard interview question with Python solution. Topics: graph, bfs, hash-table Companies: amazon, google, microsoft, bloomberg, linkedin Level: swe3, senior BFS: BFS level by level. Replace each character with a-z. If result is in word set and unvisited, enqueue. Bidirectional BFS: BFS from both ends simultaneously. Expand the smaller frontier each step. Stop when frontiers meet. Determine if edges form a valid tree using Union-Find or DFS. Google, LinkedIn interview question with Python solution. Topics: graph, dfs, union-find Companies: google, linkedin, amazon, microsoft Level: swe2, swe3 Union-Find: Check n-1 edges first. Union-Find: adding an edge between nodes in the same component creates a cycle. DFS: DFS from node 0 tracking parent to avoid false cycles. Tree is valid if all n nodes are visited. Count connected components in undirected graph using Union-Find or DFS. Google, LinkedIn interview question with Python solution. Topics: graph, dfs, union-find Companies: google, linkedin, amazon, microsoft Level: swe2, swe3 Union-Find: Initialize n components. For each edge, union two nodes. Each successful union decrements component count. DFS: Build adjacency list. DFS from each unvisited node marking all reachable nodes. Count DFS initiations. Derive alien language order using DFS topological sort with cycle detection. Amazon, Google, Airbnb hard interview question. Topics: graph, topological-sort, dfs Companies: amazon, google, meta, microsoft, airbnb Level: swe3, senior DFS Topological Sort: Build directed graph from adjacent word comparisons. DFS topological sort with 3-state cycle detection. Find shortest 8-directional clear path in binary matrix using BFS in O(n^2). Amazon, Google interview question with Python solution. Topics: graph, bfs, matrix Companies: amazon, google, bloomberg, microsoft Level: swe2, swe3 BFS: BFS from (0,0) in 8 directions. Mark visited by setting cells to 1. First arrival at (n-1,n-1) is shortest path. Capture surrounded regions in a board using DFS from borders in O(m*n). Amazon, Google, Bloomberg interview question. Topics: graph, dfs, bfs, matrix Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 DFS from Border: Mark all border-connected "O"s as "S" (safe). Flip remaining "O" to "X", then "S" back to "O". Solve Rotting Oranges with multi-source BFS in O(m*n). Amazon, Google, Bloomberg medium interview question with Python solution. Topics: graph, bfs, matrix Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Multi-Source BFS: Enqueue all initially rotten oranges with time=0. BFS outward decrementing fresh count. Return max time if fresh==0. Check if path exists between two nodes using BFS or Union-Find. Easy graph question for new grads with Python solution. Topics: graph, dfs, bfs, union-find Companies: amazon, google, microsoft Level: new-grad, swe2 BFS: BFS from source. Return True if destination is reached. Union-Find: Union all edges. Check if source and destination share the same root. Find maximum island area using DFS in O(m*n). Amazon, Google, Bloomberg medium interview question with Python solution. Topics: graph, dfs, bfs, matrix Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 DFS: For each unvisited 1, DFS counting cells by marking them 0. Return max count seen. Find minimum signal delay using Dijkstra's algorithm. Amazon, Google, Uber interview question with Python solution. Topics: graph, dijkstra, heap Companies: amazon, google, microsoft, uber Level: swe3, senior Dijkstra's Algorithm: Min-heap Dijkstra from k. Relax edges greedily. Answer is max shortest distance; -1 if any node unreachable. Find the town judge using net degree scoring in O(E). Easy graph question for new grads with complete Python solution. Topics: graph, array, hash-table Companies: amazon, google, microsoft Level: new-grad, swe2 Net Score: Net score: +1 for being trusted, -1 for trusting. Judge has score exactly n-1. Check graph bipartiteness using BFS 2-coloring in O(V+E). Amazon, Google, Bloomberg interview question with Python solution. Topics: graph, bfs, dfs Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 BFS 2-Coloring: Assign colors 0/1 via BFS. If any neighbor shares the same color, not bipartite. Implement Kruskal's MST with Union-Find in O(E log E). Amazon, Google, Microsoft hard interview question with Python solution. Topics: graph, union-find, sorting, greedy Companies: amazon, google, microsoft, bloomberg Level: swe3, senior Kruskal's with Union-Find: Sort edges by weight. Greedily add edges using Union-Find, skipping cycle-creating edges. Sum weights of n-1 chosen edges. Merge accounts with shared emails using Union-Find. Amazon, Google, Meta interview question with Python solution. Topics: graph, union-find, dfs, sorting Companies: amazon, google, meta, bloomberg Level: swe3, senior Union-Find: Map each email to a parent. Union all emails in the same account. Group by root then reconstruct. Find the redundant edge creating a cycle using Union-Find. Amazon, Google interview question with Python solution. Topics: graph, union-find, dfs Companies: amazon, google, microsoft Level: swe2, swe3 Union-Find: Process edges in order. When union fails (both endpoints in same component), that edge is redundant. Fill rooms with distances to nearest gate using multi-source BFS in O(m*n). Meta, Google, Amazon interview question. Topics: graph, bfs, matrix Companies: meta, google, amazon, bloomberg Level: swe2, swe3 Multi-Source BFS: Enqueue all gate positions. BFS outward; update each INF room with current distance. Count distinct ways to climb n stairs using DP (Fibonacci) in O(n) O(1). Classic Amazon, Google, Apple interview question. Topics: dynamic-programming, math Companies: amazon, google, microsoft, bloomberg, apple Level: new-grad, swe2 DP (Bottom-Up): dp[i] = dp[i-1] + dp[i-2]. Use two variables instead of full array. Recursive with Memoization: Top-down recursion with memo cache. Base cases: n=1 -> 1, n=2 -> 2. Maximize robbery without adjacent houses using DP in O(n) O(1). Amazon, Google, Bloomberg medium interview question. Topics: dynamic-programming, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 DP O(1) Space: At each house, max is either skip it (prev1) or rob it (prev2 + current). Track just two variables. DP Array: Build dp array where dp[i] = max money robbing up to house i. Circular house robber using two-pass linear DP in O(n). Amazon, Google medium interview question with Python solution. Topics: dynamic-programming, array Companies: amazon, google, microsoft Level: swe2, swe3 Two-Pass DP: Since first and last are adjacent, solve two linear subproblems: rob houses 0..n-2 and rob houses 1..n-1. Return the max. Find LIS length using DP O(n^2) or binary search O(n log n). Amazon, Google, LinkedIn medium interview question. Topics: dynamic-programming, binary-search, array Companies: amazon, google, microsoft, bloomberg, linkedin Level: swe2, swe3 DP O(n^2): dp[i] = length of LIS ending at index i. For each i, check all j < i where nums[j] < nums[i]. Binary Search (Patience Sorting) O(n log n): Maintain a tails array where tails[i] = smallest tail of increasing subsequence of length i+1. Binary search to place each element. Find minimum coins to make amount using bottom-up DP in O(amount*coins). Amazon, Google, Goldman Sachs interview question. Topics: dynamic-programming, array, breadth-first-search Companies: amazon, google, microsoft, goldman-sachs, bloomberg Level: swe2, swe3 Bottom-Up DP: dp[i] = min coins to make amount i. Initialize to infinity. For each amount, try every coin. BFS: BFS treats amount as a graph. Each node is an amount; edges are coin subtractions. BFS finds shortest path to 0. Check if string can be segmented into dictionary words using DP in O(n^2). Amazon, Google, Meta, Bloomberg interview question. Topics: dynamic-programming, trie, hash-table Companies: amazon, google, meta, microsoft, bloomberg Level: swe2, swe3 Bottom-Up DP: dp[i] = True if s[:i] can be formed. For each i, check all j < i where dp[j] is True and s[j:i] is in the word set. Count unique paths in m x n grid using DP in O(m*n). Amazon, Google, Bloomberg medium interview question with Python solution. Topics: dynamic-programming, math, combinatorics Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 DP O(m*n): dp[i][j] = paths to reach cell (i,j) = paths from top + paths from left. DP O(n) Space: Use a single row dp. Update in-place: dp[j] += dp[j-1]. Determine if you can reach the last index using greedy O(n) or DP. Amazon, Google, Bloomberg medium interview question. Topics: dynamic-programming, greedy, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Greedy: Track max reachable index. If current index ever exceeds max_reach, return False. DP: dp[i] = True if index i is reachable. For each reachable i, mark all positions i+1 to i+nums[i] as reachable. Find minimum jumps to reach last index using greedy in O(n). Amazon, Google, Bloomberg medium interview question. Topics: dynamic-programming, greedy, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Greedy: Track current jump end and farthest reachable. When i reaches current_end, increment jumps and set current_end = farthest. Find LCS length using 2D DP in O(m*n). Amazon, Google, Microsoft, Bloomberg medium interview question with Python solution. Topics: dynamic-programming, string Companies: amazon, google, microsoft, bloomberg, oracle Level: swe2, swe3 Bottom-Up DP: 2D DP table. If text1[i-1] == text2[j-1]: dp[i][j] = dp[i-1][j-1] + 1, else dp[i][j] = max(dp[i-1][j], dp[i][j-1]). Space-Optimized DP: Use two rows instead of the full 2D table. Find minimum edit distance between two strings using 2D DP in O(m*n). Amazon, Google, Bloomberg hard interview question. Topics: dynamic-programming, string Companies: amazon, google, microsoft, bloomberg, linkedin Level: swe3, senior Bottom-Up DP: dp[i][j] = min operations to convert word1[:i] to word2[:j]. If chars match, take diagonal. Else 1 + min of insert/delete/replace. Partition array into equal subsets using 0/1 knapsack DP in O(n*sum). Amazon, Google, Bloomberg medium interview question. Topics: dynamic-programming, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 DP with Bitset: Use a set of reachable sums. For each number, add it to all existing reachable sums. Check if target (sum/2) is reachable. DP Array: Boolean array dp where dp[s] = can reach sum s. Traverse in reverse to avoid reuse. Count ways to assign +/- to reach target sum using DFS memoization or DP. Amazon, Google, Meta interview question. Topics: dynamic-programming, dfs, array Companies: amazon, google, meta, bloomberg Level: swe2, swe3 DFS with Memoization: Recursive DFS: at each index choose + or -. Memoize on (index, current_sum). DP with Hash Map: Use a counter dict mapping sum -> count. For each number update all sums by adding or subtracting the number. Count string decoding ways using DP in O(n). Amazon, Google, Meta, Bloomberg medium interview question with Python solution. Topics: dynamic-programming, string Companies: amazon, google, meta, bloomberg, microsoft Level: swe2, swe3 Bottom-Up DP: dp[i] = ways to decode s[:i]. Add dp[i-1] if s[i-1] is 1-9, add dp[i-2] if s[i-2:i] is 10-26. Space-Optimized DP: Only need prev2 and prev1 instead of full dp array. Maximize profit with at most 2 stock transactions using state machine DP in O(n). Amazon, Google, Goldman Sachs hard interview question. Topics: dynamic-programming, array Companies: amazon, google, goldman-sachs, bloomberg Level: swe3, senior State Machine DP: Track 4 states: cost of first buy, profit after first sell, cost of second buy, profit after second sell. Update greedily. Find minimum palindrome partition cuts using 2D DP in O(n^2). Amazon, Google, Bloomberg hard interview question. Topics: dynamic-programming, string Companies: amazon, google, bloomberg Level: swe3, senior DP with Palindrome Precomputation: Precompute is_pal[i][j]. Then dp[i] = min of (dp[j-1] + 1) for all j <= i where s[j:i+1] is palindrome. Wildcard pattern matching with ? and * using 2D DP in O(m*n). Amazon, Google, Bloomberg hard interview question. Topics: dynamic-programming, string, greedy Companies: amazon, google, microsoft, bloomberg Level: swe3, senior Bottom-Up DP: dp[i][j] = True if s[:i] matches p[:j]. Handle "*" as match-zero (dp[i][j-1]) or match-one-more (dp[i-1][j]). Regex pattern matching with . and * using 2D DP in O(m*n). Amazon, Google, Microsoft hard interview question. Topics: dynamic-programming, string, recursion Companies: amazon, google, microsoft, bloomberg Level: swe3, senior Bottom-Up DP: dp[i][j] = s[:i] matches p[:j]. For "*": zero occurrences (dp[i][j-2]) or match one more (dp[i-1][j] if chars match). Find maximum product subarray by tracking min and max in O(n). Amazon, Google, Bloomberg medium interview question. Topics: dynamic-programming, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 DP Track Min and Max: Track current max and min products. A negative number flips max and min. Update global max. Find minimum path sum in triangle using bottom-up DP in O(n^2). Amazon, Google, Bloomberg medium interview question. Topics: dynamic-programming, array Companies: amazon, google, bloomberg, microsoft Level: swe2, swe3 Bottom-Up DP In-Place: Start from second-to-last row, add minimum of the two children below. Result is triangle[0][0]. Find minimum path sum in m x n grid using DP in O(m*n). Amazon, Google, Bloomberg medium interview question. Topics: dynamic-programming, matrix Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 DP In-Place: Modify grid in-place. dp[i][j] = grid[i][j] + min of left and top neighbors. Maximize coins by bursting balloons using interval DP in O(n^3). Amazon, Google hard interview question with Python solution. Topics: dynamic-programming, divide-and-conquer Companies: amazon, google, bloomberg Level: senior, staff Interval DP: Add boundary 1s. dp[l][r] = max coins bursting all balloons between l and r exclusive. Try each k as the last balloon burst. Solve 0/1 knapsack problem using 2D DP or space-optimized 1D DP in O(n*W). Amazon, Google, Goldman Sachs interview question. Topics: dynamic-programming, array Companies: amazon, google, microsoft, goldman-sachs Level: swe2, swe3 2D DP: dp[i][w] = max value using first i items with capacity w. Either skip item i or take it. 1D DP (Space-Optimized): Use 1D dp array, traverse weights in reverse to avoid using same item twice. Solve rod cutting problem using bottom-up DP in O(n^2). Amazon, Google, Microsoft interview question with Python solution. Topics: dynamic-programming, array Companies: amazon, google, microsoft Level: swe2, swe3 Bottom-Up DP: dp[i] = max revenue for rod of length i. Try all cuts j from 1 to i. Solve egg drop problem with minimum trials using DP in O(k log n). Amazon, Google, Goldman Sachs hard interview question. Topics: dynamic-programming, binary-search, math Companies: amazon, google, goldman-sachs, bloomberg Level: senior, staff DP on Trials: dp[m][k] = max floors checkable with m moves and k eggs. dp[m][k] = dp[m-1][k-1] + dp[m-1][k] + 1. Find min m where dp[m][k] >= n. Implement merge sort from scratch in O(n log n). Amazon, Google, Microsoft interview question with complete Python solution. Topics: sorting, divide-and-conquer, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Recursive Merge Sort: Recursively split array in half. Merge two sorted halves by comparing elements and building result. In-Place Merge Sort: Sort in-place using index boundaries instead of slicing, reducing memory allocation. Implement quicksort with Lomuto partition or randomized pivot in O(n log n). Amazon, Google interview question. Topics: sorting, divide-and-conquer, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Lomuto Partition Scheme: Pick last element as pivot. Partition: elements <= pivot go left. Recursively sort both halves. Randomized Pivot: Randomly swap pivot before partitioning to avoid worst-case O(n^2) on sorted input. Implement heap sort in-place using max-heap in O(n log n) O(1) space. Amazon, Google, Microsoft interview question. Topics: sorting, heap, array Companies: amazon, google, microsoft Level: swe2, swe3 Heap Sort In-Place: Build max-heap in O(n). Then repeatedly swap root with last, reduce heap size, and heapify down. Find k-th largest using min-heap O(n log k) or quickselect O(n). Amazon, Google, Meta, Bloomberg interview question. Topics: sorting, heap, divide-and-conquer, array Companies: amazon, google, meta, microsoft, bloomberg Level: swe2, swe3 Min-Heap of Size k: Maintain a min-heap of size k. For each element, push to heap; if size > k, pop the min. The top of heap is the k-th largest. Quickselect: Use quickselect (partial quicksort). Partition around pivot; recurse only into the partition containing position n-k. Sort 0s, 1s, 2s in-place using Dutch National Flag 3-pointer technique in O(n). Amazon, Google interview question. Topics: sorting, two-pointers, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Dutch National Flag (3 Pointers): Three pointers: low (next 0 spot), mid (current), high (next 2 spot). Advance mid: swap 0 to low, skip 1, swap 2 to high. Merge overlapping intervals after sorting in O(n log n). Amazon, Google, Meta, Bloomberg medium interview question. Topics: sorting, array, intervals Companies: amazon, google, meta, microsoft, bloomberg Level: swe2, swe3 Sort and Merge: Sort by start. Iterate; if current start <= last end, merge by extending end. Otherwise append new interval. Insert and merge a new interval into sorted non-overlapping intervals in O(n). Amazon, Google, Meta interview question. Topics: sorting, array, intervals Companies: amazon, google, meta, bloomberg Level: swe2, swe3 Three-Phase Linear Scan: Phase 1: add all non-overlapping intervals before new. Phase 2: merge all overlapping. Phase 3: add remaining. Binary search in rotated sorted array in O(log n). Amazon, Google, Meta, Bloomberg medium interview question with Python solution. Topics: binary-search, array Companies: amazon, google, meta, microsoft, bloomberg Level: swe2, swe3 Modified Binary Search: At each step, determine which half is sorted. If target is in sorted half, search there; otherwise search the other half. Find peak element using binary search in O(log n). Amazon, Google, Bloomberg medium interview question with Python solution. Topics: binary-search, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Binary Search: If nums[mid] < nums[mid+1], the peak is to the right. Otherwise it is to the left (inclusive of mid). Search sorted 2D matrix using binary search in O(log(m*n)). Amazon, Google, Bloomberg medium interview question. Topics: binary-search, matrix, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Binary Search on Virtual 1D Array: Treat the matrix as a sorted 1D array of length m*n. Binary search using virtual index mapping. Find median of two sorted arrays using binary search in O(log(min(m,n))). Amazon, Google, Goldman Sachs hard interview question. Topics: binary-search, array, divide-and-conquer Companies: amazon, google, microsoft, bloomberg, goldman-sachs Level: swe3, senior Binary Search on Partition: Binary search partition in shorter array. Ensure left partition has (m+n+1)//2 elements total. Check cross-border conditions. Find minimum in rotated sorted array using binary search in O(log n). Amazon, Google, Bloomberg interview question. Topics: binary-search, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Binary Search: If nums[mid] > nums[hi], the min is in the right half. Otherwise min is in left half including mid. Compute h-index by sorting citations in O(n log n). Google, Amazon, Bloomberg interview question with Python solution. Topics: sorting, array, binary-search Companies: google, amazon, bloomberg Level: swe2, swe3 Sort and Scan: Sort descending. Walk through: if citations[i] >= i+1, h = i+1. Return the last valid h. Find minimum conference rooms using min-heap or two sorted arrays in O(n log n). Amazon, Google, Meta interview question. Topics: sorting, heap, intervals Companies: amazon, google, meta, bloomberg, microsoft Level: swe2, swe3 Min-Heap of End Times: Sort by start. Use min-heap of end times. If next meeting starts after earliest ending, reuse that room. Two Sorted Arrays: Sort start and end times separately. Use two pointers; if next start < current end, need another room. Arrange numbers to form largest value using custom comparator sort in O(n log n). Amazon, Google, Bloomberg interview question. Topics: sorting, string, greedy Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Custom Sort: Custom comparator: for two numbers a and b, prefer a first if str(a)+str(b) > str(b)+str(a). Edge case: all zeros. Find all unique triplets summing to zero using sort and two pointers in O(n^2). Amazon, Google, Meta, Bloomberg interview question. Topics: two-pointers, sorting, array Companies: amazon, google, meta, microsoft, bloomberg Level: swe2, swe3 Sort + Two Pointers: Sort array. For each index i, use two pointers lo=i+1 and hi=n-1. Move pointers based on sum. Skip duplicates. Find all unique quadruplets summing to target using sort and two pointers in O(n^3). Amazon, Google interview question. Topics: two-pointers, sorting, array Companies: amazon, google, microsoft Level: swe2, swe3 Sort + Two Nested Loops + Two Pointers: Sort. Two outer loops fix first two elements. Inner two pointers find the remaining pair. Skip duplicates. Find max water container using two pointers in O(n). Amazon, Google, Meta, Bloomberg medium interview question. Topics: two-pointers, array, greedy Companies: amazon, google, meta, bloomberg, microsoft Level: swe2, swe3 Two Pointers: Start pointers at both ends. Area = min(h[lo], h[hi]) * (hi-lo). Move shorter pointer inward. Compute trapped rain water using two pointers O(n) O(1) or DP. Amazon, Google, Meta, Bloomberg hard interview question. Topics: two-pointers, dynamic-programming, stack, array Companies: amazon, google, meta, bloomberg, microsoft Level: swe3, senior Two Pointers: Two pointers lo/hi. Track max_left and max_right. Process side with smaller max; water at that side = max - height. DP Precompute Max: Precompute max_left[i] and max_right[i] arrays. Water at i = min(max_left[i], max_right[i]) - height[i]. Find minimum window substring using sliding window in O(|s|+|t|). Amazon, Google, Meta hard interview question. Topics: sliding-window, hash-table, string, two-pointers Companies: amazon, google, meta, bloomberg, microsoft Level: swe3, senior Sliding Window: Track needed char counts. Expand right pointer adding chars. When window is valid, contract left minimizing window. Find longest substring without repeating characters using sliding window in O(n). Amazon, Google, Meta, Bloomberg interview question. Topics: sliding-window, hash-table, string, two-pointers Companies: amazon, google, meta, bloomberg, microsoft Level: swe2, swe3 Sliding Window with Dict: Track last index of each char. When duplicate found, jump left to max(left, last_index+1). Track max window length. Check if s2 contains permutation of s1 using fixed sliding window in O(n). Amazon, Google, Meta interview question. Topics: sliding-window, hash-table, string, two-pointers Companies: amazon, google, meta, bloomberg Level: swe2, swe3 Fixed Sliding Window: Count chars in s1. Slide window of length len(s1) over s2, updating counts. Match when all counts are 0. Find all anagram start indices using fixed sliding window in O(n). Amazon, Google, Meta, Bloomberg interview question. Topics: sliding-window, hash-table, string Companies: amazon, google, meta, bloomberg Level: swe2, swe3 Fixed Sliding Window: Slide window of size len(p). Use have/need counters to track when window is a valid anagram. Find longest substring with at most k replacements using sliding window in O(n). Amazon, Google, Bloomberg interview question. Topics: sliding-window, hash-table, string Companies: amazon, google, bloomberg, microsoft Level: swe2, swe3 Sliding Window: Expand window right. Track frequency of most common char. If window_size - max_freq > k, slide left by 1. Find max consecutive 1s with k flips using sliding window in O(n). Amazon, Google, Bloomberg interview question. Topics: sliding-window, array, two-pointers Companies: amazon, google, bloomberg Level: swe2, swe3 Sliding Window: Expand window right. When zero count exceeds k, move left. Track max window size. Find max fruits with 2 baskets using sliding window in O(n). Amazon, Google, Bloomberg interview question. Topics: sliding-window, hash-table, array Companies: amazon, google, bloomberg Level: swe2, swe3 Sliding Window with At Most 2 Distinct: Sliding window tracking count of each fruit type. When more than 2 types, shrink window from left. Count subarrays with exactly k distinct integers using at-most-K trick in O(n). Amazon, Google, Bloomberg hard question. Topics: sliding-window, hash-table, array Companies: amazon, google, bloomberg Level: swe3, senior At Most K Trick: exactly(k) = at_most(k) - at_most(k-1). Helper counts subarrays with at most k distinct using sliding window. Find minimum subarray with sum >= target using sliding window in O(n). Amazon, Google, Bloomberg medium interview question. Topics: sliding-window, two-pointers, array, binary-search Companies: amazon, google, bloomberg, microsoft Level: swe2, swe3 Sliding Window: Expand right pointer adding elements. When sum >= target, record length and shrink left pointer. Find longest subarray of 1s after deleting one element using sliding window. Amazon, Google interview question. Topics: sliding-window, array, dynamic-programming Companies: amazon, google, bloomberg Level: swe2, swe3 Sliding Window (at most one zero): Sliding window allowing at most one 0 in window. Answer is max(window_size - 1) since we must delete one element. Count subarrays with exactly k odd numbers using prefix sum in O(n). Amazon, Google, Bloomberg interview question. Topics: sliding-window, hash-table, array, math Companies: amazon, google, bloomberg Level: swe2, swe3 Prefix Sum + Hash Map: Count prefix sums of (num % 2). For each prefix, look up (prefix - k) in map. Validate bracket string using a stack in O(n). Classic Amazon, Google, Meta easy interview question with Python solution. Topics: stack, string Companies: amazon, google, meta, bloomberg, microsoft Level: new-grad, swe2 Stack: Push opening brackets onto stack. For closing brackets, check if stack top is the matching opener. Design a min stack with O(1) getMin using dual stacks. Amazon, Google, Meta, Bloomberg medium interview question. Topics: stack, design Companies: amazon, google, meta, bloomberg, microsoft Level: swe2, swe3 Dual Stack: Maintain main stack and min_stack. Min stack stores the current minimum at each point. Push min to min_stack on each push. Evaluate RPN expression using a stack in O(n). Amazon, Google, Bloomberg, LinkedIn medium interview question. Topics: stack, array, math Companies: amazon, google, bloomberg, linkedin Level: swe2, swe3 Stack: Push numbers. On operator, pop two values, apply operation, push result. Final stack top is the answer. Find days until warmer temperature using monotonic stack in O(n). Amazon, Google, Bloomberg medium interview question. Topics: stack, array, monotonic-stack Companies: amazon, google, bloomberg, microsoft Level: swe2, swe3 Monotonic Stack: Stack of indices in decreasing temperature order. When current temp > stack top, pop and record gap. Find largest rectangle in histogram using monotonic stack in O(n). Amazon, Google, Bloomberg hard interview question. Topics: stack, array, monotonic-stack Companies: amazon, google, bloomberg, microsoft Level: swe3, senior Monotonic Stack: Maintain increasing stack of indices. When current bar is shorter, pop and compute area. Use sentinel 0 at start and end. Implement queue using two stacks with amortized O(1) operations. Amazon, Google easy design interview question. Topics: stack, queue, design Companies: amazon, google, microsoft, bloomberg Level: new-grad, swe2 Two Stacks (Amortized O(1)): Input stack for push. Output stack for pop/peek. Transfer all from input to output when output is empty. Implement stack using queues with O(n) push. Amazon, Google easy design interview question with Python solution. Topics: stack, queue, design Companies: amazon, google, microsoft Level: new-grad, swe2 Single Queue (rotate on push): After pushing new element, rotate queue (n-1 times) so new element is at the front. Find sliding window maximum using monotonic deque in O(n). Amazon, Google, Bloomberg hard interview question. Topics: stack, queue, sliding-window, array, monotonic-stack Companies: amazon, google, bloomberg, microsoft Level: swe3, senior Monotonic Deque: Maintain deque of indices in decreasing value order. Front is always the window max. Remove indices out of window. Find next greater element using monotonic stack in O(m+n). Amazon, Google, Bloomberg easy interview question. Topics: stack, array, hash-table, monotonic-stack Companies: amazon, google, bloomberg Level: new-grad, swe2 Monotonic Stack + Hash Map: Process nums2 with monotonic stack. Build a map from value to its next greater. Look up each nums1 element. Evaluate arithmetic expression with stack in O(n). Amazon, Google, Bloomberg medium interview question with Python solution. Topics: stack, string, math Companies: amazon, google, bloomberg, microsoft Level: swe2, swe3 Stack: Parse left to right. On + push num, on - push -num, on * or / pop stack top and push result. Sum stack at end. Find the single non-duplicate number using XOR in O(n) O(1). Classic Amazon, Google, Meta easy bit manipulation question. Topics: bit-manipulation, array Companies: amazon, google, meta, bloomberg Level: new-grad, swe2 XOR: XOR all elements. a XOR a = 0, a XOR 0 = a. All pairs cancel leaving the single element. Count 1 bits using Brian Kernighan's algorithm in O(k). Amazon, Google easy bit manipulation interview question. Topics: bit-manipulation Companies: amazon, google, bloomberg Level: new-grad, swe2 Brian Kernighan: n & (n-1) clears the lowest set bit. Count iterations until n becomes 0. Built-in / Shift: Count set bits by shifting right and checking LSB, or use bin(n).count("1"). Reverse 32 bits of an integer using bit shifting in O(32). Amazon, Google easy bit manipulation interview question. Topics: bit-manipulation Companies: amazon, google, bloomberg Level: new-grad, swe2 Bit by Bit: For each of 32 bits, shift result left by 1, add LSB of n, then shift n right by 1. Find missing number using math sum or XOR in O(n) O(1). Amazon, Google, Bloomberg easy interview question. Topics: bit-manipulation, math, array Companies: amazon, google, bloomberg, microsoft Level: new-grad, swe2 Math (Sum): Expected sum = n*(n+1)/2. Actual sum = sum(nums). Missing = expected - actual. XOR: XOR all indices 0..n with all values. Pairs cancel, missing index remains. Check if number is power of two using bit trick n & (n-1) in O(1). Amazon, Google easy bit manipulation question. Topics: bit-manipulation, math Companies: amazon, google, bloomberg Level: new-grad, swe2 Bit Trick: n > 0 and (n & (n-1)) == 0. Powers of 2 have exactly one set bit; n-1 has all lower bits set; AND is 0. Count set bits for 0..n using DP bit trick in O(n). Amazon, Google easy bit manipulation and DP question. Topics: bit-manipulation, dynamic-programming Companies: amazon, google, bloomberg Level: new-grad, swe2 DP with Bit Trick: dp[i] = dp[i >> 1] + (i & 1). The count for i equals count for i/2 plus the last bit of i. Add two integers without + using XOR and AND carry in O(1). Amazon, Google, Bloomberg medium bit manipulation question. Topics: bit-manipulation, math Companies: amazon, google, bloomberg Level: swe2, swe3 Bit Manipulation: XOR gives bits where exactly one is set (sum without carry). AND<<1 gives carry. Repeat until carry=0. Reverse integer digits with overflow check in O(log n). Amazon, Google, Bloomberg medium interview question. Topics: math Companies: amazon, google, bloomberg, microsoft Level: swe2, swe3 Math: Extract digits with mod 10. Build reversed number. Check 32-bit bounds before returning. Check if integer is a palindrome without string conversion. Amazon, Google easy math interview question. Topics: math Companies: amazon, google, bloomberg, microsoft Level: new-grad, swe2 Reverse Half: Negative or trailing-zero numbers are not palindromes. Reverse second half of digits and compare with first half. String Conversion: Convert to string and compare with its reverse. Convert integer to Roman numeral using greedy approach in O(1). Amazon, Google, Bloomberg medium interview question. Topics: math, string, hash-table Companies: amazon, google, bloomberg, microsoft Level: swe2, swe3 Greedy with Value Table: Table of values from 1000 to 1 including subtractive cases. Greedily subtract largest value, append symbol. Convert Roman numeral to integer using right-to-left scan in O(n). Amazon, Google easy math interview question. Topics: math, string, hash-table Companies: amazon, google, bloomberg, microsoft Level: new-grad, swe2 Right to Left Scan: Scan right to left. If current value < previous value, subtract; otherwise add. Convert Excel column title to number using base-26 in O(n). Amazon, Google easy math interview question. Topics: math, string Companies: amazon, google, bloomberg, microsoft Level: new-grad, swe2 Base-26 Conversion: Treat each char as a base-26 digit. A=1..Z=26. Accumulate result = result*26 + (ord(c)-64). Determine if a number is happy using hash set or Floyd's cycle detection in O(log n). Amazon, Google easy math question. Topics: math, hash-table, two-pointers Companies: amazon, google, bloomberg Level: new-grad, swe2 Hash Set for Cycle Detection: Compute sum of digit squares. If seen before, not happy. If reaches 1, happy. Floyd's Cycle Detection: Fast pointer moves two steps, slow moves one. If they meet at 1, happy. If they meet elsewhere, unhappy. Compute integer square root using binary search in O(log x). Amazon, Google easy interview question with Python solution. Topics: math, binary-search Companies: amazon, google, bloomberg, microsoft Level: new-grad, swe2 Binary Search: Binary search: find largest k where k*k <= x. Narrow range [0, x]. Find GCD of strings using math GCD of lengths in O(m+n). Amazon, Google easy math and string interview question. Topics: math, string Companies: amazon, google, bloomberg Level: new-grad, swe2 Math GCD: If str1+str2 == str2+str1, a GCD string exists. Its length is gcd(len(str1), len(str2)). Find the element appearing once in O(n) time O(1) space using XOR bit manipulation. Classic Amazon Google interview question. Topics: bit-manipulation, array, math Companies: amazon, google, microsoft, meta, bloomberg Level: new-grad, swe2 XOR Bit Manipulation: XOR all numbers together. Pairs cancel out (a^a=0) and 0^x=x leaves the single number. Math (2*sum(set) - sum): 2 * sum(set(nums)) - sum(nums) equals the single number because each duplicate is counted once in the set. Find the element appearing once when all others appear 3 times. Bit counting and state machine approaches in Python. Topics: bit-manipulation, array, math Companies: google, amazon, microsoft, bloomberg Level: swe2, swe3 Bit Count Modulo 3: For each of the 32 bit positions, count how many numbers have that bit set. If count % 3 != 0, the single number has that bit set. State Machine (ones, twos): Use two bitmasks: ones tracks bits seen once, twos tracks bits seen twice. When a bit is seen 3 times it resets to 0 in both. Find two numbers appearing once using XOR partitioning in O(n) time O(1) space. Google Amazon interview question. Topics: bit-manipulation, array, math Companies: google, amazon, microsoft Level: swe2, swe3 XOR Partitioning: XOR all to get a^b. Find a set bit in a^b and use it to split numbers into two groups, each containing one unique number. XOR each group. HashSet: Use a set: add elements not seen, remove if already present. What remains are the two unique numbers. Count set bits in an integer using Brian Kernighan algorithm and bit shifting. Classic bit manipulation interview question. Topics: bit-manipulation, math Companies: apple, microsoft, amazon, google Level: new-grad, swe2 Brian Kernighan Algorithm: n & (n-1) clears the lowest set bit. Count how many times until n becomes 0. Bit Check Each Position: Check each of the 32 bit positions by ANDing with 1 and right-shifting. Reverse bits of a 32-bit unsigned integer using bit manipulation. Apple Amazon interview question with complete Python solution. Topics: bit-manipulation, math Companies: apple, amazon, microsoft Level: new-grad, swe2 Bit by Bit Reversal: For each of 32 positions, take the LSB of n, add to result, shift n right and result left. Python String Reversal: Format as 32-bit binary string, reverse it, convert back to int. Find the missing number in range [0,n] using Gauss formula or XOR in O(n) time O(1) space. Amazon Microsoft interview question. Topics: bit-manipulation, math, array Companies: amazon, microsoft, google, bloomberg Level: new-grad, swe2 Gauss Sum Formula: Expected sum is n*(n+1)/2. Subtract actual sum to find missing number. XOR Approach: XOR all indices 0..n and all values. Each present number cancels its index; missing index remains. Check if a number is power of two in O(1) using bit trick n&(n-1)==0. Classic bit manipulation interview question. Topics: bit-manipulation, math, recursion Companies: amazon, google, microsoft Level: new-grad, swe2 Bit Trick: A power of two has exactly one bit set. n & (n-1) clears the lowest set bit; if result is 0, n was a power of two. Repeated Division: Repeatedly divide by 2. If we reach 1, it is a power of two. Count 1 bits for every number 0 to n in O(n) using DP relationship dp[i]=dp[i>>1]+(i&1). Topics: bit-manipulation, dynamic-programming, math Companies: amazon, google, microsoft, bloomberg Level: new-grad, swe2 DP with Right Shift: dp[i] = dp[i // 2] + (i % 2). Dividing by 2 right-shifts, LSB contributes 1 if odd. Brian Kernighan per element: For each number, repeatedly clear lowest bit to count set bits. Add two integers without + operator using XOR and carry bit manipulation. Amazon Google interview question. Topics: bit-manipulation, math Companies: amazon, google, microsoft, meta Level: swe2, swe3 Bit Manipulation with Carry: XOR gives bits that differ (sum without carry). AND<<1 gives carry. Repeat until carry is zero. Use mask for Python 32-bit handling. Recursive: Recursively compute sum and carry until no carry remains. Reverse digits of a 32-bit integer with overflow handling. Amazon Bloomberg interview question with two Python solutions. Topics: math Companies: amazon, bloomberg, apple, microsoft Level: new-grad, swe2 Pop and Push Digits: Extract digits from x using modulo, build reversed number, check 32-bit overflow. String Reversal: Convert to string, reverse, handle sign and leading zeros, check overflow. Check if integer is palindrome by reversing half the number. Amazon Microsoft Bloomberg interview question. Topics: math Companies: amazon, microsoft, bloomberg, apple Level: new-grad, swe2 Reverse Half the Number: Reverse the second half of x and compare with first half. Negative numbers and multiples of 10 (except 0) are not palindromes. String Conversion: Convert to string and check if it equals its reverse. Convert integer to Roman numeral using greedy approach. Amazon Bloomberg Microsoft interview question with complete Python solution. Topics: math, string-matching Companies: amazon, bloomberg, microsoft, uber Level: swe2, swe3 Greedy with Value-Symbol Table: Define value-symbol pairs including subtractive forms in descending order. Greedily subtract largest possible value. Digit by Digit Table: Pre-define Roman representations for each digit position (thousands, hundreds, tens, ones). Convert Roman numeral to integer using right-to-left scan. Amazon Google Bloomberg easy interview question. Topics: math, string-matching Companies: amazon, bloomberg, microsoft, apple, google Level: new-grad, swe2 Right to Left Scan: Scan right to left. If current symbol value is less than the maximum seen so far, subtract it; otherwise add it. Left to Right Peek Next: Scan left to right. If current value < next value, subtract current; otherwise add it. Convert Excel column title to number using base-26 arithmetic. Microsoft Amazon interview question. Topics: math Companies: microsoft, amazon, bloomberg Level: new-grad, swe2 Base-26 Conversion: Treat as base-26 number where A=1, B=2, ..., Z=26. Process each character left to right. functools.reduce: Use reduce to fold the base-26 accumulation over the string. Determine happy number using Floyd cycle detection or hashset. Amazon Microsoft Google interview question. Topics: math, fast-slow-pointers, hash-map Companies: amazon, microsoft, google, bloomberg Level: new-grad, swe2 Fast-Slow Pointers (Floyd): Treat the sequence as a linked list. Use slow/fast pointers to detect cycle. If fast reaches 1, happy. HashSet Cycle Detection: Track seen values in a set. If n becomes 1 return True; if n repeats return False. Compute integer square root using binary search or Newton method. Amazon Google Bloomberg interview question. Topics: math, binary-search Companies: amazon, google, bloomberg, microsoft Level: new-grad, swe2 Binary Search: Binary search in [0, x]. Find largest m where m*m <= x. Newton's Method: Newton's iteration: r = (r + x/r) / 2 converges to sqrt(x) quadratically. Implement GCD and LCM using Euclidean algorithm recursively and iteratively. Google Amazon math interview question. Topics: math, number-theory, recursion Companies: google, amazon, microsoft, bloomberg Level: new-grad, swe2 Euclidean Algorithm: gcd: repeatedly replace (a,b) with (b, a%b) until b=0. lcm: a*b//gcd(a,b). Recursive GCD: Recursive Euclidean: gcd(a,b) = a if b==0 else gcd(b, a%b). Count primes less than n using Sieve of Eratosthenes in O(n log log n). Classic math interview question. Topics: math, number-theory Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Sieve of Eratosthenes: Create boolean array, mark all multiples of each prime p starting from p^2 as composite. Segmented Sieve (memory efficient): Use a standard sieve for small primes up to sqrt(n), then sieve segments of size sqrt(n). Implement pow(x,n) in O(log n) using recursive halving and iterative bit manipulation. Google Amazon interview question. Topics: math, recursion, divide-and-conquer, bit-manipulation Companies: google, amazon, microsoft, bloomberg, facebook Level: swe2, swe3 Recursive Fast Exponentiation: Halve n each step: if n even x^n=(x^2)^(n/2), if n odd multiply by x. Handle negative n. Iterative Bit Manipulation: Use bits of n to decide which powers of x to multiply. Square x each step, multiply result when bit is set. Multiply two large numbers represented as strings without converting to int. Amazon Google interview question. Topics: math, string-matching, array Companies: amazon, google, microsoft, bloomberg, facebook Level: swe2, swe3 Grade School Multiplication: Each pair of digits (i,j) contributes to positions (i+j, i+j+1) in the result array. Build array, handle carries, convert to string. Built-in Conversion (reference): Convert strings to int using ord arithmetic only, multiply, convert back without int(). Add two binary strings and return the sum as binary string. Amazon Google easy interview question. Topics: math, bit-manipulation, string-matching Companies: amazon, google, microsoft, bloomberg, apple Level: new-grad, swe2 Two Pointer from Right: Use pointers starting from end of each string. Add digits + carry, build result in reverse. Python int Conversion: Convert both binary strings to int using base 2, add, convert result back to binary string. Add two large numbers represented as strings using grade school algorithm. Amazon Google interview question. Topics: math, string-matching Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Grade School Addition: Add digit by digit from right with carry, using ord to convert chars to ints. zip_longest approach: Use itertools.zip_longest to pair up reversed strings, add digits + carry. Count occurrences of digit 1 in all numbers from 0 to n using mathematical position analysis. Hard Google Amazon interview. Topics: math, number-theory, dynamic-programming Companies: google, amazon, bloomberg, microsoft Level: swe3, senior Mathematical Position Analysis: For each digit position p (1,10,100...), calculate how many 1s appear in that position across all numbers 0..n. Digit DP: Use digit DP counting 1s digit by digit with tight constraints. Find nth ugly number (factors 2,3,5) using three pointer DP in O(n). Google Amazon interview question. Topics: math, dynamic-programming, heap, two-pointers Companies: google, amazon, bloomberg, microsoft Level: swe2, swe3 Three Pointers DP: Maintain three pointers p2, p3, p5 into the ugly array. Each step take the minimum of dp[p2]*2, dp[p3]*3, dp[p5]*5. Min Heap: Use a min-heap. Pop the minimum, push *2, *3, *5 of popped value. Skip duplicates with a seen set. Find minimum perfect squares summing to n using DP and BFS. Google Amazon interview question with two Python solutions. Topics: dynamic-programming, bfs, math, number-theory Companies: google, amazon, microsoft, bloomberg Level: swe2, swe3 Dynamic Programming: dp[i] = minimum squares summing to i. For each i, try all perfect squares <= i. BFS Level by Level: Treat as shortest path: BFS level = number of squares used. Return level when n is reached. Implement merge sort from scratch in Python. Covers recursive divide-and-conquer approach with O(n log n) time complexity. Topics: sorting, divide-and-conquer, recursion Companies: google, amazon, microsoft, meta, bloomberg Level: new-grad, swe2 Recursive Merge Sort: Divide the array in half, recursively sort each half, then merge the two sorted halves by comparing elements one at a time. In-place Merge Sort: Sort in place by modifying the input array directly during merge, using O(log n) stack space for recursion. Implement quicksort with randomized pivot in Python. Covers Lomuto and three-way partition approaches with complexity analysis. Topics: sorting, divide-and-conquer, recursion Companies: google, amazon, meta, microsoft, apple Level: new-grad, swe2, swe3 Randomized QuickSort (Lomuto partition): Pick a random pivot, swap it to the end, then partition the array so all elements less than pivot are on the left. Recurse on both sides. Three-Way Partition (Dutch Flag): Use Dutch National Flag three-way partition to handle duplicates efficiently. Partition into <pivot, ==pivot, >pivot. Implement heap sort in Python using a max-heap. In-place O(n log n) sorting with detailed heapify explanation. Topics: sorting, heap Companies: microsoft, amazon, google, bloomberg Level: new-grad, swe2 Heap Sort (in-place max-heap): Build a max-heap in-place with O(n) heapify. Then repeatedly swap root (max) with last element, reduce heap size, and sift down. Find the kth largest element using min-heap O(n log k) and quickselect O(n). Top Amazon, Google, Meta interview question. Topics: heap, sorting, divide-and-conquer Companies: amazon, google, meta, microsoft, apple, uber, linkedin Level: swe2, swe3 Min-Heap of size k: Maintain a min-heap of size k. For each element, push it. If heap exceeds k, pop the minimum. The root is always the kth largest. Quickselect: Use quickselect: partition around a random pivot. If the pivot lands at position k-1 from the end, it is the answer. Recurse only on the relevant partition. Sort colors (0,1,2) in one pass using Dutch National Flag algorithm with three pointers. Classic Amazon and Microsoft interview question. Topics: array, sorting, two-pointers, dutch-flag Companies: amazon, microsoft, google, meta, bloomberg, uber Level: new-grad, swe2 Dutch National Flag (one pass): Use three pointers: low (boundary of 0s), mid (current), high (boundary of 2s). Swap 0s left and 2s right while advancing mid. Two-pass count sort: Count occurrences of 0, 1, 2, then overwrite the array. Simple but two passes. Merge overlapping intervals in Python with sort and scan approach. O(n log n) solution for Google, Amazon, Meta interviews. Topics: array, sorting, interval Companies: google, amazon, microsoft, meta, bloomberg, uber, linkedin, apple Level: swe2, swe3 Sort and Merge: Sort intervals by start time. Iterate through and merge the current interval with the last interval in result if they overlap (start <= last end). Insert and merge a new interval into a sorted non-overlapping interval list. O(n) linear scan solution for Google and Amazon interviews. Topics: array, interval, binary-search Companies: google, amazon, microsoft, linkedin, bloomberg Level: swe2, swe3 Linear Scan Three Phases: Add all intervals ending before new interval starts. Merge all overlapping intervals. Add all remaining intervals. Binary search in a rotated sorted array in O(log n). Essential Amazon, Google, Apple interview question with clear Python solution. Topics: binary-search, array Companies: amazon, google, microsoft, meta, apple, bloomberg, uber Level: swe2, swe3 Binary Search on Rotated Array: At each step, determine which half is sorted. If the target lies in the sorted half, search there. Otherwise search the other half. Find a peak element in O(log n) using binary search. Google interview question with detailed explanation. Topics: binary-search, array Companies: google, microsoft, amazon, meta Level: swe2, swe3 Binary Search: If nums[mid] < nums[mid+1], slope is going up so peak is to the right. Otherwise slope is going down (or mid is peak) so peak is to the left or at mid. Search a sorted 2D matrix in O(log(mn)) by treating it as a 1D array. Amazon and Microsoft interview question. Topics: binary-search, matrix, array Companies: amazon, microsoft, google, bloomberg, apple Level: swe2, swe3 Binary Search (treat as 1D): Treat the m*n matrix as a sorted 1D array. Binary search on indices 0 to m*n-1. Convert mid index to row=mid//n, col=mid%n. Find median of two sorted arrays in O(log(min(m,n))) using binary search partition. Hard Google and Amazon interview problem. Topics: binary-search, divide-and-conquer, array Companies: google, amazon, microsoft, meta, apple, uber, bloomberg Level: swe3, senior, staff Binary Search on partition: Binary search on the smaller array to find partition point. Left side of both arrays combined = half of total elements. Median comes from max of left parts and min of right parts. Merge then find median (O(m+n)): Merge both sorted arrays fully, then return the middle element(s). Simpler but does not meet the O(log(m+n)) constraint. Find minimum element in rotated sorted array in O(log n) with binary search. Amazon, Google interview question. Topics: binary-search, array Companies: amazon, microsoft, google, apple, bloomberg Level: swe2, swe3 Binary Search: Binary search: if nums[mid] > nums[right], minimum is in right half. Otherwise minimum is in left half (including mid). Calculate researcher h-index in Python using sort or counting sort. Google and LinkedIn interview question with O(n) solution. Topics: array, sorting, binary-search Companies: google, amazon, bloomberg, linkedin Level: swe2, swe3 Sort descending: Sort descending. h is the largest index+1 where citations[i] >= i+1. After sort, citations[i] >= i+1 means at least i+1 papers with >= i+1 citations. Counting Sort O(n): Use bucket counting: bucket[i] = papers with exactly i citations (cap at n). Scan from right; accumulate count; first position where count >= i is h-index. Find minimum conference rooms needed with min-heap approach. O(n log n) solution for Amazon, Google, Meta interviews. Topics: heap, sorting, interval, greedy Companies: amazon, google, microsoft, meta, bloomberg, uber, linkedin Level: swe2, swe3, senior Min-Heap of end times: Sort by start. Maintain a min-heap of end times (rooms in use). For each meeting, if the earliest-ending room ends before this starts, reuse it. Otherwise allocate a new room. Two sorted arrays (events): Create separate sorted arrays of start times and end times. Use two pointers: when a new meeting starts, if earliest end has passed, decrement rooms needed. Arrange numbers to form largest number using custom comparator sort. Amazon and Google interview question. Topics: sorting, greedy, strings Companies: amazon, microsoft, google, bloomberg, uber Level: swe2, swe3 Custom Comparator Sort: Convert numbers to strings. Custom sort: a comes before b if str(a)+str(b) > str(b)+str(a). Join sorted strings and handle leading zeros. Count smaller elements to the right using merge sort in O(n log n). Hard Google and Amazon interview problem. Topics: sorting, divide-and-conquer, binary-search Companies: google, amazon, meta, microsoft Level: swe3, senior Merge Sort with index tracking: Merge sort on (value, original_index) pairs. During merge, whenever a right-half element is placed before a left-half element, all remaining left-half elements get +1 count. Sort a linked list in O(n log n) using merge sort with slow/fast pointer split. Amazon and Google interview question. Topics: linked-list, sorting, divide-and-conquer, two-pointers Companies: amazon, microsoft, google, meta, bloomberg Level: swe2, swe3 Merge Sort (top-down recursive): Find midpoint with slow/fast pointers, split into two halves, sort each half recursively, then merge the two sorted lists. Find top k frequent elements using heap O(n log k) or bucket sort O(n). Amazon, Google, Meta interview question. Topics: heap, hash-map, sorting, bucket-sort Companies: amazon, google, meta, microsoft, bloomberg, uber, apple Level: swe2, swe3 Min-Heap: Count frequency of each element. Maintain min-heap of size k keyed by frequency. Final heap contains the k most frequent elements. Bucket Sort O(n): Count frequencies. Create frequency buckets where bucket[i] holds all elements with frequency i. Read from highest bucket downward until k elements collected. Find top k frequent words sorted by frequency then lexicographically using a min-heap. Amazon and Google interview question. Topics: heap, hash-map, sorting, strings Companies: amazon, google, microsoft, bloomberg, apple Level: swe2, swe3 Min-Heap with negated frequency: Count frequencies. Use a min-heap of (-frequency, word) tuples. Python heaps are min-heaps; negating frequency makes highest frequency float up. Pop when size > k. Find k closest elements to x in sorted array using binary search on window boundary. Google and Amazon interview question. Topics: binary-search, array, two-pointers, sliding-window Companies: google, amazon, microsoft, linkedin Level: swe2, swe3 Binary Search on window left boundary: Binary search for the left start of the k-element window. At each mid, compare distance of arr[mid] vs arr[mid+k] to x to decide which side the window should be on. Find kth smallest in sorted matrix using binary search or min-heap. Google and Goldman Sachs interview question. Topics: binary-search, heap, matrix Companies: google, amazon, microsoft, goldman-sachs, bloomberg Level: swe3, senior Binary Search on value: Binary search on answer in range [matrix[0][0], matrix[n-1][n-1]]. Count elements <= mid using sorted row property. Find smallest value with count >= k. Min-Heap k-way merge: Push first element of each row into min-heap. Pop k times; each pop, push the next element in same row. Find k pairs with smallest sums from two sorted arrays using min-heap. Google interview question with O(k log k) solution. Topics: heap, array, k-way-merge Companies: google, amazon, microsoft, bloomberg Level: swe3, senior Min-Heap: Initialize heap with (sum, i=0..min(k,len(nums1)), j=0). Pop smallest, record pair, push next j for same i. Sort string characters by frequency using Counter and heap. Amazon and Google interview question with clean O(n log n) solution. Topics: hash-map, heap, sorting, strings Companies: amazon, google, microsoft, bloomberg Level: new-grad, swe2 Counter + Sort: Count character frequencies. Sort unique characters by frequency descending. Build result by repeating each character by its frequency count. Reorder array into wiggle pattern using sort and interleave. Google and Amazon interview question. Topics: array, sorting, dutch-flag Companies: google, amazon, microsoft Level: swe3, senior Sort + interleave: Sort array. Place upper half (larger values) at odd indices and lower half (smaller) at even indices, both from back to front to handle duplicate medians. Assign relative ranks and medals to athletes by score. Easy sorting problem for Amazon and Microsoft interviews. Topics: array, sorting, heap Companies: amazon, microsoft, bloomberg Level: new-grad, swe2 Sort by index: Create list of (score, index) pairs, sort by score descending. Assign medal or rank string to each index in that order. Find all unique triplets summing to zero using sort and two pointers in O(n^2). Amazon, Google, Meta interview question. Topics: array, two-pointers, sorting Companies: amazon, google, meta, microsoft, apple, bloomberg, uber, adobe Level: swe2, swe3 Sort + Two Pointers: Sort the array. For each index i, use two pointers left=i+1 and right=n-1. Move pointers based on sum. Skip duplicates by advancing past equal values. Find all unique quadruplets summing to target using nested loops and two pointers. Amazon and Google interview question. Topics: array, two-pointers, sorting Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Sort + Two Nested Loops + Two Pointers: Sort array. Two outer loops fix first two elements, two pointers scan remaining. Skip duplicates at all four positions. Find maximum water container area using two pointers in O(n). Amazon, Google, Meta, Apple interview question. Topics: array, two-pointers, greedy Companies: amazon, google, meta, microsoft, apple, bloomberg, uber, adobe Level: swe2, swe3 Two Pointers: Start with left=0, right=n-1. Area = min(height[left], height[right]) * (right-left). Move the pointer with shorter height inward to potentially find larger area. Compute trapped rain water in O(n) time O(1) space using two pointers. Hard Amazon, Google, Meta interview problem. Topics: array, two-pointers, stack, dynamic-programming Companies: amazon, google, microsoft, meta, apple, bloomberg, uber, goldman-sachs Level: swe3, senior Two Pointers O(1) space: Two pointers from each end. Track max_left and max_right. The side with smaller max determines the water at that position. Move that pointer inward. Precompute left/right max arrays: Precompute max height to the left and right of each position. Water at each position is min(left_max, right_max) - height[i]. Find minimum window substring using sliding window and frequency maps in O(|s|+|t|). Hard Amazon, Google, Meta interview. Topics: sliding-window, hash-map, two-pointers, strings Companies: amazon, google, meta, microsoft, bloomberg, uber, linkedin Level: swe3, senior Sliding Window with Frequency Map: Expand window right pointer. Once all chars of t covered, try shrinking from left. Track "formed" count (chars meeting their required frequency). Update min window whenever formed == required. Find longest substring without repeating characters using sliding window in O(n). Classic Amazon, Google, Meta interview question. Topics: sliding-window, hash-map, strings, two-pointers Companies: amazon, google, meta, microsoft, apple, bloomberg, uber, adobe Level: new-grad, swe2 Sliding Window with Set: Expand right. If character already in window set, shrink left until it is removed. Track max window length. Sliding Window with HashMap (O(n) jumps): Store last seen index of each character. When a repeat is found, jump left pointer directly to last_seen[char]+1 instead of shrinking one step at a time. Check if string contains permutation of s1 using fixed sliding window with frequency arrays. Amazon and Microsoft interview question. Topics: sliding-window, hash-map, strings, two-pointers Companies: amazon, microsoft, google, bloomberg, meta Level: swe2, swe3 Fixed Sliding Window with frequency arrays: Maintain frequency count arrays of size 26 for s1 and current window. Slide window of length len(s1) across s2, updating counts. If arrays match, return True. Find all anagram start indices using sliding window in O(|s|). Amazon, Google, Meta interview question. Topics: sliding-window, hash-map, strings Companies: amazon, google, meta, microsoft, bloomberg Level: swe2, swe3 Sliding Window with "matches" counter: Track count of characters with matching frequencies between window and p. When matches == 26, window is an anagram. Slide and update matches count. Find longest substring after k replacements using sliding window in O(n). Amazon and Google interview question. Topics: sliding-window, hash-map, strings, two-pointers Companies: amazon, google, microsoft, bloomberg, uber Level: swe2, swe3 Sliding Window: Expand window right. Valid if (window_size - max_char_count) <= k. When invalid, slide window right by moving left pointer. Track global max_count (never decrease it since smaller windows cannot give better answer). Maximize consecutive ones with k zero flips using sliding window in O(n). Google and Amazon interview question. Topics: sliding-window, array, two-pointers Companies: google, amazon, microsoft, bloomberg Level: swe2, swe3 Sliding Window: Expand right. Count zeros in window. When zeros > k, shrink left until zeros <= k. Track max window size. Find max fruits with 2 baskets using sliding window with at most 2 distinct types. Amazon and Google interview question. Topics: sliding-window, hash-map, array Companies: amazon, google, microsoft Level: swe2, swe3 Sliding Window - at most 2 distinct: Sliding window maintaining at most 2 distinct fruit types in a frequency map. When map has 3 types, shrink left until one type is removed. Count subarrays with exactly k distinct integers using at-most trick with sliding window. Hard Google interview question. Topics: sliding-window, hash-map, array Companies: google, amazon, meta Level: swe3, senior Sliding Window: exact = atMost(k) - atMost(k-1): Subarrays with exactly k distinct = subarrays with at most k distinct - subarrays with at most k-1 distinct. The atMost function uses a sliding window. Find minimum subarray with sum >= target using sliding window in O(n). Amazon and Google interview question. Topics: sliding-window, array, binary-search, two-pointers Companies: amazon, google, microsoft, bloomberg, linkedin Level: swe2, swe3 Sliding Window: Expand right adding to current sum. Whenever sum >= target, try shrinking from left and update minimum length. Find longest subarray of 1s after deleting one element using sliding window. Amazon and Google interview question. Topics: sliding-window, array, dynamic-programming Companies: amazon, google, microsoft Level: swe2, swe3 Sliding Window with at most 1 zero: Sliding window allowing at most 1 zero. Result is max window length - 1 (one element must be deleted). Count subarrays with exactly k odd numbers using prefix sum in O(n). Amazon and Google interview question. Topics: sliding-window, prefix-sum, array Companies: amazon, google, bloomberg Level: swe2, swe3 Prefix Sum: Track cumulative odd count. For each position, if (odd_count - k) seen before, those starting positions give valid subarrays. Store prefix odd counts in a hash map. Count subarrays with product less than k using sliding window in O(n). Amazon and Google interview question. Topics: sliding-window, array, two-pointers Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Sliding Window: Expand right, multiply product. When product >= k, shrink left by dividing. Count of new valid subarrays ending at right = right - left + 1. Minimum edge removals to reduce x to zero using complement sliding window. Google and Amazon interview question. Topics: sliding-window, array, prefix-sum, hash-map Companies: google, amazon, microsoft Level: swe2, swe3 Sliding Window on complement: Instead of removing from edges, find the longest subarray in the middle with sum = total - x. Answer is n minus that length. Find maximum sum subarray with unique elements using sliding window in O(n). Amazon and Google interview question. Topics: sliding-window, hash-map, array Companies: amazon, google, microsoft Level: swe2, swe3 Sliding Window with Set: Maintain a set of current window elements and running sum. When a duplicate is found, remove elements from the left until the duplicate is gone. Count substrings with all three characters a, b, c using last-seen index trick in O(n). Google interview question. Topics: sliding-window, hash-map, strings Companies: google, amazon, bloomberg Level: swe2, swe3 Sliding Window: Track last seen index of each of a, b, c. For each right position, the number of valid subarrays ending at right equals min(last_a, last_b, last_c) + 1. Find minimum replacement window to balance QWER string using sliding window. Google interview question. Topics: sliding-window, strings, two-pointers Companies: google, amazon Level: swe3, senior Sliding Window: Count frequencies. Slide a window: outside window, all character counts must be <= n/4. Shrink left when possible. Track minimum valid window size. Compute sliding window median using two heaps with lazy deletion in O(n log k). Hard Google and Amazon interview problem. Topics: sliding-window, heap, two-heaps Companies: google, amazon, meta, bloomberg Level: senior, staff Two Heaps with Lazy Deletion: Maintain max-heap (lower half) and min-heap (upper half). Use lazy deletion: track counts of elements to remove. Balance heaps after each slide. Median comes from heap tops. Maximize card points from edges using complement sliding window. Amazon and Google interview question. Topics: sliding-window, array, prefix-sum Companies: amazon, google, microsoft Level: swe2, swe3 Sliding Window on middle subarray: Total - minimum window sum of size (n-k). Slide a window of size n-k and find the minimum sum. Answer is total - that minimum. Find longest subarray with max-min <= limit using monotonic deques. Google and Amazon interview question. Topics: sliding-window, deque, monotonic-stack Companies: google, amazon, meta Level: swe3, senior Sliding Window with Two Deques: Maintain two deques: max_deque (decreasing) and min_deque (increasing). Max-min gives range of window. When range > limit, shrink left, removing from deques if they point to left index. Maximize satisfied customers using sliding window on grumpy minutes. Amazon and Google interview question. Topics: sliding-window, array Companies: amazon, google, bloomberg Level: swe2, swe3 Sliding Window: Base satisfied customers when not grumpy. Add sliding window of size minutes to find maximum extra customers gained (grumpy minutes converted). Result = base + max_extra. Find minimum k-bit flips to make all ones using greedy sliding window. Hard Google interview problem. Topics: sliding-window, array, greedy, bit-manipulation Companies: google, amazon, meta Level: senior, staff Sliding Window with flip tracker: Use a deque to track flip endpoints. For each position, current flip state = len(deque) % 2. If flip needed (nums[i] XOR flips == 0), flip and add end position. If window expired, pop from deque. Validate matching parentheses using a stack in O(n). Classic Amazon, Google, Meta interview question. Topics: stack, strings Companies: amazon, google, meta, microsoft, bloomberg, apple, uber Level: new-grad, swe2 Stack: Use a stack. Push open brackets. For each closing bracket, check if the top of the stack is the corresponding open bracket. If stack is empty or mismatch, return False. Design a stack with O(1) push, pop, top, and getMin. Classic Amazon, Google, Apple interview question. Topics: stack, design Companies: amazon, google, microsoft, meta, bloomberg, apple Level: new-grad, swe2 Auxiliary min stack: Maintain two stacks: main stack and min_stack. min_stack[i] = minimum of all elements up to position i. Push to both; pop from both; getMin returns min_stack top. Single stack storing (val, min) pairs: Store tuples (value, current_min) in a single stack. Each push records the running minimum. Evaluate RPN arithmetic expression using a stack in O(n). Amazon, Microsoft, Bloomberg interview question. Topics: stack, array, math Companies: amazon, microsoft, bloomberg, google, linkedin Level: swe2, swe3 Stack: Iterate tokens. Push numbers onto stack. For each operator, pop two operands, compute result, push back. Final stack element is the answer. Find days until warmer temperature using monotonic stack in O(n). Amazon, Google, Microsoft interview question. Topics: stack, array, monotonic-stack Companies: amazon, google, microsoft, bloomberg, uber, meta Level: swe2, swe3 Monotonic Stack: Maintain a monotonic decreasing stack of indices. For each day, pop all indices where current temperature is warmer; record the wait. Push current index. Find largest rectangle in histogram using monotonic stack in O(n). Hard Amazon, Google, Goldman Sachs interview problem. Topics: stack, array, monotonic-stack Companies: amazon, google, microsoft, meta, bloomberg, goldman-sachs Level: swe3, senior, staff Monotonic Stack: Maintain a monotonic increasing stack of (index, height) pairs. When a shorter bar is encountered, pop taller bars and compute their maximum rectangles using the current index as the right boundary. Implement FIFO queue using two stacks with amortized O(1) operations. Amazon and Microsoft interview design question. Topics: stack, queue, design Companies: amazon, microsoft, google, bloomberg Level: new-grad, swe2 Two Stacks with lazy transfer: Push always goes to in_stack. Pop/peek: if out_stack is empty, transfer all from in_stack to out_stack. Then operate on out_stack. Implement LIFO stack using queues with rotation approach. Amazon and Google interview design question. Topics: stack, queue, design Companies: amazon, google, microsoft Level: new-grad, swe2 One Queue with rotation: Push x to queue, then rotate all previous elements to the back (dequeue and enqueue n-1 times). Now x is at the front, simulating LIFO. Find sliding window maximum using monotonic deque in O(n). Hard Amazon, Google, Meta interview problem. Topics: deque, sliding-window, monotonic-stack, array Companies: amazon, google, meta, microsoft, bloomberg, uber Level: swe3, senior Monotonic Deque: Maintain a deque of indices with decreasing values. Front is always the max of current window. Remove front when it falls out of window. Remove from back when adding larger elements. Find next greater element for each number using monotonic stack and hash map in O(n). Amazon interview question. Topics: stack, array, hash-map, monotonic-stack Companies: amazon, microsoft, bloomberg Level: new-grad, swe2 Monotonic Stack + Hash Map: Compute next greater element for each element in nums2 using a monotonic stack. Store results in a hash map. Answer for each element of nums1 is a lookup. Find next greater element in circular array using monotonic stack with double pass. Amazon and Google interview question. Topics: stack, array, monotonic-stack Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Monotonic Stack with 2x pass: Iterate 2n indices. Use i % n for circular indexing. Monotonic decreasing stack stores indices. When current > stack top element, pop and record next greater. Evaluate arithmetic expression with parentheses using a stack in O(n). Hard Google, Amazon interview problem. Topics: stack, strings, math Companies: google, amazon, microsoft, bloomberg, meta Level: swe3, senior Stack for parentheses: Track current result and sign. On "(", push current result and sign to stack, reset. On ")", pop saved result and sign and combine. Accumulate number before processing operator. Evaluate expression with +, -, *, / using stack in O(n). Amazon, Google, Meta interview question. Topics: stack, strings, math Companies: amazon, google, microsoft, bloomberg, meta, uber Level: swe2, swe3 Stack with operator handling: Iterate through string building current number. At each operator (or end), apply the previous operator to the current number: push for +/-, compute immediately for */. Sum the stack. Find lexicographically smallest string after removing duplicates using greedy monotonic stack. Google interview question. Topics: stack, greedy, strings, monotonic-stack Companies: google, amazon, meta Level: swe3, senior Greedy Monotonic Stack: Count last occurrences. Maintain stack (result). For each char: if already in stack, skip. Else pop stack top while top > current char AND top appears again later. Push current char. Find smallest number after removing k digits using greedy monotonic stack. Google and Amazon interview question. Topics: stack, greedy, strings, monotonic-stack Companies: google, amazon, microsoft, bloomberg Level: swe2, swe3 Greedy Monotonic Stack: Maintain monotonic increasing stack. For each digit, pop the stack top when it is larger than current digit and k > 0. Append current digit. After all digits, remove remaining k from end. Strip leading zeros. Detect 132 pattern in array using monotonic stack from right in O(n). Google and Amazon interview question. Topics: stack, array, monotonic-stack Companies: google, amazon, microsoft Level: swe3, senior Monotonic Stack from right: Scan right to left. Maintain a decreasing stack. Whenever we pop (current > stack top), that popped value is "k" (the middle). If we ever find a value smaller than k, we found nums[i] < k < nums[j]. Compute score of balanced parentheses string using a stack in O(n). Google and Bloomberg interview question. Topics: stack, strings Companies: google, amazon, bloomberg Level: swe2, swe3 Stack: Push 0 onto stack for each "(". For each ")", if top is 0 it was "()" so replace with 1; else pop, double it, add to new top (cumulative at that level). Simulate asteroid collisions using a stack in O(n). Amazon and Google interview question. Topics: stack, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Stack: Push each asteroid. If current is negative and top is positive, they collide. Pop the stack if current wins. If equal, both explode. Current is destroyed if stack top wins. Compute stock price span online using monotonic stack with O(1) amortized per call. Amazon and Google interview question. Topics: stack, design, monotonic-stack Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Monotonic Stack: Stack of (price, span) pairs, monotonically decreasing by price. When new price >= top price, pop and add span. Push (price, total_span). Return total_span. Compute sum of subarray minimums using contribution technique with monotonic stack in O(n). Amazon and Google interview question. Topics: stack, array, monotonic-stack, dynamic-programming Companies: amazon, google, meta, microsoft Level: swe3, senior Monotonic Stack - contribution technique: For each element arr[i], find the number of subarrays where it is the minimum: left_count = distance to previous smaller, right_count = distance to next smaller or equal. Contribution = arr[i] * left_count * right_count. Find maximal rectangle in binary matrix using histogram and monotonic stack. Hard Amazon, Google interview problem. Topics: stack, matrix, array, dynamic-programming, monotonic-stack Companies: amazon, google, microsoft, meta, bloomberg Level: swe3, senior, staff Histogram + Monotonic Stack: Build cumulative height histogram row by row (height[j] = consecutive 1s above, reset to 0 on "0"). Apply largest rectangle in histogram algorithm on each row. Count car fleets arriving at destination using sort and stack in O(n log n). Amazon and Google interview question. Topics: stack, array, sorting, monotonic-stack Companies: amazon, google, microsoft Level: swe2, swe3 Sort + Stack: Sort cars by position descending. Compute time to target for each. Use a stack: if current car arrives faster than stack top (closer car), they merge (same fleet, current does not add). Else push. Decode encoded string with k[encoded_string] format using two stacks. Amazon, Google, Bloomberg interview question. Topics: stack, strings, recursion Companies: amazon, google, microsoft, bloomberg, meta Level: swe2, swe3 Two-stack approach: Maintain a count_stack and string_stack. On digit, accumulate count. On "[", push current string and count to stacks, reset. On "]", pop count and base, repeat current and concatenate. Find maximum width ramp using prefix minimum stack and right scan in O(n). Google interview question. Topics: stack, array, two-pointers, monotonic-stack Companies: google, amazon Level: swe3, senior Monotonic Stack + Right Scan: Build decreasing stack of indices (prefix minimums, left candidates). Then scan right to left: for each j, pop stack while nums[stack.top] <= nums[j] and record j - stack.top. Count visible people in queue using monotonic stack scan from right. Hard Google and Amazon interview problem. Topics: stack, array, monotonic-stack Companies: google, amazon, meta Level: swe3, senior Monotonic Stack from right: Scan right to left. Maintain a decreasing monotonic stack. For each person i, pop all shorter people from stack (they are visible to i). The first taller person in the stack (if any) is also visible. Count = pops + (1 if stack non-empty). Find minimum insertions to make parentheses string valid using counter in O(n). Amazon and Google interview question. Topics: stack, strings, greedy Companies: amazon, google, bloomberg Level: swe2, swe3 Greedy Counter: Track open (unmatched opens) and close (unmatched closes). For "(" increment open. For ")" if open > 0 decrement open (matched), else increment close. Answer = open + close. Find kth largest element using min-heap of size k. Amazon, Google, Meta interview question with heap focus. Topics: heap, sorting Companies: amazon, google, meta, microsoft, apple, bloomberg Level: swe2, swe3 heapq.nlargest: Use heapq.nlargest which internally maintains a min-heap of size k, returning the kth largest element as heap[0]. Manual min-heap of size k: Build heap manually, pushing each element and popping when size exceeds k. The heap root is the kth largest. Find streaming median using two heaps (max + min) with O(log n) insert, O(1) median. Amazon, Google, Meta hard interview. Topics: heap, two-heaps, design, sorting Companies: amazon, google, microsoft, meta, bloomberg, apple Level: swe3, senior Two Heaps (max-heap + min-heap): lo is a max-heap (negated in Python) for the lower half. hi is a min-heap for the upper half. Always maintain len(lo) >= len(hi). On add: push to lo first, then balance. Merge k sorted linked lists using min-heap O(n log k) or divide and conquer. Amazon, Google, Meta hard interview. Topics: heap, linked-list, k-way-merge, divide-and-conquer Companies: amazon, google, microsoft, meta, bloomberg, apple, uber Level: swe3, senior Min-Heap: Initialize heap with (val, index, node) for each list head. Pop min, attach to result, push next node from same list. Use index as tiebreaker. Divide and Conquer: Recursively merge lists in pairs (like merge sort). Each level merges n total nodes across k/2 pairs, log k levels total. Minimize CPU intervals for task scheduling with cooldown using formula or heap simulation. Amazon, Google, Meta interview. Topics: heap, greedy, hash-map, array Companies: amazon, google, microsoft, meta, bloomberg, uber Level: swe2, swe3 Math formula: Count task frequencies. The minimum time is max(len(tasks), (max_freq-1)*(n+1) + count_of_tasks_with_max_freq). The formula accounts for idles between most frequent tasks. Max-Heap Simulation: Simulate scheduling: use a max-heap (negated freq). Each cycle of n+1, pick the most frequent tasks, reduce counts. Count total time including any idles. Rearrange string so no two adjacent characters are equal using max-heap. Amazon and Google interview question. Topics: heap, greedy, hash-map, strings Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Max-Heap: Count frequencies. If max_freq > (n+1)//2, impossible. Else use max-heap: pop two most frequent at a time, append both, push back if remaining count > 0. Find k closest points to origin using max-heap O(n log k) or sort O(n log n). Amazon, Google, Meta interview question. Topics: heap, array, sorting, divide-and-conquer Companies: amazon, google, meta, microsoft, uber, linkedin, bloomberg Level: swe2, swe3 Max-Heap of size k: Use a max-heap of size k (negate distance for Python min-heap). For each point, if heap is smaller than k push it. Otherwise if distance < heap max, replace. Return heap elements. Sort by distance: Sort all points by their squared Euclidean distance (no need for sqrt). Return the first k. Find smallest range covering elements from k sorted lists using min-heap. Hard Google and Amazon interview problem. Topics: heap, array, sorting, k-way-merge, sliding-window Companies: google, amazon, meta, bloomberg Level: senior, staff Min-Heap + global max tracking: Initialize heap with first element of each list. Track current_max. Pop min, update range [min, max] if better, push next from same list. Stop when any list exhausted. Find nth ugly number using three pointers DP in O(n) or min-heap. Google and Amazon interview question. Topics: heap, dynamic-programming, math Companies: google, amazon, microsoft, bloomberg Level: swe2, swe3 Dynamic Programming with three pointers: Maintain dp array and three pointers for factors 2, 3, 5. Each step, next ugly = min of the three candidates. Advance pointer(s) that produced the minimum. Min-Heap: Use a min-heap initialized with 1. Pop the smallest, push its 2x, 3x, 5x multiples if not seen. Return after n pops. Find nth super ugly number with custom primes using k-pointer DP in O(nk). Google interview question. Topics: heap, dynamic-programming, array Companies: google, amazon Level: swe3, senior DP with k pointers: Generalize ugly number II: maintain one pointer per prime. At each step, next = min of dp[pointers[i]] * primes[i]. Advance all pointers that produced the min. Maximize capital for IPO using greedy two-heap approach. Hard Amazon and Google interview problem. Topics: heap, greedy, sorting, two-heaps Companies: amazon, google, microsoft Level: swe3, senior Two Heaps (min by capital + max by profit): Sort projects by capital into a min-heap. Maintain a max-heap of profits for affordable projects. For each of k rounds: push all affordable projects to max-heap, pop highest profit, add to w. Find furthest building using greedy ladder/bricks allocation with min-heap. Amazon and Google interview question. Topics: heap, greedy, array Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Min-Heap for ladder climbs: Greedily allocate ladders to the largest climbs. Maintain a min-heap of size ladders tracking climbs assigned to ladders. When heap is full and new climb comes in, reassign the smallest ladder-climb to bricks if possible. Simulate single-threaded CPU task scheduling with min-heap in O(n log n). Amazon and Google interview question. Topics: heap, sorting, array Companies: amazon, google, microsoft, bloomberg Level: swe3, senior Min-Heap Simulation: Sort tasks by enqueue time. Simulate CPU: maintain current time and min-heap of (processing_time, index). At each step, push all tasks with enqueue_time <= current_time. Pop shortest, update current_time. Solve the skyline problem using event-based max-heap in O(n log n). Hard Google and Amazon interview problem. Topics: heap, divide-and-conquer, sorting, binary-search Companies: google, amazon, microsoft, bloomberg, apple Level: senior, staff Event-based Max-Heap: Create events: (x, -h) for start and (x, h) for end. Sort events (end before start at same x). Maintain a max-heap of active heights. When max height changes, add to result. Find employee free time by merging intervals and detecting gaps. Hard Amazon, Google, Airbnb interview problem. Topics: heap, interval, sorting, k-way-merge Companies: amazon, google, bloomberg, airbnb Level: swe3, senior Flatten, Sort, Find Gaps: Collect all intervals from all employees, sort by start time. Merge overlapping intervals, then find gaps between consecutive merged intervals. Find minimum cost to hire k workers using ratio sort and max-heap. Hard Google interview problem. Topics: heap, greedy, sorting, two-heaps Companies: google, amazon, meta Level: senior, staff Sort by ratio + max-heap for quality sum: Sort workers by wage/quality ratio. For each worker as the "captain" (highest ratio), choose the k-1 workers with smallest quality from all those seen. Cost = ratio_captain * sum_of_k_qualities. Use max-heap to maintain k smallest qualities. Design seat reservation system with min-heap for O(log n) reserve and unreserve. Amazon and Google interview design question. Topics: heap, design Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Min-Heap: Initialize min-heap with all seat numbers. reserve() pops min. unreserve() pushes seat number back. Heap always gives smallest available seat. Maximize subsequence score (sum * min) using sort and min-heap in O(n log n). Amazon and Google interview question. Topics: heap, greedy, sorting, array Companies: amazon, google, meta Level: swe3, senior Sort by nums2 desc + min-heap: Sort pairs by nums2 descending. Maintain a min-heap of size k for nums1 values and their running sum. For each position (which fixes the min of nums2), compute score = sum * nums2[i]. Find minimum refueling stops using greedy max-heap retroactive approach. Hard Amazon and Google interview problem. Topics: heap, greedy, dynamic-programming, array Companies: amazon, google, meta Level: senior, staff Greedy Max-Heap: Simulate driving. When stuck (fuel < 0 after reaching next position), retroactively refuel at the largest station seen so far (max-heap). Count refuels. If heap empty and still stuck, return -1. Find kth smallest fraction from prime array using min-heap in O(k log n). Google and Amazon interview question. Topics: heap, array, binary-search Companies: google, amazon, meta Level: swe3, senior Min-Heap: Initialize min-heap with fractions arr[0]/arr[j] for each denominator j. Pop k times: each pop, if numerator index i+1 < j, push arr[i+1]/arr[j]. Return arr[i], arr[j] of the kth pop. Minimize array deviation using max-heap with multiply/divide operations. Hard Google interview problem. Topics: heap, greedy, array Companies: google, amazon, meta Level: senior, staff Max-Heap: Convert all odds to even (multiply by 2). Push to max-heap. Track min. Pop max: if even, divide by 2, push back; update min; compute max-min. Stop when max is odd (cannot divide further). Maximize team performance (speed sum * min efficiency) using sort and min-heap. Hard Google interview problem. Topics: heap, greedy, sorting, array Companies: google, amazon, meta, bloomberg Level: senior, staff Sort by efficiency + min-heap: Sort engineers by efficiency descending. For each as the minimum efficiency, pick k highest speeds from seen engineers (min-heap). Performance = speed_sum * efficiency. Find kth largest element in data stream using min-heap of size k with O(log k) per insert. Amazon and Google interview. Topics: heap, design, binary-search Companies: amazon, google, microsoft, bloomberg Level: new-grad, swe2 Min-Heap of size k: Maintain a min-heap of size k. The root is always the kth largest. On add, push val and pop if size > k. Return root. Design streaming top-k frequent elements tracker using frequency map and heap. Amazon and Google interview design question. Topics: heap, hash-map, design Companies: amazon, google, twitter, bloomberg Level: swe3, senior HashMap + heapq.nlargest: Maintain a frequency counter. On each add, increment freq[num] and return heapq.nlargest(k) by frequency. Assign tasks to servers greedily using two heaps (free and busy). Amazon and Google interview question. Topics: heap, array, two-heaps Companies: amazon, google, microsoft Level: swe3, senior Two Heaps (free + busy): Free heap: (weight, idx). Busy heap: (end_time, weight, idx). At time j (0-indexed task), move done servers to free. If no free server, advance time to next completion. Assign lightest free server. Find minimum time to swim across grid using Dijkstra min-heap or binary search BFS. Hard Google interview problem. Topics: heap, graph, bfs, binary-search, union-find Companies: google, amazon, meta, bloomberg Level: senior, staff Dijkstra / Min-Heap: Treat problem as finding path from (0,0) to (n-1,n-1) minimizing the maximum elevation encountered. Use Dijkstra with priority key = max(current_t, grid[r][c]). Binary Search + BFS: Binary search on answer t (0..n^2-1). For each t, BFS/DFS checking if path exists from (0,0) to (n-1,n-1) using only cells with elevation <= t. Implement LRU cache with O(1) ops using OrderedDict and doubly linked list. Topics: lru-cache, design-patterns, hash-map, collections Companies: amazon, google, microsoft, meta, bloomberg Level: swe2, swe3 OrderedDict: OrderedDict maintains order. move_to_end on access marks MRU. popitem(last=False) evicts LRU. Doubly Linked List + HashMap: DLL for order, dict for O(1) access. head=LRU, tail=MRU. Remove and insert before tail on access. Implement Least Frequently Used cache with O(1) ops using two dicts and OrderedDict buckets. Topics: lfu-cache, design-patterns, hash-map, collections Companies: amazon, google, microsoft, meta Level: swe3, senior Two Dicts + Min Freq: key_val, key_freq dicts plus freq_keys (freq->OrderedDict). Track min_freq. On access increment freq, move to next bucket. Thread-safe Singleton using Python metaclass with locking. Advanced OOP interview question. Topics: metaclasses, concurrency, design-patterns, oop Companies: amazon, google, microsoft, meta Level: swe3, senior Metaclass with Lock: Override __call__ in metaclass. Lock prevents race condition. Class-keyed dict stores instances. Implement Observer pattern with abstract observers and stock price notification. Amazon Google OOP interview. Topics: design-patterns, oop, object-design Companies: amazon, google, microsoft, meta, bloomberg Level: swe2, swe3 ABC Observer: Abstract Observer with update(). Subject provides subscribe/unsubscribe/notify. Concrete classes implement update(). Implement Python iterator protocol with custom Range, Flatten, and Chain iterators. Topics: iterators, generators, oop, protocols Companies: google, amazon, microsoft Level: swe2, swe3 Iterator Protocol: __iter__ returns self. __next__ advances and raises StopIteration when done. Stack-based flatten. Implement context managers with class protocol and @contextmanager decorator. Advanced Python interview. Topics: context-managers, oop, exceptions, decorators Companies: google, amazon, microsoft, meta Level: swe2, swe3 Class and Decorator Context Managers: __enter__ sets up, __exit__ tears down. @contextmanager: yield splits setup/teardown. Retry decorator with exponential backoff. Amazon Google Stripe interview question. Topics: decorators, exceptions, closures, functools Companies: amazon, google, microsoft, stripe, netflix Level: swe2, swe3 Retry with Exponential Backoff: Loop up to max_attempts, catch specified exceptions, multiply delay. Re-raise on final failure. Build memoize decorator with LRU eviction and cache statistics. Google Amazon Python interview. Topics: decorators, memoization, closures, functools, dynamic-programming Companies: google, amazon, microsoft, meta Level: swe2, swe3 Memoize with LRU and Stats: OrderedDict cache keyed by (args, kwargs_tuple). move_to_end on hit, popitem on overflow. cache_info() reports stats. Flatten arbitrarily nested iterables with yield from recursive generator. Advanced Python interview. Topics: generators, iterators, recursion, typing Companies: google, amazon, microsoft Level: swe2, swe3 Recursive Generator: yield from for sub-iterables. Exclude str/bytes to yield as atomic items. Iterative Stack: Explicit iterator stack avoids recursion depth limits. Implement lazy_property that caches on first access using non-data descriptor protocol. Topics: descriptors, oop, decorators, caching Companies: google, amazon, microsoft Level: swe3, senior Non-Data Descriptor: No __set__, so Python checks instance.__dict__ first. Store result there to bypass descriptor on next access. Typed dataclasses with runtime validation using __post_init__. Advanced Python interview. Topics: dataclasses, typing, oop, descriptors Companies: google, amazon, microsoft, stripe Level: swe2, swe3 __post_init__ Validation: @dataclass with __post_init__ for validation. ClassVar for constraints. Custom validators per field. Payment processor ABC with CreditCard and PayPal implementations using template method. Topics: abstract-classes, oop, design-patterns Companies: stripe, paypal, amazon, google, visa Level: swe2, swe3 ABC Payment Hierarchy: PaymentProcessor ABC with template method process(). Subclasses implement charge() and refund(). Track attribute changes with __getattr__ and __setattr__. Advanced Python OOP interview. Topics: descriptors, oop, metaclasses Companies: google, amazon, microsoft Level: swe3, senior Attribute History Tracking: __setattr__ logs changes. object.__setattr__ for internal state avoids recursion. __getattr__ for missing attrs. Use typing.Protocol for Comparable interface with structural subtyping. Advanced Python interview. Topics: protocols, typing, oop, abstract-classes Companies: google, amazon, microsoft Level: swe3, senior Protocol with Generic Functions: Protocol defines interface via structural typing. Concrete classes need not inherit. Generic functions accept any Comparable. Async producer-consumer with asyncio.Queue, backpressure, and graceful shutdown. Topics: async-await, generators, concurrency Companies: google, amazon, netflix, microsoft Level: swe3, senior asyncio Queue Pipeline: Producer puts items, sends None sentinel per consumer. Consumers loop until None. asyncio.gather runs all. asyncio.gather with semaphore and timeout. Google Netflix async interview. Topics: async-await, concurrency Companies: google, amazon, netflix, stripe Level: swe2, swe3 gather with Semaphore and Timeout: asyncio.gather runs concurrently. Semaphore limits parallelism. wait_for adds per-task timeout. return_exceptions avoids one failure killing all. Thread-safe token bucket rate limiter with lazy refill. Amazon Google Stripe Cloudflare interview. Topics: rate-limiting, design-patterns, system-design-coding, concurrency Companies: amazon, google, stripe, cloudflare, netflix Level: swe3, senior Lazy Token Bucket: Lazily refill on consume based on elapsed time. Lock for thread safety. Optional blocking mode. Parallel task processing with ThreadPoolExecutor and progress tracking. Amazon Google interview. Topics: concurrency, async-await, functools Companies: amazon, google, microsoft, netflix Level: swe2, swe3 ThreadPoolExecutor with Progress: Submit all tasks, use as_completed for progress, handle per-task exceptions, map for ordered results. Implement defaultdict from scratch with __missing__. Classic Python OOP interview. Topics: collections, oop, hash-map Companies: google, amazon, microsoft Level: new-grad, swe2 __missing__ Implementation: Inherit dict, override __missing__ to call default_factory and store result. Implement Trie with insert, search, autocomplete, delete. Amazon Google interview. Topics: trie, oop, hash-map, string-matching Companies: amazon, google, microsoft, meta, bloomberg Level: swe2, swe3 Trie with Autocomplete: TrieNode with children dict and is_end. DFS for autocomplete. Recursive post-order delete. Implement Graph with BFS, DFS, cycle detection, topological sort. Amazon Google interview. Topics: graph, bfs, dfs, oop, topological-sort Companies: amazon, google, microsoft, meta, bloomberg Level: swe2, swe3 Graph with BFS DFS Topo Sort: BFS with deque. DFS recursive. Cycle detection via coloring. Topo sort via DFS post-order. Build MinHeap with insert, extract, build_heap. Amazon Google interview. Topics: heap, array, oop Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Array-Based MinHeap: Append and sift up on insert. Swap root with last, pop, sift down on extract. Build by sifting down from n//2-1. Fixed-size circular buffer with head/tail pointers and overwrite mode. Topics: array, design-patterns, queue, system-design-coding Companies: amazon, google, microsoft, nvidia, bloomberg Level: swe2, swe3 Head/Tail Pointer Buffer: Fixed array with head and tail. count tracks size. Modular arithmetic for wrap-around. Bloom filter with optimal bit array and double hashing. Google Databricks Cloudflare interview. Topics: hash-map, bit-manipulation, system-design-coding Companies: google, amazon, databricks, cloudflare, netflix Level: swe3, senior, staff Double Hashing Bloom Filter: bytearray as bit array. Two base hashes (MD5, SHA1) derive k positions. Optimal m and k from n and p. Implement consistent hashing with virtual nodes. Amazon Google Netflix distributed systems interview. Topics: hash-map, system-design-coding, design-patterns, sorting Companies: amazon, google, databricks, netflix, cloudflare, uber Level: swe3, senior, staff Virtual Node Hash Ring: Hash each node v times onto ring (sorted list). Key lookup: hash key, bisect for successor node. LRU cache design with O(1) get/put using OrderedDict. Classic Amazon Google system design coding. Topics: lru-cache, system-design-coding, hash-map, design-patterns Companies: amazon, google, microsoft, meta, bloomberg Level: swe2, swe3 OrderedDict O(1): OrderedDict preserves insertion order. move_to_end marks MRU. popitem(last=False) evicts LRU. LFU cache with O(1) ops using frequency buckets. Hard Amazon Google interview. Topics: lfu-cache, system-design-coding, hash-map, design-patterns Companies: amazon, google, microsoft, meta Level: swe3, senior Freq Bucket + Min Freq Tracking: Three dicts: key->val, key->freq, freq->OrderedDict(keys). min_freq for O(1) eviction. Hit counter counting requests in last 300 seconds. Deque and circular array approaches. Amazon Google interview. Topics: system-design-coding, queue, design-patterns, sliding-window Companies: amazon, google, microsoft, bloomberg, dropbox Level: swe2, swe3 Deque Sliding Window: Deque stores hit timestamps. getHits pops timestamps older than 5 minutes. Circular Array O(1): Fixed array of 300 (seconds, count) pairs. Index by timestamp%300. Reset stale buckets. Rate limiter with sliding window per user. Amazon Google Stripe Cloudflare interview. Topics: rate-limiting, system-design-coding, sliding-window, design-patterns Companies: amazon, google, stripe, cloudflare, netflix Level: swe3, senior Sliding Window Counter: Per-user deque of timestamps. Pop stale, check count, append if allowed. Fixed Window Counter (simpler): Track (window_start, count) per user. Reset on new window. Twitter design with heap-based k-way merge for news feed. Amazon Meta Google system design coding. Topics: system-design-coding, heap, hash-map, design-patterns Companies: twitter, meta, amazon, google, linkedin Level: swe2, swe3 Heap K-Way Merge: Each user has tweet list. getNewsFeed heap-merges followees tweets, returns top 10. Global timestamp orders tweets. In-memory file system with mkdir, ls, addFile using trie. Amazon Google Dropbox interview. Topics: trie, system-design-coding, hash-map, design-patterns Companies: amazon, google, microsoft, dropbox Level: swe2, swe3 Trie Node File System: Each node is a dir or file with children dict and content. Path segments traverse the trie. In-memory KV store with TTL expiry and lazy deletion. Amazon Redis Google interview. Topics: system-design-coding, hash-map, design-patterns, caching Companies: amazon, google, microsoft, redis, stripe Level: swe2, swe3 Lazy Expiration + Background Cleanup: Store (value, expiry). get checks expiry and deletes if stale. Optional background thread purges periodically. In-memory DB with set/get/scan and transaction support. Amazon Snowflake Databricks interview. Topics: system-design-coding, hash-map, sorting, design-patterns Companies: amazon, google, microsoft, snowflake, databricks Level: swe3, senior In-Memory DB with Transactions: Nested defaultdict for storage. Sorted scan with prefix filter. Transaction stack stores undo log. URL shortener with base62 encoding, custom aliases, expiry, and click tracking. Topics: system-design-coding, hash-map, design-patterns Companies: amazon, google, microsoft, twitter, bitly Level: swe2, swe3 Counter + Base62 Encoding: Increment counter, encode to base62 for short key. Two dicts: short->url and url->short for dedup. Track clicks and expiry. Leaderboard with addScore, top K, reset using heap. Amazon Google interview. Topics: system-design-coding, heap, sorting, hash-map Companies: amazon, google, microsoft, gaming-companies Level: swe2, swe3 HashMap + heapq.nlargest: Store scores in dict. top(K) uses heapq.nlargest O(n log K). Parking lot OOP design with vehicles, spots, tickets and fee calculation. Amazon Google Uber interview. Topics: system-design-coding, object-design, oop, design-patterns Companies: amazon, google, microsoft, uber, bloomberg Level: swe2, swe3 OOP Parking Lot System: Vehicle, Spot, Floor, ParkingLot, Ticket classes. park() finds first compatible spot. leave() calculates fee by time. Vending machine using State design pattern. Amazon Google OOP system design interview. Topics: system-design-coding, object-design, oop, design-patterns Companies: amazon, google, microsoft Level: swe2, swe3 State Pattern Vending Machine: VendingMachine holds state. Each State subclass implements transitions. Invalid ops raise in each state. Multi-elevator system with SCAN scheduling algorithm. Amazon Google senior engineer interview. Topics: system-design-coding, object-design, oop, design-patterns, sorting Companies: amazon, google, microsoft, bloomberg Level: swe3, senior SCAN Algorithm Multi-Elevator: Each Elevator has current floor, direction, and sorted queues for up/down. Assign request to nearest elevator. SCAN sweeps then reverses. Library management with checkout, return, reservations, and fines. Amazon Microsoft OOP interview. Topics: system-design-coding, object-design, oop Companies: amazon, microsoft, google, bloomberg Level: swe2, swe3 Library OOP Design: Book, BookCopy, Member, Library classes. Checkout assigns available copy. Return calculates fine. Reservation queue notifies next member. Restaurant table reservation with interval overlap detection. Amazon Airbnb Uber interview. Topics: system-design-coding, object-design, oop, interval Companies: amazon, google, uber, airbnb Level: swe2, swe3 Interval Overlap Reservation: Per-table reservation list. Check overlap with each existing reservation. Find smallest capacity >= party_size. Thread-safe movie booking with seat locking and confirmation. Amazon Netflix interview. Topics: system-design-coding, object-design, oop, concurrency Companies: amazon, google, netflix, uber Level: swe2, swe3 Thread-Safe Movie Booking: Seat has status, lock, expiry. bookSeat atomically checks and locks. Payment confirms. Cancel releases. Chat system with 1:1 and group messaging OOP design. Meta Discord Amazon interview. Topics: system-design-coding, object-design, oop, design-patterns Companies: meta, amazon, google, discord, slack Level: swe2, swe3 Chat System OOP: Conversation keyed by sorted user pair. Group has member set and message list. Unread counter per user-conversation. Autocomplete with trie and frequency tracking. Top 3 results by frequency. Amazon Google interview. Topics: trie, system-design-coding, heap, string-matching Companies: amazon, google, microsoft, meta, linkedin Level: swe2, swe3 Trie with Frequency Tracking: Trie with freq dict at each end node. On input: walk trie to current node, DFS for all sentences, return top 3 by (-freq, text). Merge K sorted log streams with heap-based k-way merge. Amazon Datadog interview. Topics: system-design-coding, heap, k-way-merge, sorting Companies: amazon, google, datadog, splunk, cloudflare Level: swe3, senior K-Way Merge with Heap: Per-stream sorted list. Merge query: push first log of each stream, pop-min into result, push next from same stream. Task scheduler with priority heap and thread workers. Amazon Google Airflow interview. Topics: system-design-coding, heap, design-patterns, concurrency Companies: amazon, google, microsoft, celery, airflow Level: swe2, swe3 Priority Heap Scheduler: Min-heap with (-priority, ready_time, id, func). Worker thread pops when ready_time <= now. ThreadPoolExecutor for concurrent execution. In-memory pub/sub with async delivery and worker threads. Amazon Kafka Google interview. Topics: system-design-coding, design-patterns, concurrency, object-design Companies: amazon, google, meta, kafka, stripe Level: swe3, senior Async Pub/Sub with Worker Threads: Per-subscriber Queue. Dedicated worker thread per subscriber drains queue. publish enqueues to all subscribers. Implement event sourcing with append-only log, snapshots, and state replay. Amazon Stripe Netflix interview. Topics: system-design-coding, design-patterns, object-design, caching Companies: amazon, google, stripe, netflix, databricks Level: swe3, senior, staff Event Store with Snapshots: Append-only event list. Reducer function applies each event to state. Snapshots checkpoint state. Replay from latest snapshot + subsequent events. Thread-safe circuit breaker with CLOSED/OPEN/HALF_OPEN states. Amazon Netflix Google interview. Topics: system-design-coding, design-patterns, concurrency, rate-limiting Companies: amazon, google, netflix, stripe, uber Level: swe3, senior Thread-Safe Circuit Breaker: State machine with CLOSED/OPEN/HALF_OPEN. Failure threshold opens circuit. Timeout allows HALF_OPEN test. Success closes circuit. API gateway with middleware pipeline: auth, rate limiting, caching, routing. Amazon Netflix senior interview. Topics: system-design-coding, design-patterns, rate-limiting, caching Companies: amazon, google, netflix, cloudflare, stripe Level: senior, staff Middleware Pipeline API Gateway: Chain of middleware: auth -> rate limit -> cache -> route -> backend. Each middleware calls next() or returns early. Route registry maps path to handler. Product search suggestions with sorted list and binary search. Amazon Google LinkedIn interview. Topics: trie, system-design-coding, string-matching, sorting Companies: amazon, google, microsoft, linkedin, meta Level: swe2, swe3 Sorted List + Binary Search: Sort products. For each prefix, bisect to find start, take up to 3 matching products. Implement Knuth-Morris-Pratt string matching. Find all pattern occurrences in O(n+m) time. Google Amazon interview. Topics: string, two-pointers Companies: google, amazon, microsoft Level: senior, staff KMP with Failure Function: Build a partial match table (failure function) for the pattern, then use it to skip unnecessary comparisons during search. Implement Rabin-Karp string search with rolling hash. Polynomial hashing and collision handling. Google interview. Topics: string, hash-table Companies: google, facebook, microsoft Level: senior, staff Rolling Hash: Compute hash of pattern and rolling hash of each text window. On hash match, verify character by character. Implement Z-algorithm for string matching and Z-array construction in O(n). Google Amazon senior interview. Topics: string, two-pointers Companies: google, amazon Level: senior, staff Z-Array Construction: Maintain a Z-box [L, R]. For each position, reuse previous results where possible. Find longest palindromic substring using Manacher's O(n) algorithm and expand-around-center. Amazon Google interview. Topics: string, dynamic-programming Companies: amazon, google, microsoft, apple Level: senior, staff Manacher's Algorithm O(n): Transform string with separators, then use Manacher's to find palindrome radii in linear time. Expand Around Center O(n^2): For each center (including between characters), expand outward while palindrome holds. Partition string into all palindrome substrings using backtracking and DP. Amazon Google interview. Topics: backtracking, dynamic-programming, string Companies: amazon, google, facebook Level: swe2, senior Backtracking with DP Palindrome Check: Use DP to precompute is_palindrome[i][j], then backtrack adding valid palindrome prefixes. Solve Merge Intervals in Python with sorting and greedy merge. O(n log n) time complexity with detailed explanation. Topics: array, sorting, interval Companies: google, amazon, microsoft, facebook, bloomberg Level: new-grad, swe2, swe3 Sort and Merge: Sort intervals by start. Iterate and merge when current start <= last merged end. Insert and merge an interval into a sorted non-overlapping interval list in O(n) time using linear scan. Topics: array, interval Companies: google, amazon, linkedin, microsoft Level: new-grad, swe2, swe3 Linear Scan: Three-phase linear scan: add non-overlapping before, merge overlapping, add remaining. Find minimum intervals to remove to make rest non-overlapping using greedy sort by end time in O(n log n). Topics: array, sorting, interval, greedy Companies: google, amazon, microsoft Level: swe2, swe3 Greedy - Sort by End: Sort by end time. Greedily select intervals with earliest end. Count removed = total - kept. Determine if a person can attend all meetings with no overlaps using sorting in O(n log n) time. Topics: array, sorting, interval Companies: amazon, microsoft, bloomberg, facebook Level: new-grad, swe2 Sort and Check: Sort by start. If any meeting starts before previous ends, return False. Find minimum conference rooms needed using min-heap or two sorted arrays approach in O(n log n) time. Topics: array, sorting, interval, heap, two-pointers Companies: amazon, google, microsoft, bloomberg, uber, facebook Level: swe2, swe3, senior Min-Heap: Sort by start. Min-heap tracks earliest ending room. Reuse room if it ends before new meeting starts. Two Sorted Arrays: Separate start and end times sorted. Use two pointers to track concurrent meetings. Find common free time for all employees by flattening, sorting, merging intervals and finding gaps. Topics: array, sorting, interval, heap Companies: google, amazon, uber, airbnb Level: swe3, senior, staff Flatten Sort and Find Gaps: Flatten all intervals, sort by start, merge overlapping, then collect gaps between merged intervals. Find intersections of two sorted interval lists using two pointers in O(m+n) time. Topics: array, two-pointers, interval Companies: facebook, google, amazon, linkedin Level: swe2, swe3 Two Pointers: Two pointers. Intersection = [max(starts), min(ends)]. Advance pointer with smaller end. Count remaining intervals after removing covered ones using sorting in O(n log n) time. Topics: array, sorting, interval, greedy Companies: amazon, google Level: swe2, swe3 Sort and Track Max End: Sort by start asc, end desc. An interval is not covered if its end exceeds max end seen so far. Find minimum video clips to cover event duration using greedy interval jumping in O(n log n) time. Topics: array, interval, greedy, dynamic-programming Companies: google, amazon Level: swe3, senior Greedy Jump: Greedy: sort clips. At each position extend as far as possible with available clips. Count jumps. Find minimum arrows to burst all balloons using greedy sort by end time in O(n log n) time. Topics: array, sorting, interval, greedy Companies: amazon, google, microsoft Level: swe2, swe3 Greedy Sort by End: Sort by end. Shoot at current balloon end. New arrow only when next start > current arrow pos. Implement a calendar booking system without double bookings using binary search in O(n) per operation. Topics: array, binary-search, interval, design-patterns Companies: google, amazon, microsoft Level: swe2, swe3 Binary Search with SortedList: Maintain sorted list of events. Use bisect to find insertion point and check neighbors for overlap. Implement calendar with at most double bookings using two interval lists to track overlaps. Topics: array, binary-search, interval, design-patterns Companies: google, amazon Level: swe3, senior Two Lists: Singles and Doubles: Maintain two lists: single bookings and double bookings. Reject if triple booking would occur. Track maximum k-booking using difference array with sorted dict in O(n) per booking. Topics: interval, segment-tree, design-patterns, binary-search Companies: google, amazon Level: senior, staff Difference Array with Sorted Dict: Difference array approach: +1 at start, -1 at end. Prefix sum gives concurrent events at any point. Summarize a data stream as disjoint intervals with efficient merge operations. Topics: interval, binary-search, design-patterns, sorted-list Companies: google, amazon, stripe Level: senior, staff Sorted List with Merge: Maintain sorted disjoint intervals. On addNum, find and merge all touching/overlapping intervals. Implement a Range Module tracking number ranges with add, remove, and query operations on intervals. Topics: interval, segment-tree, design-patterns, binary-search Companies: google, amazon, stripe Level: senior, staff Sorted Intervals List: Maintain sorted disjoint intervals. Add merges overlapping, remove splits overlapping intervals. Count range sums within bounds using merge sort on prefix sums in O(n log^2 n) time. Topics: array, prefix-sum, divide-and-conquer, binary-search, sorting Companies: google, amazon, jane-street Level: senior, staff Merge Sort on Prefix Sums: Build prefix sums. Use merge sort to count pairs (i,j) where prefix[j]-prefix[i] in [lower,upper]. Simulate falling squares and compute maximum height after each drop using interval overlap detection. Topics: array, interval, segment-tree, sorting Companies: google, amazon Level: senior, staff Brute Force with Interval Heights: For each square, find max height of overlapping previous squares. New height = base + size. Compute total area covered by overlapping rectangles using sweep line with coordinate compression. Topics: array, interval, segment-tree, sorting, prefix-sum Companies: google, amazon, jane-street Level: senior, staff Coordinate Compression + Sweep Line: Sweep line on x-axis with coordinate-compressed y-axis. Track active y segments to compute covered length. Find smallest interval containing each query using sort and min-heap in O((n+q) log n) time. Topics: array, sorting, interval, heap, binary-search Companies: google, amazon, stripe Level: senior, staff Sort + Min-Heap: Sort intervals by start, queries by value. Sweep with min-heap of active intervals keyed by size. Count flowers blooming at each arrival time using binary search on sorted start and end arrays. Topics: array, sorting, binary-search, interval, prefix-sum Companies: google, amazon, databricks Level: swe3, senior Binary Search on Sorted Start/End: Sort starts and ends separately. For each person: blooming = #started_by_t - #ended_before_t. Find the smallest starting interval >= each interval end using binary search in O(n log n) time. Topics: array, binary-search, interval, sorting Companies: amazon, google Level: swe2, swe3 Binary Search on Sorted Starts: Sort (start, index) pairs. For each interval end, binary search in sorted starts for >= end. Partition string into maximum parts where each letter appears in one part using greedy last-occurrence approach. Topics: string, greedy, interval, two-pointers Companies: amazon, google, facebook, microsoft Level: swe2, swe3 Last Occurrence Greedy: Track last index of each char. Expand current partition until current index equals partition end. Find minimum CPU intervals for task scheduling with cooldown using math formula or max-heap simulation. Topics: array, greedy, heap, interval, sorting Companies: amazon, google, facebook, microsoft, bloomberg Level: swe2, swe3, senior Math Formula: Math: answer = max(total_tasks, (max_freq-1)*(n+1)+count_of_max_freq_tasks) Greedy with Max-Heap: Max-heap simulation: each cycle of n+1 slots, execute most frequent tasks. Count car fleets arriving at destination by sorting by position and using a monotonic stack approach. Topics: array, sorting, monotonic-stack, interval Companies: amazon, google, microsoft Level: swe2, swe3 Sort by Position Descending + Stack: Sort by position desc. A car joins fleet ahead if its arrival time <= fleet in front. Use stack. Determine reachability in Jump Game VII using prefix sum of reachable positions in O(n) time. Topics: string, bfs, prefix-sum, sliding-window, interval Companies: amazon, google Level: swe3, senior Prefix Sum BFS: Prefix sum of reachable positions. Position j reachable if any position in [j-maxJump, j-minJump] is reachable. Find minimum eating speed using binary search on the answer in O(n log m) time. Topics: array, binary-search Companies: amazon, google, facebook, uber Level: swe2, swe3 Binary Search on Speed: Binary search on eating speed. Feasibility check: sum of ceil(pile/k) for all piles <= h. Find minimum ship capacity to deliver all packages within D days using binary search on the answer. Topics: array, binary-search Companies: amazon, google, facebook Level: swe2, swe3 Binary Search on Capacity: Binary search on capacity in range [max(w), sum(w)]. Greedy check if packages can be shipped in D days. Find minimum days to form m bouquets of k adjacent flowers using binary search in O(n log max_day). Topics: array, binary-search Companies: amazon, google, bloomberg Level: swe2, swe3 Binary Search on Days: Binary search on the day. Feasibility: greedily count consecutive bloomed flowers forming bouquets. Minimize the largest subarray sum when splitting into k parts using binary search on the answer. Topics: array, binary-search, dynamic-programming, greedy Companies: google, amazon, facebook, bloomberg Level: swe3, senior Binary Search on Answer: Binary search on the max subarray sum. Greedily count splits needed for a given max sum. Maximize minimum distance between balls using binary search on the answer after sorting positions. Topics: array, binary-search, sorting Companies: amazon, google, airbnb Level: swe3, senior Binary Search on Minimum Distance: Sort positions. Binary search on min distance. Greedy feasibility: place balls maximizing spacing. Find target in mountain array using three binary searches: find peak, search ascending, search descending. Topics: array, binary-search, divide-and-conquer Companies: google, amazon, facebook Level: swe3, senior Three Binary Searches: Three binary searches: find peak, search ascending left half, search descending right half. Search for a target in rotated sorted array with duplicates using modified binary search. Topics: array, binary-search Companies: amazon, google, microsoft, facebook Level: swe2, swe3 Binary Search with Duplicate Handling: Binary search. When lo==mid, advance lo. Otherwise determine sorted half and prune. Find the duplicate number in O(n) time O(1) space using Floyd's cycle detection algorithm. Topics: array, two-pointers, binary-search, bit-manipulation Companies: amazon, google, facebook, microsoft, bloomberg Level: swe2, swe3 Floyd's Cycle Detection: Model array as linked list (index->value). Duplicate creates cycle. Floyd's algorithm finds cycle entry. Find the first bad version using binary search to minimize API calls in O(log n) time. Topics: binary-search Companies: amazon, facebook, microsoft, linkedin Level: new-grad, swe2 Binary Search: Standard binary search. Converge lo and hi to the leftmost bad version. Find next greatest letter in circular sorted array using binary search in O(log n) time. Topics: array, binary-search Companies: amazon, google Level: new-grad, swe2 Binary Search: bisect_right finds first position after target. Modulo handles wraparound. Count negatives in row/column sorted matrix using staircase traversal in O(m+n) time. Topics: array, binary-search, matrix Companies: amazon, google, microsoft Level: new-grad, swe2 Staircase from Top-Right: Start top-right. Negative -> count remaining rows, move left. Non-negative -> move down. Find kth smallest element in sorted matrix using binary search on value with staircase count. Topics: matrix, binary-search, heap, sorting Companies: amazon, google, facebook, microsoft Level: swe2, swe3 Binary Search on Value: Binary search on value range. Count elements <= mid using staircase. Converge to kth smallest. Find kth smallest pairwise distance using binary search on distance with sliding window count. Topics: array, binary-search, sorting, two-pointers Companies: google, amazon, stripe Level: senior, staff Binary Search + Sliding Window: Sort array. Binary search on distance value. Count pairs with distance <= mid using sliding window. Find kth smallest in m x n multiplication table using binary search with O(m log mn) complexity. Topics: binary-search, math Companies: google, amazon, jane-street Level: senior, staff Binary Search on Value: Binary search on value. Count(x) = sum(min(x//i, n) for i in 1..m). Find smallest value with count >= k. Implement weighted random selection using prefix sum and binary search in O(log n) per pick. Topics: array, binary-search, prefix-sum, math Companies: google, amazon, facebook, uber, airbnb Level: swe2, swe3 Prefix Sum + Binary Search: Build prefix sums. Random int in [1, total]. Binary search prefix array to find weighted index. Design a time-based key-value store with O(log n) get using HashMap and binary search. Topics: hash-map, binary-search, design-patterns Companies: google, amazon, facebook, stripe, uber Level: swe2, swe3 HashMap + Binary Search: HashMap of sorted (timestamp, value) lists. Binary search for largest timestamp <= query. Precompute election leaders at each timestamp and answer queries with binary search in O(log n). Topics: array, binary-search, hash-map Companies: google, amazon Level: swe3, senior Precompute + Binary Search: Precompute leader at each timestamp. For query t, binary search for latest vote time <= t. Find peak index in mountain array using binary search on slope direction in O(log n) time. Topics: array, binary-search Companies: amazon, google, microsoft Level: new-grad, swe2 Binary Search: Binary search. If arr[mid] < arr[mid+1], rising slope so peak is right. Else peak is left. Search sorted 2D matrix using staircase approach from top-right corner in O(m+n) time. Topics: array, binary-search, matrix, divide-and-conquer Companies: amazon, google, facebook, microsoft, bloomberg Level: swe2, swe3 Staircase Search from Top-Right: Start top-right. Value > target: move left (eliminate column). Value < target: move down (eliminate row). Compute integer square root using binary search without built-in sqrt in O(log x) time. Topics: math, binary-search Companies: amazon, google, microsoft, bloomberg Level: new-grad, swe2 Binary Search: Binary search in [1, x//2]. When lo > hi, hi is floor(sqrt(x)). Find H-Index from sorted citations array using binary search in O(log n) time. Topics: array, binary-search Companies: facebook, google, amazon Level: swe2, swe3 Binary Search: Binary search on h. Check if citations[n-h] >= h (at least h papers with >= h citations). Find minimum train speed to arrive on time using binary search on speed in O(n log max) time. Topics: array, binary-search Companies: amazon, google, uber Level: swe2, swe3 Binary Search on Speed: Binary search on speed. Sum ceiling times for all but last train plus actual last train time. Find minimum time for buses to complete totalTrips using binary search on time value. Topics: array, binary-search Companies: amazon, google, leetcode Level: swe2, swe3 Binary Search on Time: Binary search on total time. Feasibility: sum of t//time[i] for all buses >= totalTrips. Maximize candies per child by binary searching on candy count with pile splitting feasibility check. Topics: array, binary-search Companies: amazon, google Level: swe2, swe3 Binary Search on Candy Count: Binary search on candy count m. Feasibility: sum(c//m for c in candies) >= k children. Minimize maximum bag size after splitting with limited operations using binary search on the answer. Topics: array, binary-search Companies: amazon, google, facebook Level: swe2, swe3 Binary Search on Max Size: Binary search on max bag size. Operations needed for bag n with limit m: ceil(n/m) - 1. Find maximum path sum in binary tree using DFS with global max tracking in O(n) time. Topics: binary-tree, dfs, dynamic-programming, recursion Companies: amazon, google, facebook, microsoft, bloomberg Level: swe3, senior DFS with Global Max: DFS returns max one-sided path sum. At each node compute full path sum and update global max. Place minimum cameras in binary tree using greedy post-order DFS with three-state node classification. Topics: binary-tree, dfs, greedy, dynamic-programming Companies: google, amazon, facebook Level: senior, staff Greedy DFS: Post-order DFS. Place camera when child is uncovered. Greedy: place cameras as high as possible. Find minimum coin moves in binary tree using DFS excess calculation in O(n) time. Topics: binary-tree, dfs, recursion Companies: amazon, google, facebook Level: swe3, senior DFS Excess Calculation: DFS returns excess coins. Each edge move = |excess|. Total moves = sum of excess over all subtrees. Find maximum width of binary tree using BFS with position indices and normalization in O(n). Topics: binary-tree, bfs, dfs Companies: amazon, google, facebook Level: swe2, swe3 BFS with Index Normalization: BFS with node position indices. Left child = 2*i, right child = 2*i+1. Normalize to prevent overflow. Count nodes in complete binary tree in O(log^2 n) by comparing heights to detect perfect subtrees. Topics: binary-tree, binary-search, dfs Companies: amazon, google, microsoft Level: swe2, swe3 Binary Search on Height: Compare left-spine and right-spine heights. If equal: perfect subtree. Else recurse both sides. Sum all root-to-leaf numbers in binary tree using DFS with running number accumulation. Topics: binary-tree, dfs, recursion Companies: amazon, google, facebook, microsoft Level: swe2, swe3 DFS with Running Number: DFS with running number. At each node: cur = cur*10 + val. Return cur at leaves, sum of children otherwise. Count paths with target sum using DFS with prefix sum hash map in O(n) time. Topics: binary-tree, dfs, prefix-sum, hash-map Companies: amazon, google, facebook, microsoft Level: swe2, swe3 Prefix Sum Hash Map: DFS with prefix sum hash map. At each node, check if (cur_sum - target) exists in map. Backtrack on exit. Flatten binary tree to linked list in-place using Morris traversal approach in O(n) O(1) space. Topics: binary-tree, dfs, recursion, linked-list Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Iterative with Stack: Morris-style: for each node with left, find rightmost of left subtree, connect to right, move left to right. Get right side view of binary tree using BFS level order traversal taking last node per level. Topics: binary-tree, bfs, dfs Companies: amazon, facebook, google, microsoft, bloomberg Level: swe2, swe3 BFS Level Order: BFS level by level. Take the last node value at each level as the right-side visible node. Find all duplicate subtrees by serializing each subtree and counting occurrences with a hash map. Topics: binary-tree, dfs, hash-map, serialization Companies: amazon, google, facebook Level: swe2, swe3 Post-order Serialization: Post-order DFS serializes each subtree. Hash map counts occurrences; collect on second occurrence. Implement LRU Cache in Python with O(1) get and put using OrderedDict or a doubly linked list + hash map. Includes full solutions with test cases. Topics: design-patterns, hash-map, linked-list, caching Companies: amazon, google, meta, microsoft, uber, bloomberg Level: swe2, swe3, senior OrderedDict (Pythonic): Use collections.OrderedDict. move_to_end() marks recently used; popitem(last=False) evicts LRU. Doubly Linked List + HashMap: Manual DLL with sentinel head/tail. HashMap stores key -> node. O(1) insert/delete/lookup. Implement an LFU Cache in Python with O(1) get and put. Covers three-dict solution and doubly linked list per frequency bucket approach. Topics: design-patterns, hash-map, linked-list, caching Companies: amazon, google, meta, microsoft, databricks Level: swe3, senior, staff Three-dict O(1) solution: key_val: key->val, key_freq: key->freq, freq_keys: freq->OrderedDict(key). min_freq tracks eviction target. Doubly Linked List per frequency: Each frequency bucket is a DLL of nodes. Moving a node to next bucket is O(1). Maintains true LRU order within each bucket. Design a simplified Twitter with postTweet, follow, unfollow, and getNewsFeed in Python. Uses a max-heap to merge per-user tweet lists efficiently. Topics: design-patterns, heap, hash-map, object-design Companies: twitter, amazon, google, meta, uber Level: swe2, swe3, senior Heap merge of per-user tweet lists: Store tweets per user with timestamp. getNewsFeed uses a max-heap seeded with the latest tweet from each followed user, then pops up to 10. Simple list merge (brute force): Collect all tweets from self + followees, sort by timestamp descending, return top 10. Simpler but slower. Implement the Snake Game in Python using a deque and set for O(1) body collision detection. Full solution with food eating and wall boundary logic. Topics: design-patterns, deque, hash-map, object-design Companies: amazon, google, microsoft, apple, bloomberg Level: swe2, swe3, senior Deque + set for O(1) collision: Deque stores body cells (row, col). Set mirrors deque for O(1) membership. New head computed from direction, tail removed before self-collision check to handle tail-chasing correctly. Deque only (O(n) collision check): Same deque approach but uses 'in' on deque for collision check. Simpler but O(n) per move for large snakes. Implement a Hit Counter in Python that counts hits in the past 5 minutes. Covers O(1) circular buffer and queue-based approaches with full test cases. Topics: design-patterns, queue, array, object-design Companies: amazon, google, microsoft, stripe, bloomberg Level: swe2, swe3, senior Circular buffer (O(1) always): Two arrays of size 300: times[i] stores the timestamp that last wrote slot i, counts[i] stores hits at that timestamp. Slot index = timestamp % 300. Queue-based (intuitive): Store (timestamp, count) pairs in a deque. On getHits, pop entries older than 300 seconds from front. Implement a Phone Directory in Python with O(1) get, check, and release operations using a set of available numbers or queue with boolean array. Topics: design-patterns, sets, object-design, hash-map Companies: google, amazon, microsoft, linkedin, bloomberg Level: swe2, swe3 Set of available numbers: Keep a set of free numbers. get() pops any element O(1). check() is O(1) membership. release() adds back O(1). Queue + boolean array: Queue of free numbers for O(1) get. Boolean array for O(1) check. Release adds back to queue only if not already free. Implement an in-memory file system in Python supporting ls, mkdir, addContentToFile, and readContentFromFile using a trie with dict children. Topics: design-patterns, trie, object-design, dicts Companies: google, amazon, microsoft, meta, airbnb, uber Level: swe3, senior, staff Trie with dict children: Each node stores children dict and file content string. Traversal splits path on '/'. ls checks if terminal node is file or dir. Flat dict paths: Two flat dicts: dirs (set of dir paths) and files (file path -> content). ls iterates flat dict to find direct children. Implement a Trie (Prefix Tree) in Python with insert, search, and startsWith operations. Covers TrieNode dict approach and compact defaultdict solution. Topics: trie, design-patterns, strings, dicts Companies: google, amazon, meta, microsoft, apple, bloomberg, uber Level: swe2, swe3, senior TrieNode with dict children: Each node stores a dict of char->TrieNode and a boolean is_end. Dynamic children dict avoids fixed 26-slot arrays. Nested defaultdict (compact): Use nested defaultdict to avoid explicit TrieNode class. Terminator key signals end of word. Design a WordDictionary in Python with addWord and wildcard search using a Trie and DFS. Full solution with dot wildcard matching and test cases. Topics: trie, dfs, backtracking, strings Companies: google, amazon, meta, microsoft, bloomberg, linkedin Level: swe2, swe3, senior Trie with DFS for wildcard: Standard trie insertion. Search uses recursive DFS; when '.' is encountered, recursively check all children nodes. Dict of word lengths: Group words by length. search checks length match, then each stored word character by character allowing dots as wildcards. Simpler but higher memory overhead per lookup. Solve Word Search II in Python using a Trie combined with DFS backtracking on the board. Includes trie pruning optimization and full test cases. Topics: trie, backtracking, dfs, matrix Companies: amazon, google, meta, microsoft, bloomberg, airbnb Level: swe3, senior, staff Trie + DFS with pruning: Build trie from words. DFS from every cell, following trie branches. Record found words and delete trie nodes to avoid revisiting. Trie + DFS (class-based TrieNode): Same algorithm but with an explicit TrieNode class. Cleaner code, easier to extend. Implement a LIFO stack using only queues in Python. Covers one-queue rotation trick and two-queue swap approach with full test cases. Topics: stack, queue, design-patterns Companies: amazon, google, microsoft, bloomberg, adobe Level: new-grad, swe2 One queue, rotate on push: Use one deque. After appending new element, rotate (n-1) elements to front. Now front is always the top of stack. Two queues: q1 holds stack elements (top at front). On push, enqueue to q2, drain q1 into q2, then swap references. Implement a FIFO queue using two stacks in Python with amortized O(1) pop. Covers two-stack inbox/outbox approach and recursive one-stack solution. Topics: queue, stack, design-patterns Companies: amazon, google, meta, microsoft, bloomberg Level: new-grad, swe2 Two stacks - amortized O(1): inbox for pushes, outbox for pops/peeks. Transfer only when outbox empty. Each element moves at most twice total, giving amortized O(1). One stack with recursion: Pop all elements recursively to reach the bottom (front), perform operation, re-push everything. Elegant but O(n) per operation. Implement a Min Stack in Python that retrieves the minimum element in O(1). Covers auxiliary min stack and tuple-pair approaches with test cases. Topics: stack, design-patterns Companies: amazon, google, meta, microsoft, bloomberg, uber, apple Level: new-grad, swe2, swe3 Auxiliary min stack: Two stacks: main stack and min_stack. min_stack top always holds the minimum of the current stack state. Store (val, min) pairs: Each stack element is a tuple (value, current_min). Avoids a second stack, same time/space asymptotically. Implement a Max Stack in Python with O(log n) popMax using a max-heap and lazy deletion. Also covers the simpler two-stack O(n) approach. Topics: stack, design-patterns, heap, linked-list Companies: amazon, google, meta, bloomberg, stripe Level: swe3, senior, staff Heap + DLL with lazy deletion: DLL maintains stack order. Max-heap stores (-val, uid). popMax: pop heap lazily skipping deleted nodes, remove DLL node via uid lookup. Two stacks (O(n) popMax): Two stacks: main and max_stack (tracks max at each level). popMax is O(n): pop to temp until max found, push back. Simpler code. Solve Sliding Window Maximum in Python using a monotonic decreasing deque for O(n) time. Includes full walkthrough and test cases. Topics: deque, sliding-window, monotonic-stack, array Companies: amazon, google, meta, microsoft, bloomberg, uber, bytedance Level: swe3, senior, staff Monotonic decreasing deque: Deque stores indices in decreasing order of nums value. Front = current max index. Pop back when new element is larger; pop front when out of window. Brute force O(n*k): For each window position, take the max of k elements. Simple but too slow for large inputs. Solve Sliding Window Minimum in Python using a monotonic increasing deque for O(n) time. Includes sparse table RMQ alternative and test cases. Topics: deque, sliding-window, monotonic-stack, array Companies: amazon, google, microsoft, bloomberg, palantir Level: swe2, swe3, senior Monotonic increasing deque: Deque stores indices in increasing order of nums value (front = min). Pop back when new element is smaller; pop front when index falls outside window. Segment tree approach: Build a segment tree for range minimum queries. Each window query is O(log n), total O(n log n). Overkill here but demonstrates the general pattern. Find the first unique character in a character stream in Python using OrderedDict or a lazy-eviction deque. Full solutions with test cases. Topics: design-patterns, queue, hash-map, strings, deque Companies: amazon, google, meta, microsoft, twitter, bloomberg Level: swe2, swe3, senior OrderedDict + count: OrderedDict preserves insertion order. Count dict tracks frequency. showFirstUnique scans OrderedDict for first key with count 1. Deque with lazy eviction: Deque stores all added chars. count dict tracks frequency. showFirstUnique pops from front while count > 1 (lazy), then returns front or # if empty. Implement a HashMap from scratch in Python using separate chaining with prime buckets or a direct address table. Full solutions with test cases. Topics: hash-map, design-patterns, array, linked-list Companies: amazon, google, meta, microsoft, bloomberg, oracle Level: new-grad, swe2 Separate chaining with prime buckets: Array of 1009 buckets (prime reduces clustering). Each bucket is a list of (key, value) pairs. Operations scan the small chain list. Direct address table (for small key range): Use a fixed-size array of size max_key+1. Direct index gives O(1) for all operations. Only feasible when key range is small. Implement a HashSet from scratch in Python using separate chaining or a bytearray bitset. Full solutions with add, remove, contains and test cases. Topics: sets, design-patterns, hash-map, array Companies: amazon, google, microsoft, bloomberg, oracle, adobe Level: new-grad, swe2 Separate chaining with lists: Array of 1009 buckets, each a list of keys. add/remove/contains scan the small bucket list. Bitset / boolean array: Boolean array of size max_key+1. add sets True, remove sets False, contains returns the boolean. O(1) all operations. Implement a CombinationIterator in Python using itertools, a lazy bitmask generator, or a backtracking generator. Full solutions with test cases. Topics: design-patterns, backtracking, recursion, array Companies: google, amazon, meta, microsoft, bloomberg, palantir Level: swe2, swe3, senior Pre-generated list (itertools): Generate all combinations at init using itertools.combinations. Store as list in reverse for O(1) pop-from-back in lexicographic order. Lazy bitmask generator: Iterate all 2^n bitmasks in order; yield those with exactly k set bits. Builds combinations lazily without storing all upfront. Backtracking generator: Use a Python generator with backtracking to yield combinations lazily one at a time. next() calls next() on the generator object. Solve N-ary Tree Level Order Traversal in Python using BFS queue and recursive DFS with depth tracking. Includes full code with test cases. Topics: binary-tree, bfs, queue Companies: google, amazon, microsoft Level: new-grad, swe2 BFS with queue: Use a queue. Snapshot the queue size at each level, process exactly that many nodes, push all children. O(n) time and space. Recursive DFS: DFS with depth tracking. Pass the current depth and append the node value to result[depth]. O(n) time, O(h) stack space where h is height. Find the maximum depth of an N-ary tree in Python using recursive DFS and iterative BFS. Includes complexity analysis and test cases. Topics: binary-tree, dfs, bfs Companies: amazon, facebook, google Level: new-grad Recursive DFS: Recursively compute 1 + max depth of all children. If no children, return 1. If root is None, return 0. Iterative BFS: BFS level by level, counting levels. Return the total level count. Solve Diameter of Binary Tree in Python with DFS height tracking. Includes iterative post-order solution, complexity analysis, and test cases. Topics: binary-tree, dfs, recursion Companies: amazon, google, facebook, microsoft, apple Level: new-grad, swe2 DFS with global max: For each node compute height of left and right subtrees. The local diameter = left_h + right_h. Track global max. Return height = 1 + max(left_h, right_h). Iterative post-order: Iterative post-order traversal using a stack. Store heights in a dict keyed by node. Update diameter at each node. Find the LCA of deepest leaves in a binary tree using Python DFS. Two clean approaches with full code and complexity analysis. Topics: binary-tree, dfs, recursion Companies: google, amazon, facebook Level: swe2, swe3 DFS returning (node, depth): Each recursive call returns (LCA candidate, max depth in subtree). If left depth == right depth, current node is LCA. Otherwise recurse into the deeper side. Two-pass: find depth then LCA: First DFS to find max depth. Second DFS to find LCA of all nodes at max depth. Check if a binary tree is complete using Python BFS with None sentinel and array index approaches. Full code and test cases included. Topics: binary-tree, bfs Companies: amazon, facebook, google, microsoft Level: swe2, swe3 BFS with None sentinel: BFS. Once a None is dequeued, set a flag. If any subsequent non-None node is dequeued, return False. Array index check: Number nodes with BFS index (root=1, left=2i, right=2i+1). The tree is complete iff count of nodes equals max index. Replace each node with the sum of its cousins using Python BFS. Level-sum and sibling-sum trick explained with full code. Topics: binary-tree, bfs, dfs, hash-map Companies: google, amazon Level: swe2, swe3 BFS two-pass: BFS. At each level compute total level sum. Then for each parent node, sibling sum = left.val + right.val. Assign each child: cousin_sum = level_sum - sibling_sum. Validate an Even-Odd tree using Python BFS with level-by-level parity and ordering checks. Full code with test cases. Topics: binary-tree, bfs Companies: amazon, google, microsoft Level: swe2 BFS level validation: BFS. At each level, check: even level -> values must be odd and strictly increasing. Odd level -> values must be even and strictly decreasing. Find shortest directions between two binary tree nodes in Python using root-to-node paths and LCA prefix removal. Full code included. Topics: binary-tree, dfs, strings Companies: google, amazon, facebook Level: swe2, swe3 Root-to-node paths + LCA trick: Find path from root to start and root to dest. Strip common prefix (which is path to LCA). Answer = "U"*len(remaining_start) + remaining_dest. Count pseudo-palindromic root-to-leaf paths using Python DFS with XOR bitmask. Includes iterative solution and full test cases. Topics: binary-tree, dfs, bit-manipulation Companies: amazon, google, adobe Level: swe2, swe3 DFS with bitmask: XOR bitmask tracks odd/even frequency of each digit. At a leaf, check if at most one bit is set using mask & (mask-1) == 0. Iterative DFS with stack: Iterative DFS using explicit stack storing (node, mask) pairs. Same bitmask logic at leaves. Sum all nodes whose grandparent has even value using Python DFS with parent tracking. BFS alternative also included. Topics: binary-tree, dfs, bfs Companies: amazon, google Level: swe2 DFS with parent/grandparent tracking: Recursive DFS passing parent and grandparent values. Add current node value when grandparent is even. BFS with grandchildren tracking: BFS. For each even-valued node, add the values of all its grandchildren (children of children). Build a binary tree from parent-child descriptions using Python hash map. Find root by tracking child set. Full code with test cases. Topics: binary-tree, hash-map, dfs Companies: amazon, google, facebook Level: swe2, swe3 Hash map + child set: Build all nodes in a dict. Track all child values in a set. Root is the node whose value never appears as a child. Count nodes where value equals floor average of subtree using Python post-order DFS. Full code with complexity analysis and test cases. Topics: binary-tree, dfs, recursion Companies: amazon, google, microsoft Level: swe2 Post-order DFS: Each call returns (total_sum, count). At the node, total = left_sum + right_sum + node.val, cnt = left_cnt + right_cnt + 1. Check node.val == total // cnt. Find the level with maximum sum in a binary tree using Python BFS. Simple level-order traversal with sum tracking. Topics: binary-tree, bfs Companies: amazon, google, facebook Level: new-grad, swe2 BFS level sum: BFS. At each level compute sum. Track max sum and corresponding level. Return that level. Reverse values at odd levels of a perfect binary tree using Python BFS and DFS mirror swap. Full code with test cases. Topics: binary-tree, bfs, dfs Companies: google, amazon, microsoft Level: swe2, swe3 BFS with value reversal at odd levels: BFS. At odd levels collect all nodes, reverse their values (not the nodes themselves). Continue BFS normally. DFS mirror swap: DFS with two symmetric nodes. At odd levels swap their values. Recurse with outer-outer and inner-inner child pairs. Count good nodes in a binary tree where no ancestor has a greater value. Python DFS with max tracking. Iterative and recursive solutions. Topics: binary-tree, dfs Companies: google, amazon, facebook, microsoft Level: new-grad, swe2 DFS with max tracking: DFS from root, carrying max value along the path. Count the node if node.val >= max. Update max before recursing. Iterative DFS with stack: Iterative DFS using explicit stack of (node, max_so_far). Count good nodes as we go. Solve 3D Trapping Rain Water using Python min-heap BFS. Process border cells outward, accumulate trapped water. Full code with complexity analysis. Topics: matrix, heap, bfs, greedy Companies: google, amazon, facebook, microsoft, bloomberg Level: swe3, senior, staff Min-heap BFS (3D water fill): Push all border cells into a min-heap. BFS inward always processing the lowest boundary cell. Water at interior cell = max(0, boundary_height - cell_height). Update boundary to max(boundary_height, cell_height). Find the largest square of 1s in a binary matrix using Python DP. Includes O(mn) and O(n) space solutions with full code. Topics: dynamic-programming, matrix Companies: amazon, google, facebook, microsoft, apple, bloomberg Level: swe2, swe3, senior DP 2D table: dp[i][j] = max side when bottom-right is (i,j). Transition: min of three neighbors + 1. Track global max side. DP O(n) space: Use a 1D dp array and a prev variable to store dp[i-1][j-1]. Reduces space to O(n). Find the maximal rectangle of 1s in a binary matrix using Python histogram with monotonic stack. DP left/right approach also included. Topics: dynamic-programming, stack, matrix, monotonic-stack Companies: amazon, google, facebook, microsoft, bloomberg, goldman-sachs Level: swe3, senior Histogram + monotonic stack: Convert each row into heights (running count of consecutive 1s above). Apply largest-rectangle-in-histogram with a monotonic stack for each row. DP left/right/height arrays: For each cell track: height (consecutive 1s above), left boundary (leftmost contiguous 1 in current row), right boundary. Area = height*(right-left). Find the longest consecutive sequence in O(n) using Python hash set. Union-Find alternative included. Full code with test cases. Topics: array, hash-map, sets Companies: amazon, google, facebook, microsoft, linkedin, uber Level: swe2, swe3 Hash set O(n): Build a set. For each num where num-1 is not in the set (sequence start), count consecutive nums. Each element is visited at most twice. Union-Find approach: Union each num with num+1 if both exist. Track component sizes. Max size is the answer. Find the first missing positive integer in O(n) time O(1) space using cyclic sort and index marking in Python. Complete solutions with test cases. Topics: array, sorting Companies: amazon, google, facebook, microsoft, bloomberg, stripe Level: swe3, senior Cyclic sort: For each index, swap nums[i] into its correct position (index nums[i]-1) while 1 <= nums[i] <= n and nums[i] != nums[nums[i]-1]. Then find the first index where nums[i] != i+1. Index marking (sign flip): First pass: replace non-positives and out-of-range with n+1. Second pass: for each value v in [1,n], negate nums[v-1]. Third pass: first non-negative index+1 is the answer. Solve Text Justification in Python using greedy line packing and space distribution. Full simulation with edge cases and test output. Topics: strings, greedy Companies: google, amazon, facebook, microsoft, bloomberg, uber Level: swe3, senior Greedy line packing: Group words greedily. For each non-last line compute total extra spaces, distribute left to right. Last line is left-justified with single spaces and trailing spaces. Solve Jump Game VI with max score using Python DP and monotonic deque for O(n) sliding window max. Full code with test cases. Topics: dynamic-programming, deque, sliding-window Companies: amazon, google, microsoft, linkedin Level: swe2, swe3 DP + monotonic deque: dp[i] = nums[i] + max(dp[i-k..i-1]). Maintain a max-deque of dp values within the window. Deque front is always the max. DP + segment tree (for clarity): Use a segment tree for range max queries. dp[i] = nums[i] + range_max(dp, i-k, i-1). O(n log n). Solve minimum cost stick cutting using Python interval DP. Both bottom-up table and top-down memoized recursion explained with full code. Topics: dynamic-programming, interval Companies: amazon, google, facebook, bloomberg Level: swe3, senior Interval DP: Sort cuts, add 0 and n as boundaries. dp[i][j] = min cost to cut the segment [cuts[i], cuts[j]]. For each sub-segment try every cut as the last one. Memoized recursion: Top-down DP. rec(i, j) = min cost for all cuts strictly inside [cuts[i], cuts[j]]. Try each cut as the first cut in that segment. Find the largest color value along any path in a directed graph using Python topological sort and DP. Cycle detection included. Topics: graph, topological-sort, dynamic-programming, hash-map Companies: google, amazon, facebook, coinbase Level: senior, staff Kahn's topological sort + DP: Build adjacency list and in-degree. Kahn's BFS topological sort. dp[u][c] = max color-c count on path ending at u. Propagate: dp[v][c] = max(dp[v][c], dp[u][c] + (colors[v]==c)). Answer = max over all nodes and colors. If not all nodes processed, cycle exists. Find minimum completion time for parallel courses using Python topological sort and critical path DP. Full code with test cases. Topics: graph, topological-sort, dynamic-programming Companies: google, amazon, facebook, linkedin, databricks Level: senior, staff Topological sort critical path: Kahn's BFS topological sort. dp[i] = earliest completion time. When processing course u, update each dependent v: dp[v] = max(dp[v], dp[u] + time[v-1]). Answer = max(dp). Count valid vowel strings of length n using Python DP state transitions and matrix exponentiation. Full code with modular arithmetic. Topics: dynamic-programming, math, combinatorics Companies: google, amazon, facebook Level: swe3, senior DP on vowel states: Track count of strings ending with each vowel. Update using the allowed transitions (reversed: which vowels can precede each vowel). Iterate n-1 times. Matrix exponentiation: Model transitions as a 5x5 matrix. Use fast matrix exponentiation for very large n. O(26^3 * log n) but with only 5 vowels it is O(5^3 * log n). Solve Strange Printer with minimum turns using Python interval DP. Merge matching characters to reduce turns. Full code with test cases. Topics: dynamic-programming, interval, recursion Companies: google, amazon, facebook, bloomberg Level: senior, staff Interval DP bottom-up: dp[i][j] = min turns for s[i..j]. Base: dp[i][i]=1. For each character s[k] in (i,j] where s[k]==s[i], dp[i][j] = min(dp[i][j], dp[i+1][k] + dp[k][j]) (s[i] merges with s[k]). Memoized recursion: Top-down DP. Deduplicate consecutive chars first. rec(i,j) = min turns for s[i..j]. Try merging s[i] with each matching s[k]. Find minimum days to disconnect an island grid using Python DFS. Exploit the observation that the answer is always 0, 1, or 2. Topics: graph, dfs, matrix Companies: google, amazon, facebook Level: senior, staff Observation: answer <= 2 + brute force check: Count islands. If != 1 return 0. Try removing each land cell and re-count islands; if any gives != 1 return 1. Otherwise return 2. Minimize total robot travel distance to factories using Python DP with expanded slots or memoized recursion. Full code with test cases. Topics: dynamic-programming, sorting, greedy Companies: google, amazon, facebook, palantir Level: senior, staff Sort + DP on expanded factories: Sort robots and factories. Expand each factory position by its limit into individual slots. dp[i][j] = min cost to assign first i robots to first j slots. dp[i][j] = min(dp[i-1][j-1]+|r[i]-slot[j]|, dp[i][j-1]). Memoized recursion: Top-down DP with lru_cache on (robot_idx, factory_idx, capacity_used). Sort both arrays first. Minimize the max pair difference using Python binary search and greedy pair counting on a sorted array. Full code with complexity analysis. Topics: binary-search, greedy, sorting Companies: amazon, google, microsoft, bloomberg Level: swe2, swe3 Binary search + greedy pair count: Sort nums. Binary search on answer mid. Greedy: scan sorted nums, if nums[i+1]-nums[i] <= mid, take pair and skip i+1, else move forward. If pairs >= p, mid might be feasible. Count all palindromic substrings using Python expand-around-center O(n^2) and Manacher's O(n) algorithm. Full code with test cases. Topics: strings, dynamic-programming, two-pointers Companies: amazon, google, facebook, microsoft, linkedin Level: swe2, swe3 Expand around center: For each of the 2n-1 centers, expand outward while characters match. Count palindromes found. Manacher's algorithm O(n): Manacher's algorithm computes palindrome radii in O(n). Sum the ceiling of each radius+1 to count palindromes. Find the shortest palindrome by prepending characters using Python KMP failure function. O(n) solution with full explanation and test cases. Topics: strings, string-matching, two-pointers Companies: google, amazon, facebook, bloomberg Level: senior, staff KMP failure function: Construct t = s + "#" + reverse(s). Run KMP to find the longest prefix of t that is also a suffix, which gives the longest palindromic prefix of s. Two-pointer + recursion: Find the longest palindrome starting from index 0 greedily. Reverse the rest and prepend. Recurse on remaining middle part. Implement wildcard pattern matching with ? and * in Python using 2D DP and greedy two-pointer. Full solutions with complexity analysis. Topics: dynamic-programming, strings, greedy, recursion Companies: amazon, google, facebook, microsoft, bloomberg Level: swe3, senior DP 2D table: dp[i][j] = does p[:j] match s[:i]. Handle "*" by either matching empty (dp[i][j-1]) or one character (dp[i-1][j]). Greedy two-pointer: Track last "*" position in pattern and last match position in s. When mismatch, backtrack to last "*" and advance s. Implement regular expression matching with . and * in Python using 2D DP and memoized recursion. Full code with all edge cases. Topics: dynamic-programming, strings, recursion Companies: google, amazon, facebook, microsoft, bloomberg, uber Level: senior, staff DP 2D table: dp[i][j] = match. "*" can mean zero (dp[i][j-2]) or extend if preceding element matches (dp[i-1][j]). "." matches any character. Recursive with memoization: Top-down recursion. Base cases: empty pattern, empty string. Handle "*" by trying zero or one match. Cache results. Compute the minimum edit distance (Levenshtein) between two strings using Python 2D DP and space-optimized O(n) version. Full code with test cases. Topics: dynamic-programming, strings Companies: amazon, google, facebook, microsoft, linkedin, uber, bloomberg Level: swe2, swe3, senior DP 2D table: Classic DP. dp[i][j] = Levenshtein distance for word1[:i] and word2[:j]. Three transitions: insert, delete, replace. DP O(n) space: Use a single row dp array, updating in place. Track the diagonal value with a prev variable. Find all sentence breakdowns of a string using a word dictionary in Python with memoized backtracking and DP pruning. Full code with test cases. Topics: dynamic-programming, backtracking, memoization, trie, strings Companies: amazon, google, facebook, microsoft, bloomberg, apple Level: swe3, senior Backtracking with memoization: Recursive backtrack from index i. Try all dict words that match at i. Memoize (index -> list of sentences from that index). DP precompute + backtrack: First DP pass checks if s[i:] is breakable. Then backtrack only on reachable indices (pruning invalid branches). Find all concatenated words formed from shorter words using Python DP Word Break and Trie DFS. Full code with test cases. Topics: dynamic-programming, trie, dfs, strings Companies: amazon, google, facebook, microsoft Level: senior, staff DP word break per word: Sort words by length. Maintain a set of shorter words. For each word, run Word Break DP: dp[i]=True if s[:i] can be formed from shorter words. A word is concatenated if dp[n] is True and it uses at least 2 pieces. Trie + DFS: Build a Trie of all words. For each word, DFS through trie matching characters. On end-of-word node, recursively check remainder. Count segments; if >= 2, it is a concatenated word. Count distinct subsequences of s equal to t using Python 2D DP and O(n) space optimized version. Full code with test cases. Topics: dynamic-programming, strings Companies: amazon, google, facebook, bloomberg Level: swe3, senior DP 2D table: dp[i][j] = ways to form t[:j] using s[:i]. Match: use dp[i-1][j-1] (use s[i]) + dp[i-1][j] (skip s[i]). No match: dp[i-1][j] (skip s[i]). DP O(n) space: Use a 1D dp array, update right to left to avoid overwriting values needed for current row. Check if s3 is an interleaving of s1 and s2 using Python 2D DP and O(n) space optimization. Full code with test cases. Topics: dynamic-programming, strings, recursion Companies: amazon, google, facebook, microsoft, bloomberg Level: swe2, swe3 DP 2D table: dp[i][j] = is s3[:i+j] an interleaving of s1[:i] and s2[:j]. Transition uses either s1[i-1] or s2[j-1] to extend s3[i+j-1]. DP O(n) space: Optimize to a 1D dp array by noting that dp[i][j] only depends on dp[i-1][j] and dp[i][j-1]. Find all shortest word ladder transformation sequences using Python BFS with parent map and backtracking. Bidirectional BFS also included. Topics: graph, bfs, backtracking, hash-map, strings Companies: amazon, google, facebook, microsoft, bloomberg, uber Level: senior, staff BFS layer-by-layer + backtrack: BFS layer by layer. For each word at current layer, find all one-letter neighbors in wordList. Record parent->children. Stop after finding endWord level. Backtrack from endWord using parent map. Bidirectional BFS + backtrack: Expand from both beginWord and endWord simultaneously, meeting in the middle. Significantly reduces the BFS frontier. Then backtrack through the merged parent map. Python interview question: use named regex capture groups to extract and decompose email addresses from unstructured text. Topics: regex, string, comprehensions Companies: paypal, visa, datadog, splunk, oracle, discord Level: new-grad, swe2, swe3 Named Groups with finditer: Single regex with named capture groups, finditer for lazy match streaming Compiled pattern with list comprehension: Pre-compile regex once at module level, list comprehension over match objects Python interview: parse structured log lines using compiled regex with named capture groups for timestamp, level, service, and message. Topics: regex, string, collections Companies: datadog, splunk, snowflake, discord, slack, oracle Level: new-grad, swe2, swe3 Compiled regex with named groups: Pre-compiled regex pattern with named groups, returns None on no match Parse with split fallback for message: fullmatch anchors both ends; strip message trailing whitespace Python interview: validate and normalize international phone numbers using regex, extracting country code and subscriber number. Topics: regex, string Companies: paypal, visa, coinbase, oracle, discord, bytedance Level: new-grad, swe2, swe3 Strip then validate digit count: Strip non-digits, infer country code from digit count and leading + Regex pattern with alternation: Two dedicated regexes: one for US/Canada, one for international with explicit country code Python interview: filter a 2D grid with nested list comprehensions using multiple conditions on row index and value. Topics: comprehensions, lists Companies: nvidia, snowflake, bytedance, dropbox, oracle, discord Level: new-grad, swe2 Nested comprehension with enumerate: Single nested comprehension with enumerate for indices, three-condition filter Generator expression wrapped in list(): Inner generator with early continue on odd rows, yielding matching tuples Python interview: invert a dictionary with duplicate values, aggregating keys into sorted lists using dict comprehension and defaultdict. Topics: comprehensions, dicts, collections Companies: snowflake, redis, datadog, oracle, visa, dropbox Level: new-grad, swe2, swe3 defaultdict then dict comprehension: Group with defaultdict, then dict comprehension with sorted() on each group itertools.groupby approach: Sort by value, then groupby to collect keys, dict comprehension for output Python interview: use set comprehensions and symmetric difference to detect feature flag drift between deployment environments. Topics: comprehensions, sets Companies: discord, slack, snowflake, datadog, nvidia, dropbox Level: new-grad, swe2 Set operator symmetric_difference: Set comprehensions to deduplicate, then symmetric_difference for O(n+m) set operation Set comprehension explicit form: Explicit set comprehensions for each side then union - shows the definition clearly Python interview: implement an infinite Fibonacci generator that supports mid-iteration reset via generator.send(), demonstrating two-way generator communication. Topics: generators, iterators Companies: jane-street, nvidia, bytedance, coinbase, snowflake, oracle Level: swe2, swe3 Generator with send() and reset logic: yield expression captures sent value; truthy value resets a, b to 0, 1 Class-based generator with __iter__/__next__: Iterator class with explicit send() method; reset rewinds state before yielding next Python interview: build a four-stage lazy ETL generator pipeline with reader, filter, transform, and batcher stages that process data without loading it all into memory. Topics: generators, iterators, functools Companies: snowflake, datadog, splunk, redis, oracle, bytedance Level: swe2, swe3 Four-stage generator pipeline with islice batcher: Chain of generator functions; islice pulls exactly size items per batch without buffering upstream Functional composition with a pipeline helper: compose_pipeline wires stages left-to-right; make_batcher factory parameterizes chunk size Python interview: implement a retry decorator factory with exponential backoff, configurable exceptions, and functools.wraps signature preservation. Topics: decorators, closures, exceptions Companies: paypal, coinbase, discord, slack, datadog, visa Level: swe2, swe3 Decorator factory with exponential backoff: Three-level nesting: factory -> decorator -> wrapper; delay doubles in loop before sleeping Retry with jitter and selective exception types: Adds jitter (up to 10% of delay) to prevent thundering-herd; re-raises on final attempt Python interview: implement a token bucket rate limiting decorator with thread-safe token state, configurable burst, and block or raise behavior. Topics: decorators, closures, async-await Companies: discord, slack, paypal, coinbase, bytedance, nvidia, redis Level: swe2, swe3 Token bucket with threading.Lock: Floating-point token bucket; elapsed time since last check adds fractional tokens; Lock prevents race on shared state Sliding window counter (simpler, less burst-friendly): Sliding window stores timestamps of recent calls; evicts old entries; no fractional tokens Python interview: implement a type-safe generic Stack[T] using TypeVar and Generic with push, pop, peek, __iter__, and from_iterable. Topics: typing, oop, generics Companies: nvidia, jane-street, snowflake, coinbase, oracle, dropbox Level: swe2, swe3 Generic Stack with all methods: list-backed with Generic[T] type parameter; __iter__ uses reversed() for top-to-bottom order Stack with __slots__ and size limit option: __slots__ reduces per-instance memory; optional maxsize enforced in push Python interview: define a Comparable Protocol using structural subtyping and implement a generic top_k function using only protocol-defined methods. Topics: protocols, typing, oop Companies: jane-street, nvidia, snowflake, oracle, coinbase, dropbox Level: swe2, swe3 Protocol with TypeVar bound and heapq: Min-heap of size k; push when under capacity, replace min when new item is larger; sort result descending Manual selection sort using only protocol methods: Repeated linear scan using only < and ==; removes selected max each round - demonstrates protocol sufficiency Python interview: implement a retry decorator with exponential backoff and configurable max attempts for resilient distributed systems. Topics: decorators, closures, exceptions Companies: google, stripe, amazon, netflix, bloomberg, shopify Level: swe2, swe3, senior Loop with exponential sleep: Loop over attempts, catch all exceptions, sleep with doubling delay, re-raise on exhaustion Recursive with specific exception types: Accept tuple of exception types to catch; only retry on those, let others propagate immediately Python interview: implement a memoize decorator that caches results and preserves function metadata using functools.wraps. Topics: decorators, functools, closures Companies: google, meta, amazon, microsoft, linkedin, airbnb Level: swe2, swe3, senior Dict cache with wraps: Closure over dict, tuple+frozenset key for positional+keyword args, wraps for metadata Class-based memoize with __call__: Callable class with __call__; functools.update_wrapper copies metadata onto class instance Python interview: build a timer decorator using time.perf_counter and functools.wraps to measure and log function execution time. Topics: decorators, closures, functools Companies: amazon, microsoft, bloomberg, shopify, linkedin, airbnb Level: swe2, swe3, senior try/finally with perf_counter: try/finally guarantees timing even when function raises; perf_counter for sub-millisecond accuracy Parametrized timer with logger callback: Optional-argument decorator pattern; accepts @timer or @timer(logger=...) without parentheses ambiguity Python interview: implement a sliding-window rate limiter decorator that enforces N calls per second using a deque of timestamps. Topics: decorators, closures, python-internals Companies: stripe, google, netflix, amazon, bloomberg, shopify Level: swe2, swe3, senior Sliding window with deque: Deque stores timestamps of recent calls; prune expired ones, raise if still at limit Blocking rate limiter with sleep: Thread-safe with Lock; block=True sleeps until slot available instead of raising Python interview: write a class decorator that reads type annotations and injects __init__, __repr__, and __eq__ like a mini dataclass. Topics: decorators, oop, python-internals Companies: google, meta, microsoft, airbnb, linkedin, shopify Level: swe2, swe3, senior Inject __init__, __repr__, __eq__ via setattr: Read __annotations__, define three dunder methods as closures over fields list, inject with setattr With default values support: Inspect class dict for default values; merge with positional/keyword args in __init__ Python interview: implement an infinite Fibonacci generator using yield and a take utility with itertools.islice. Topics: generators, itertools, python-internals Companies: google, amazon, microsoft, meta, linkedin, airbnb Level: swe2, swe3, senior Pure generator with itertools.islice: Yield a then update a,b simultaneously; islice avoids materializing whole sequence Generator with takewhile and index filter: Generator composes cleanly with takewhile and comprehensions for filtered subsequences Python interview: chain generator functions into a lazy pipeline that filters, transforms, and parses streaming data without intermediate lists. Topics: generators, itertools, comprehensions Companies: google, amazon, netflix, airbnb, linkedin, bloomberg Level: swe2, swe3, senior Chained generator functions: Each generator pulls from the previous; no intermediate lists; single-pass O(n) processing Composable pipeline builder: functools.reduce threads source through list of generator transformers; stages added without changing pipeline() call Python interview: implement a push-based coroutine pipeline using generator send() for two-way communication between stages. Topics: coroutines, generators, python-internals Companies: google, netflix, amazon, meta, bloomberg, stripe Level: swe3, senior Generator coroutine pipeline with send(): @coroutine auto-primes; each stage receives via yield, forwards via target.send(); close() triggers GeneratorExit Broadcast fan-out coroutine: broadcast sends each value to all downstream coroutines; grep filters before forwarding to its target Python interview: implement an async generator that transparently iterates paginated API results using async for and cursor-based pagination. Topics: asyncio, generators, coroutines Companies: stripe, shopify, google, meta, netflix, amazon Level: swe3, senior Async generator with cursor loop: Async generator loops fetching pages; inner for loop yields individual items; stops on null cursor or empty page With rate limiting and retry: Adds configurable inter-page delay for rate limiting and retry with exponential backoff per page fetch Python interview: implement a database transaction context manager with __enter__/__exit__ for commit on success and rollback on exception. Topics: context-managers, oop, exceptions Companies: amazon, stripe, google, bloomberg, microsoft, netflix Level: swe2, swe3, senior __enter__/__exit__ with commit/rollback: exc_type is None signals clean exit -> commit; any exception -> rollback; return False propagates exception Savepoint-aware nested transaction: Nested transactions use savepoints; depth counter tracks nesting; only outermost calls COMMIT Python interview: use @contextlib.contextmanager to build a temporary directory context manager with guaranteed cleanup in the finally block. Topics: context-managers, generators, file-io Companies: google, amazon, microsoft, airbnb, linkedin, shopify Level: swe2, swe3, senior contextmanager generator with finally cleanup: try/yield/finally idiom; finally ensures cleanup whether body raised or returned normally Parametrized temp_dir with prefix and suffix: Optional keep=True skips rmtree for debugging; prefix/suffix customize the temp directory name Python interview: implement a reentrant context manager that tracks nesting depth and releases resources only when the outermost with block exits. Topics: context-managers, python-internals, oop Companies: google, meta, amazon, bloomberg, netflix, microsoft Level: swe3, senior Depth counter reentrant context manager: Integer depth counter; acquire only at depth 0->1 transition; release only at 1->0 transition Thread-safe reentrant lock with owner tracking: Track owner thread; same-thread reentry increments depth without re-acquiring the lock; different thread blocks Python interview: implement a descriptor class with __get__, __set__, and __set_name__ for runtime type validation on class attributes. Topics: descriptors, oop, python-internals Companies: google, meta, amazon, microsoft, stripe, bloomberg Level: swe3, senior Full descriptor with type and range validation: __set_name__ captures attribute name; __get__/__set__ use private key in instance.__dict__ to avoid recursion Descriptor with default value support: Uses mangled private name for storage; getattr with default avoids KeyError on unset attributes Python interview: implement a lazy property descriptor that computes a value on first access and caches it in the instance __dict__. Topics: descriptors, python-internals, oop Companies: google, amazon, meta, netflix, bloomberg, linkedin Level: swe2, swe3, senior Non-data descriptor caching in instance __dict__: Non-data descriptor: no __set__ means instance.__dict__ wins on lookup; first __get__ populates cache Lazy property with invalidation support: Adds invalidate() method on descriptor to pop from instance.__dict__; allows cache busting when underlying data changes Python interview: implement a read-only data descriptor that raises AttributeError on set, blocking instance __dict__ override. Topics: descriptors, oop, python-internals Companies: google, meta, amazon, stripe, bloomberg, microsoft Level: swe2, swe3, senior Data descriptor with per-instance WeakKeyDictionary: WeakKeyDictionary allows per-instance values without preventing GC; __set__ raises after first write; __delete__ also blocked Strictly read-only with class-level value: Single value on descriptor object; data descriptor priority ensures instance.__dict__ can never shadow it Python interview: implement a metaclass that automatically registers every subclass in a shared registry dict at class creation time. Topics: metaclasses, oop, python-internals Companies: google, meta, amazon, netflix, bloomberg, stripe Level: swe3, senior Metaclass __init__ with registry on base: RegistryMeta.__init__ fires at class creation; checks bases to skip root; walks MRO to find shared registry Simpler version using __init_subclass__ for comparison: __init_subclass__ is the modern alternative; metaclass version shown for completeness and to support multiple independent hierarchies Python interview: write a metaclass that enforces snake_case method naming conventions at class definition time using regex. Topics: metaclasses, python-internals, regex Companies: google, meta, bloomberg, microsoft, stripe, amazon Level: swe3, senior Metaclass __new__ with regex name check: __new__ runs before class object is created; regex rejects camelCase; helper suggests the correct snake_case name Metaclass with whitelist of allowed non-snake names: Collects all violations before raising so the error message lists all offending names at once Python interview: implement the Singleton pattern using a metaclass that overrides __call__ with thread-safe double-checked locking. Topics: metaclasses, oop, python-internals Companies: google, amazon, microsoft, bloomberg, netflix, meta Level: swe2, swe3, senior Metaclass __call__ with thread safety: Override __call__ on metaclass; double-checked locking prevents race conditions; first initialization wins Singleton with reset support for testing: reset() class method allows unit tests to get fresh instances without monkey-patching; lock protects reset too Python interview: use __init_subclass__ to enforce interface contracts on subclasses at class definition time. Topics: oop, python-internals, typing Companies: google, amazon, meta, microsoft, netflix, bloomberg Level: swe2, swe3, senior __init_subclass__ interface enforcement: __init_subclass__ fires at class creation; abstract=True keyword arg skips check for intermediate abstract classes ABC module comparison: Shows abc.ABC for comparison; key difference: abc raises at instantiation, __init_subclass__ raises at class definition Python interview: compare __slots__ and regular class memory usage, demonstrate the 40-60% reduction, and explain trade-offs. Topics: python-internals, oop, descriptors Companies: google, amazon, meta, bloomberg, netflix, microsoft Level: swe2, swe3, senior Memory benchmark with tracemalloc: sys.getsizeof shows shallow size difference; tracemalloc measures real heap usage at scale Slots inheritance and trade-offs: Shows slots trade-offs: no weakref by default, inheritance pitfalls, __dict__ escape hatch; child without __slots__ re-acquires __dict__ Python interview: implement a dynamic config object with dot-access using __getattr__ and __setattr__, avoiding recursion with object.__setattr__. Topics: python-internals, oop, descriptors Companies: amazon, google, stripe, netflix, shopify, linkedin Level: swe2, swe3, senior Dot-access config with recursive nested support: object.__setattr__ bypasses our __setattr__ for _data initialization; dict values auto-converted to nested Config Frozen config with change detection: frozen flag blocks __setattr__ after initialization; _changes list tracks all mutations for audit logging Python interview: override __missing__ in a dict subclass to auto-compute and cache values based on the missing key. Topics: python-internals, oop, closures Companies: google, amazon, meta, bloomberg, microsoft, shopify Level: swe2, swe3, senior __missing__ auto-computing dict subclass: __missing__ called by dict.__getitem__ on miss; stores result in self[key] before returning, so next access is O(1) Recursive defaultdict vs __missing__ comparison: Contrasts defaultdict (fixed factory) with __missing__ (key-aware factory); shows nested defaultdict for completeness Python interview: implement the iterator protocol with __iter__ and __next__ to create a custom range class with configurable step. Topics: python-internals, oop, generators Companies: amazon, google, microsoft, meta, linkedin, airbnb Level: swe2, swe3, senior Stateful iterator class: __iter__ resets _current enabling reuse; __next__ checks boundary condition based on step sign before advancing Separate iterator and iterable classes: Separate Iterable and Iterator; each __iter__ call creates a fresh iterator so the range can be re-iterated safely Python interview: implement a sorted collection with O(log n) __contains__ using bisect, plus __len__ and __getitem__ for sequence protocol. Topics: python-internals, oop, itertools Companies: google, amazon, meta, bloomberg, microsoft, netflix Level: swe2, swe3, senior bisect-based sorted collection: bisect_left finds insertion point; check element at that index to confirm membership; insort maintains order on add Sorted collection with range query support: irange uses both bisect_left and bisect_right with inclusive flags to implement range queries efficiently Python interview: implement a Vector class with operator overloading for element-wise addition, scalar multiplication, and dot product. Topics: oop, python-internals, typing Companies: google, amazon, meta, microsoft, bloomberg, netflix Level: swe2, swe3, senior Vector with full arithmetic operator set: Return NotImplemented (not raise) to allow Python to try reflected operation; dispatch __mul__ on isinstance check Vector with NumPy-style broadcasting: __radd__ and __rmul__ enable commutative scalar operations; normalize() uses __abs__ and __mul__ Python interview: implement a class with both __enter__/__exit__ and __aenter__/__aexit__ for dual sync/async context manager usage. Topics: context-managers, asyncio, oop Companies: stripe, google, netflix, amazon, bloomberg, meta Level: swe3, senior Dual sync/async context manager: __aenter__ and __aexit__ are async coroutines awaiting IO; both protocols return self and set acquired flag Connection pool with async/sync dual protocol: contextlib.contextmanager and asynccontextmanager produce sync and async context managers from generators without full class protocol Python interview: use Python dataclasses with __post_init__ for validation and explicit __hash__ for hashable value objects. Topics: dataclasses, oop, python-internals Companies: google, amazon, meta, stripe, bloomberg, shopify Level: swe2, swe3, senior Dataclass with validation and explicit __hash__: __post_init__ coerces to float and validates finiteness; __hash__ on (x, y) tuple ensures equal objects hash equally Frozen dataclass for true immutability: frozen=True auto-generates __hash__ and blocks __setattr__; object.__setattr__ required for post-init normalization in frozen classes Python interview: use dataclass field() with default_factory, init=False computed fields, and repr=False to build clean domain models. Topics: dataclasses, oop, python-internals Companies: google, amazon, meta, microsoft, stripe, netflix Level: swe2, swe3, senior field() with default_factory and computed fields: default_factory=list gives each instance its own list; init=False fields must be set in __post_init__; repr=False hides verbose/sensitive fields Dataclass with field metadata and validators: field(metadata=...) stores validation rules; __post_init__ uses fields() to iterate and check each; eliminates per-field if/raise boilerplate Python interview: use typing.NamedTuple to create an immutable, hashable, typed tuple with methods and default field values. Topics: typing, oop, python-internals Companies: google, amazon, meta, microsoft, bloomberg, airbnb Level: swe2, swe3, senior NamedTuple with distance method and defaults: NamedTuple is a true tuple subclass; methods defined normally; defaults on trailing fields; _replace() for updated copies NamedTuple vs dataclass comparison: Side-by-side comparison shows NamedTuple advantages: immutability, hashability, no __dict__; dataclass advantages: mutability, field() metadata Python interview: use TypedDict with total=False and NotRequired to define structured dicts with required and optional keys for mypy type checking. Topics: typing, python-internals, oop Companies: google, stripe, amazon, meta, bloomberg, shopify Level: swe2, swe3, senior TypedDict with required and optional fields: Inheritance combines required base with optional extension; total=False on child makes all child fields optional; runtime is plain dict TypedDict with NotRequired and runtime validation: NotRequired[T] marks optional keys; __required_keys__ attr (Python 3.9+) enables runtime required-key validation Python interview: implement a Generic class using TypeVar and Generic from typing, with a bounded TypeVar for type-safe comparable collections. Topics: typing, oop, python-internals Companies: google, amazon, meta, stripe, bloomberg, microsoft Level: swe2, swe3, senior Generic Stack and bounded SortedList: Generic[T] parameterizes the class; CT bound=Comparable ensures SortedList only accepts types with __lt__; Protocol for structural checking Generic Result[T, E] type: Two-parameter generic Result[T, E] models success or failure explicitly; map() chains transformations without unwrapping Python interview: use typing.Protocol with @runtime_checkable for structural duck typing without explicit inheritance. Topics: typing, oop, python-internals Companies: google, amazon, meta, microsoft, stripe, bloomberg Level: swe2, swe3, senior Protocol with runtime_checkable for duck typing: @runtime_checkable enables isinstance; Protocol checks structural match (method presence); no inheritance required Protocol for comparable and serializable: Serializable protocol defines to_dict/from_dict contract; unrelated User and Product satisfy it structurally; isinstance filters non-conforming objects Python interview: implement functools.partial from scratch, merging pre-filled positional and keyword arguments with call-site arguments. Topics: functools, closures, python-internals Companies: google, amazon, meta, microsoft, bloomberg, airbnb Level: swe2, swe3, senior Class-based partial implementation: __new__ flattens nested partials; call merges stored and call-site args/kwargs; call-site kwargs win on conflict Closure-based functional partial: Closure captures partial args/kwargs; wrapper prepends stored positional args and merges kwargs; exposes .func .args .keywords attributes Python interview: implement functools.reduce with optional initial value, handling empty iterables correctly. Topics: functools, closures, python-internals Companies: google, amazon, meta, microsoft, bloomberg, netflix Level: swe2, swe3, senior reduce with optional initializer: Sentinel _MISSING distinguishes "no initial" from None; iter() consumes lazily; first element seeds accumulator when no initial provided reduce with scan (running accumulation) variant: scan() yields intermediate accumulators (prefix reductions); useful for running totals, prefix products, and cumulative operations Python interview: implement itertools.groupby grouping consecutive equal-key elements, understanding the lazy shared-iterator design. Topics: itertools, generators, python-internals Companies: google, amazon, meta, bloomberg, netflix, airbnb Level: swe2, swe3, senior groupby with materialized groups: Materializes each group as a list; yields iter(group) for protocol compatibility; simpler but uses O(group_size) memory Lazy groupby sharing underlying iterator: True lazy implementation: _GroupIter shares _GroupByState; advancing outer iterator invalidates current group sub-iterator Python interview: implement itertools.chain and chain.from_iterable as lazy generators that concatenate multiple iterables without intermediate lists. Topics: itertools, generators, python-internals Companies: google, amazon, meta, microsoft, bloomberg, shopify Level: swe2, swe3, senior Generator-based chain: __iter__ uses yield from for each iterable; from_iterable returns special instance with generator; both fully lazy Functional chain implementations: yield from is the key primitive; chain_from_iterable enables flat-mapping; recursive flatten handles arbitrary nesting depth Python interview: implement itertools.islice that lazily slices an iterator with start, stop, and step without materializing elements. Topics: itertools, generators, python-internals Companies: google, amazon, meta, microsoft, bloomberg, airbnb Level: swe2, swe3, senior islice with start/stop/step logic: Use slice() to parse args uniformly; skip start elements; yield with inner skip loop for step > 1 islice using enumerate for index tracking: Pre-compute target indices as range(start, stop, step); iterate with enumerate and yield when index matches next target Python interview: implement itertools.product for Cartesian product of iterables using odometer-style index arrays. Topics: itertools, generators, python-internals Companies: google, amazon, meta, microsoft, bloomberg, netflix Level: swe2, swe3, senior Odometer-style index increment: Odometer analogy: increment rightmost index, carry to left when pool exhausted; repeat multiplies pools list Recursive generator approach: Recursive generator builds prefix tuple; each level appends one pool element; base case yields complete tuple Python interview: explain and fix the closure loop variable late binding gotcha using default args, functools.partial, and factory functions. Topics: closures, python-internals, functools Companies: google, amazon, meta, microsoft, bloomberg, airbnb Level: swe2, swe3, senior All three fixes with explanation: Default arg: evaluated at def time, stores current value in function object; partial: stores value in args tuple; factory: new frame binds new local i Deep dive: cell objects and LEGB: Cell objects explain the mechanism; IIFE (lambda x: lambda: x)(i) creates immediate new scope; make_handler is the idiomatic production pattern Python interview: implement an event emitter with on(), emit(), off(), and once() methods for the Observer pattern. Topics: oop, closures, python-internals Companies: amazon, netflix, shopify, stripe, bloomberg, airbnb Level: swe2, swe3, senior Event emitter with once() and error handling: defaultdict(list) stores handlers; copy list before emit to allow safe off() during dispatch; once() wraps handler to self-remove after first call Event emitter with wildcard and priority: Heap stores (negated_priority, counter, handler) tuples; wildcard * catches all events; priority ordering ensures predictable dispatch Python interview: use weakref.ref and WeakValueDictionary to build caches and event emitters that do not prevent garbage collection. Topics: python-internals, oop, closures Companies: google, amazon, meta, bloomberg, netflix, microsoft Level: swe3, senior weakref.ref and WeakValueDictionary cache: ref() returns None after GC; WeakValueDictionary automatically removes entries; finalize runs callback on collection Weak reference in event emitter to avoid leaks: WeakMethod handles bound method references; dead refs pruned during emit; subscribers not kept alive by the emitter Python interview: implement __copy__ and __deepcopy__ for custom classes, handling reference cycles with memo and selective deep copying. Topics: python-internals, oop, descriptors Companies: google, amazon, meta, microsoft, bloomberg, shopify Level: swe2, swe3, senior __copy__ and __deepcopy__ with memo cycle prevention: __copy__ copies __dict__ shallowly; __deepcopy__ registers self in memo before recursing to handle reference cycles; deepcopy recurses into each field Selective deep copy for mixed resource/data objects: Selectively skip deepcopy for shared resources (_pool); deepcopy only per-session mutable state; documents the intent explicitly Python interview: implement __getstate__ and __setstate__ for custom pickling, excluding unpicklable attributes like locks and file handles. Topics: python-internals, oop, file-io Companies: google, amazon, meta, bloomberg, netflix, airbnb Level: swe2, swe3, senior __getstate__/__setstate__ for unpicklable attributes: __getstate__ converts unpicklable objects to picklable equivalents (StringIO -> str, lock excluded); __setstate__ recreates them after deserialization Model checkpointing with reduce for protocol 2: Transient compiled state excluded from state; deserialized model requires re-compile; thread.local recreated fresh; pattern common in ML serving Python interview: extract and decompose email addresses from text using Python regex named capture groups and re.finditer. Topics: regex, python-internals, comprehensions Companies: google, amazon, meta, bloomberg, shopify, linkedin Level: swe2, swe3, senior Named groups with finditer: Named groups with character classes; finditer lazy-matches all non-overlapping emails; groupdict() returns structured dict per match Extended extraction with validation and normalization: NamedTuple Email with normalized() method; pattern limits local/domain length per RFC; deduplication using set of normalized forms Python interview: parse structured log lines into dicts using Python regex named capture groups for timestamp, level, module, and message. Topics: regex, python-internals, file-io Companies: amazon, netflix, google, bloomberg, stripe, shopify Level: swe2, swe3, senior Named group log parser with level filtering: Named groups; match() anchors to line start; timestamp converted to datetime; level filtering by rank dict; generator for streaming large files Multi-format log parser with fallback patterns: Try multiple compiled patterns in order; first match wins; _format field identifies which pattern matched; extensible by appending to PATTERNS list Python interview: validate and parse ISO 8601 datetime strings using Python regex named groups, handling optional time and timezone components. Topics: regex, python-internals, typing Companies: google, stripe, amazon, bloomberg, shopify, meta Level: swe2, swe3, senior Named group ISO 8601 parser: Non-capturing groups (?:...) for optional time section; named groups for all components; separate to_datetime converts dict to datetime with tz Flexible parser with multiple format support: Multiple patterns tried in order; most specific first; _format field records which pattern matched; flexible T-or-space separator Python interview: understand and use exception chaining with raise X from Y, explaining __cause__, __context__, and raise from None. Topics: exceptions, python-internals, oop Companies: google, amazon, meta, bloomberg, stripe, netflix Level: swe2, swe3, senior Explicit vs implicit chaining demonstration: raise X from Y sets __cause__; implicit raise in except sets __context__; raise X from None sets __suppress_context__=True hiding the chain in traceback Domain exception wrapper utility: Context manager centralizes exception translation; suppress_chain=True hides internal details; pass-through for already-domain exceptions Python interview: design a custom exception hierarchy with structured error codes, HTTP status hints, and a code-based factory method. Topics: exceptions, oop, python-internals Companies: stripe, google, amazon, bloomberg, shopify, netflix Level: swe2, swe3, senior Full exception hierarchy with error registry: Hierarchy: AppError -> domain -> specific; DEFAULT_CODE/STATUS class attributes override per class; from_gateway_code classmethod translates external codes; to_dict() for API serialization Error registry with code-based lookup and HTTP mapping: __init_subclass__ auto-registers every subclass with a CODE attribute; from_code() factory enables code-based error construction without import dependencies Implement a doubly linked list with sentinel head and tail nodes for O(1) insert and delete anywhere. Topics: doubly-linked-list, linked-list, hash-table Companies: oracle, palantir, dropbox, adobe, airbnb, goldman-sachs Level: swe2, swe3, senior Sentinel Head/Tail Pattern: Create dummy head and tail nodes permanently connected. Every real insert and delete operates between existing nodes — no None checks needed anywhere. Implement a circular doubly linked list with rotate, insert, delete while maintaining circular invariant. Topics: circular-linked-list, doubly-linked-list, linked-list Companies: oracle, adobe, coinbase, palantir, airbnb, twitter Level: swe2, swe3, senior Circular DLL with Head Pointer: Maintain only a head pointer. Since circular, head.prev is always the tail. Insert appends before head. Rotate advances head k steps. Build a deque using a doubly linked list with O(1) push_front, push_back, pop_front, pop_back. Topics: doubly-linked-list, deque, linked-list, queue, stack Companies: oracle, adobe, dropbox, twitter, kafka, cloudflare Level: swe2, swe3 Sentinel DLL Deque: Use sentinel head and tail. push_front inserts after head; push_back inserts before tail. pop operations remove from those ends. Flatten a multilevel doubly linked list with child pointers in-place using a stack. Topics: doubly-linked-list, linked-list, stack Companies: oracle, adobe, palantir, airbnb, dropbox, coinbase Level: swe2, swe3, senior Iterative Stack: Walk the list. When node has child, push current next, set child as new next, clear child. When next is None and stack non-empty, pop and reattach. Reverse every k nodes of a doubly linked list in-place, maintaining correct prev and next pointers. Topics: doubly-linked-list, linked-list, deque Companies: oracle, palantir, goldman-sachs, adobe, airbnb, coinbase Level: swe3, senior, staff Iterative Group Reversal: Walk groups of k. For each group, swap every node's prev/next, then stitch reversed group back into the surrounding list via group_prev and group_next. Implement a segment tree for O(log n) range sum queries and point updates over an array. Topics: segment-tree, binary-tree, hash-table Companies: palantir, jane-street, goldman-sachs, databricks, oracle, coinbase Level: swe3, senior, staff Recursive Segment Tree: Store tree in a 1-indexed array. Build bottom-up. query and update top-down with range checking. Node at index i has children at 2i and 2i+1. Iterative Segment Tree: Use 2n-size array where leaves start at index n. Updates walk from leaf to root; queries combine segments walking from both ends inward. Build a segment tree for O(log n) range minimum queries with point updates. Topics: segment-tree, binary-tree Companies: palantir, jane-street, databricks, goldman-sachs, oracle, airbnb Level: swe3, senior, staff Recursive RMQ Segment Tree: Same structure as sum segment tree but merge function is min. Identity element for out-of-range is positive infinity. Implement segment tree with lazy propagation for O(log n) range add updates and range sum queries. Topics: segment-tree, binary-tree Companies: jane-street, palantir, goldman-sachs, databricks, oracle, coinbase Level: senior, staff Lazy Propagation with Push Down: Store sum and lazy at each node. Before accessing children, push pending lazy down. Range add multiplies delta by segment length for the sum update. Implement a Binary Indexed Tree for O(log n) prefix sums and use it to count inversions in O(n log n). Topics: fenwick-tree, binary-tree, hash-table Companies: jane-street, palantir, goldman-sachs, databricks, oracle, airbnb Level: swe3, senior, staff BIT + Inversion Count via Coordinate Compression: BIT stores prefix sums. For inversions: process right-to-left, for each element query how many elements already seen are smaller using prefix_sum, then add current element to BIT. Implement a 2D BIT for O(log m log n) point updates and rectangle sum queries. Topics: fenwick-tree, hash-table, binary-tree Companies: jane-street, palantir, goldman-sachs, databricks, coinbase, oracle Level: senior, staff 2D Fenwick Tree: Nested lowbit loops for both dimensions. update propagates through row and column ancestors. rect_sum uses inclusion-exclusion over four corner prefix queries. Implement floor and ceiling on a BST: largest key <= k and smallest key >= k in O(h). Topics: bst, binary-tree Companies: oracle, palantir, jane-street, adobe, airbnb, goldman-sachs Level: swe2, swe3, senior Iterative Floor and Ceiling: For floor: walk BST, track best candidate when node.val<=k, go right to find larger valid values. For ceiling: track best when node.val>=k, go left for smaller valid values. Augment a BST with subtree sizes to support O(h) rank and select order statistics operations. Topics: bst, binary-tree, sorted-list Companies: jane-street, palantir, goldman-sachs, databricks, oracle, airbnb Level: swe3, senior, staff Augmented BST with Size Field: Each node stores subtree size. Insert updates sizes on the way back up. Rank and select use left subtree sizes to determine position without full traversal. Find BST in-order successor and predecessor using parent pointers, O(h) without recursion. Topics: bst, binary-tree, linked-list Companies: oracle, palantir, adobe, twitter, airbnb, dropbox Level: swe2, swe3, senior Parent Pointer Navigation: Successor: go right then leftmost if right exists; else ascend until arriving from a left child. Predecessor mirrors for left child. Implement a self-balancing AVL tree with LL, RR, LR, RL rotations for O(log n) guaranteed operations. Topics: bst, binary-tree Companies: jane-street, palantir, goldman-sachs, oracle, databricks, coinbase Level: senior, staff Full AVL Tree with Four Rotations: Store height at each node. After insertion, recompute heights on the way up. Check balance factor and apply LL/RR/LR/RL rotations. Return new subtree root after each rotation. Serialize a BST to compact pre-order string and reconstruct using BST bounds in O(n). Topics: bst, binary-tree, queue Companies: oracle, palantir, adobe, dropbox, airbnb, twitter Level: swe2, swe3, senior Pre-order Serialize, Bounded Deserialize: Serialize with pre-order DFS (no nulls). Deserialize using a deque of values with min/max bounds — each value is placed only if it falls within bounds, achieving O(n) reconstruction. Implement a trie with wildcard '?' search matching any single character using DFS branching. Topics: trie, hash-table, stack Companies: oracle, adobe, dropbox, twitter, airbnb, cloudflare Level: swe2, swe3, senior Trie with DFS Wildcard Branching: Standard trie with children dict. search uses DFS: for normal char navigate to child; for '?' recursively try all existing children and return True if any branch matches. Build a trie ranking autocomplete suggestions by insertion frequency, returning top-k results for any prefix. Topics: trie, heap, hash-table, sorted-list Companies: oracle, adobe, dropbox, airbnb, twitter, coinbase Level: swe2, swe3, senior Trie with Frequency and DFS Collection: Each node stores children and freq field. suggest navigates to prefix endpoint, DFS collects all (freq,word) pairs. Sort by (-freq,word), return top k. Implement a Patricia (compressed) trie collapsing single-child chains into edge labels for memory efficiency. Topics: trie, hash-table Companies: jane-street, palantir, cloudflare, oracle, coinbase, databricks Level: senior, staff Patricia Trie with Edge Splitting: Edges stored as [label, child_node] keyed by first character. On insert, compute LCP with existing edge; if partial match, split edge into two at divergence point. Build a binary trie for IP routing supporting add_route and longest prefix match lookup in O(32). Topics: trie, hash-table, graph Companies: cloudflare, oracle, coinbase, databricks, palantir, jane-street Level: senior, staff Binary Trie for 32-bit IP Routing: Each node has two children (bit 0, bit 1). add_route converts CIDR to 32 bits and inserts prefix_length bits. lookup traverses all 32 bits tracking the most recent next_hop seen. Build Aho-Corasick automaton with failure links for O(n) simultaneous multi-pattern string matching. Topics: trie, queue, hash-table, graph Companies: jane-street, palantir, cloudflare, databricks, oracle, coinbase Level: senior, staff Aho-Corasick with Failure and Output Links: Build trie, BFS to set failure links pointing to longest proper suffix in trie. Output links chain to all patterns that are proper suffixes of current node path. Text scan follows failure links on mismatch. Compute the running sum for every window of size k using a deque buffer with O(n) time. Topics: deque, queue, hash-table Companies: oracle, adobe, dropbox, kafka, airbnb, twitter Level: swe2, swe3 Deque Buffer with Running Sum: Use a deque to store the k elements of the current window. Maintain a running sum, add each new element, subtract element leaving from left. Find the median of every sliding window of size k using a sorted list in O(n log k) with SortedList. Topics: sorted-list, two-heaps, heap, deque Companies: jane-street, palantir, goldman-sachs, databricks, oracle, coinbase Level: senior, staff Sorted List via bisect: Maintain window as a sorted list using bisect.insort and bisect_left for O(log k) search. Median is middle element for odd k or average of two middles for even. Find minimum jumps in O(n) using greedy sliding window — the monotonic deque DP optimization. Topics: deque, queue, graph Companies: palantir, jane-street, goldman-sachs, databricks, oracle, airbnb Level: senior, staff Greedy O(n): Track current range endpoint and farthest reachable. When exhausting current range, increment jump count and advance to farthest. Equivalent to BFS levels. Implement an LRU cache with per-entry TTL expiration combining capacity eviction and time-based expiry. Topics: lru-cache, doubly-linked-list, hash-table Companies: oracle, dropbox, cloudflare, airbnb, coinbase, twitter Level: swe3, senior, staff OrderedDict LRU with TTL Check: Use OrderedDict for O(1) move-to-end LRU. Store (value,expiry) tuples. On get, check expiry and delete if expired. On put, evict LRU if at capacity. Build a thread-safe LRU cache using threading.Lock to protect concurrent get and put operations. Topics: lru-cache, doubly-linked-list, hash-table Companies: oracle, dropbox, airbnb, kafka, coinbase, cloudflare Level: swe3, senior, staff Mutex-Protected OrderedDict LRU: Wrap all operations in threading.Lock context manager. Track hits/misses under lock. Return hit_rate in stats(). Implement LFU cache with O(1) get and put using frequency buckets backed by OrderedDicts. Topics: lfu-cache, doubly-linked-list, hash-table Companies: jane-street, palantir, oracle, airbnb, coinbase, databricks Level: senior, staff Frequency Buckets with OrderedDicts: key_freq maps key to freq; freq_keys maps freq to OrderedDict. min_freq tracks lowest. On get/put: remove from current freq bucket, add to freq+1 bucket; update min_freq. Extend LFU cache with periodic frequency aging to prevent stale hot-key dominance via frequency halving. Topics: lfu-cache, doubly-linked-list, hash-table Companies: jane-street, palantir, databricks, cloudflare, coinbase, oracle Level: senior, staff LFU with Periodic Frequency Halving: Standard LFU internals plus access_count. Every age_every accesses, call age() which snapshots all frequencies, halves them (min 1), clears freq_keys, rebuilds buckets. Use a sorted list for O(log n) rank and kth-smallest order statistics queries using bisect. Topics: sorted-list, heap, binary-tree, bst Companies: jane-street, palantir, goldman-sachs, databricks, airbnb, coinbase Level: swe3, senior Bisect-Based Sorted List: Python list maintained in sorted order via bisect.insort (O(n) insert due to shift) and bisect_left (O(log n) search). rank is bisect_left; kth_smallest is O(1) indexing. Implement a skip list with random levels for O(log n) expected search, insert, delete — as used in Redis ZSET. Topics: sorted-list, linked-list, hash-table Companies: jane-street, palantir, databricks, oracle, coinbase, goldman-sachs Level: senior, staff Probabilistic Skip List with Forward Pointer Arrays: Nodes have forward pointer arrays per level. Insert: random_level(), maintain update[], splice at each level. Delete: use update[] to remove from all levels. Merge k sorted arrays in O(n log k) using a min-heap — foundation of external sort and database merge-join. Topics: k-way-merge, heap, sorted-list Companies: palantir, jane-street, databricks, oracle, airbnb, goldman-sachs Level: swe2, swe3, senior Min-Heap K-Way Merge: Initialize heap with first element from each non-empty array as (value, array_idx, elem_idx). Extract min, append, push next from same source. Handle empty arrays by skipping. Implement external sort merge phase using a k-way heap, merging sorted runs with O(k) memory. Topics: k-way-merge, heap, sorted-list, queue Companies: databricks, palantir, oracle, jane-street, airbnb, kafka Level: senior, staff Buffered K-Way External Merge Generator: Push first element from each run into heap. On extract, advance that iterator. Wrap in try/except StopIteration. external_sort creates sorted chunks then merges. Find the median of two sorted arrays in O(log(min(m,n))) using binary search on array partitions. Topics: two-heaps, sorted-list, binary-tree Companies: jane-street, palantir, goldman-sachs, databricks, oracle, airbnb Level: senior, staff O(m+n) Merge: Merge both arrays, compute median. O(log min(m,n)) Binary Search: Binary search on partition index of smaller array. For each partition i in nums1, compute j so left halves together have (m+n+1)//2 elements. Check cross-boundary conditions. Implement streaming median with O(log n) addNum and O(1) findMedian using two balanced heaps. Topics: two-heaps, heap, sorted-list Companies: jane-street, palantir, databricks, oracle, airbnb, goldman-sachs Level: swe3, senior Two Heaps — Max-Heap Lower, Min-Heap Upper: Always push to lo (max-heap). If lo top exceeds hi top, move to hi. Size rebalancing: if lo has more than 1 extra, move excess to hi. Sliding window medians using two heaps with lazy deletion, O(n log k) total. Topics: two-heaps, heap, deque Companies: jane-street, palantir, goldman-sachs, databricks, oracle, coinbase Level: senior, staff Two Heaps with Lazy Deletion Counter: Maintain effective sizes lo_size/hi_size. On remove, mark in removed dict, decrement effective size, then rebalance. prune_top skips stale entries. Implement Union-Find with path compression and union by rank for O(alpha(n)) amortized operations. Topics: union-find, graph, hash-table Companies: palantir, oracle, databricks, airbnb, jane-street, coinbase Level: swe2, swe3, senior Path Halving + Union by Rank: find() uses path halving for compression. union() compares ranks; smaller attaches under larger. Equal ranks: increment new root rank. Track component count. Build dynamic connectivity for arbitrary hashable node identifiers using a dictionary-based Union-Find. Topics: union-find, graph, hash-table Companies: palantir, oracle, jane-street, airbnb, databricks, goldman-sachs Level: swe3, senior Dict-Based Union-Find: Use dict for parent and rank. _add() inserts node as its own root. find(), connect(), is_connected() proceed identically to array-based DSU. Implement Kruskal's Minimum Spanning Tree algorithm using Union-Find for O(E log E) time. Topics: union-find, graph, sorted-list Companies: palantir, oracle, databricks, airbnb, jane-street, goldman-sachs Level: swe3, senior Kruskal's Algorithm with Union-Find: Sort edges by weight. For each edge attempt union; if successful (different components) add to MST. Stop when n-1 edges collected. Implement rollbackable Union-Find using union-by-rank with a change stack — no path compression. Topics: union-find, stack, graph Companies: jane-street, palantir, goldman-sachs, databricks, oracle, coinbase Level: staff Union by Rank with Change History Stack: find() walks without compression. union() records state before modifying. checkpoint() returns stack length. rollback(v) reverses all changes since v. Implement a circular queue (ring buffer) with O(1) enqueue and dequeue using modular arithmetic. Topics: queue, circular-linked-list, deque Companies: oracle, kafka, adobe, dropbox, twitter, airbnb Level: swe2, swe3 Array Ring Buffer with Size Counter: Fixed array with head, tail, size. enqueue writes at tail and advances tail mod capacity. dequeue reads from head and advances head mod capacity. Implement a FIFO queue using two stacks with O(1) amortized dequeue using inbox/outbox pattern. Topics: queue, stack, deque Companies: oracle, adobe, dropbox, airbnb, twitter, palantir Level: swe2, swe3 Inbox and Outbox Stacks: enqueue pushes to inbox. dequeue pops from outbox; if outbox empty, pour inbox into outbox first reversing order. Total moves per element: 2, giving O(1) amortized. Learn how to find the shortest path in an unweighted graph using BFS in Python. Includes two solutions with complexity analysis. Topics: graph, bfs, hash-map Companies: amazon, google, meta, microsoft, uber, linkedin Level: swe2, swe3 BFS with distance tracking: Standard BFS - explore level by level, return distance when destination is found. BFS with parent map for path reconstruction: Level-by-level BFS using queue length snapshot to count distance in whole steps. Count connected components in an undirected graph using DFS and Union-Find in Python. Full solutions with complexity analysis. Topics: graph, dfs, union-find Companies: google, meta, amazon, linkedin, microsoft, stripe Level: swe2, swe3 DFS with adjacency list: Build adjacency list, iterate nodes, DFS from each unvisited node, count launches. Union-Find (Disjoint Set Union): Union-Find with path compression and union by rank. Start with n components, decrement on each successful union. Implement topological sort using Kahn's BFS algorithm in Python. Includes cycle detection and full complexity analysis. Topics: graph, bfs, topological-sort Companies: amazon, google, microsoft, uber, meta, bloomberg Level: swe2, swe3, senior Kahn's BFS with in-degree array: Build in-degree map, BFS from zero-in-degree nodes, detect cycles via result length check. Kahn's with explicit cycle detection message: Same BFS approach with explicit cycle detection logging before returning empty list. Implement topological sort using DFS postorder in Python. Includes both recursive and iterative solutions with complexity analysis. Topics: graph, dfs, topological-sort Companies: google, amazon, meta, microsoft, airbnb, stripe Level: swe2, swe3, senior Recursive DFS postorder with stack: DFS postorder: recurse into all unvisited neighbors before appending current node. Reverse for topological order. Iterative DFS postorder (avoids recursion limit): Iterative DFS with a "processed" flag to simulate postorder without hitting Python's recursion limit on large graphs. Detect cycles in a directed graph using the three-color DFS white/gray/black technique in Python with full solutions. Topics: graph, dfs Companies: google, amazon, microsoft, meta, uber, oracle Level: swe2, swe3, senior Three-color DFS (recursive): Three-color DFS marks nodes white/gray/black. Gray neighbor during traversal signals a back edge (cycle). Iterative DFS with explicit call stack simulation: Iterative simulation of recursive DFS using an explicit stack of (node, neighbor_iterator) pairs to avoid Python recursion limits. Detect cycles in an undirected graph using Union-Find with path compression in Python. Includes DFS alternative. Topics: graph, union-find Companies: amazon, google, meta, bloomberg, microsoft, linkedin Level: swe2, swe3 Union-Find with path compression and union by rank: Union-Find with path compression and union by rank. Cycle detected when two nodes already share a root. DFS-based cycle detection for comparison: DFS tracking parent to distinguish back edges from the edge we came from. Included as alternative to Union-Find. Implement Dijkstra's shortest path algorithm with a min-heap in Python. Two solutions with full complexity analysis. Topics: graph, dijkstra, heap Companies: google, uber, amazon, microsoft, meta, airbnb Level: swe3, senior Dijkstra with min-heap and lazy deletion: Min-heap with lazy deletion: push updated distances and skip stale entries when popped. Greedy relaxation of edges. Dijkstra with visited set (early termination): Same heap approach but uses a finalized set for early node skip instead of distance comparison - slightly cleaner logic. Implement Bellman-Ford algorithm in Python to handle negative edge weights and detect negative cycles. Full solutions with analysis. Topics: graph, dynamic-programming Companies: google, amazon, meta, bloomberg, stripe, microsoft Level: swe3, senior Classic Bellman-Ford with negative cycle detection: Relax all edges V-1 times using dynamic programming. V-th pass detects negative cycles. Simple and correct for all cases. Bellman-Ford with early termination optimization: Same algorithm with early exit if no edge was relaxed in a full iteration - avoids unnecessary passes on simple graphs. Implement Floyd-Warshall algorithm in Python for all-pairs shortest paths. Includes negative cycle detection and complexity analysis. Topics: graph, dynamic-programming, matrix Companies: google, amazon, bloomberg, microsoft, oracle, meta Level: swe3, senior Classic Floyd-Warshall DP: Triple nested loop DP. For each intermediate node k, relax all (i,j) pairs considering k as a waypoint. Floyd-Warshall with negative cycle detection: Same DP with post-processing check: if dist[i][i] < 0 after the algorithm, node i participates in a negative cycle. Implement Prim's Minimum Spanning Tree algorithm in Python using a min-heap. Two approaches: lazy and eager Prim's. Topics: graph, heap, dijkstra Companies: google, amazon, microsoft, airbnb, oracle, uber Level: swe3, senior Prim's with min-heap (lazy Prim's): Lazy Prim's: push all candidate edges to heap, skip already-visited nodes when popped. Simple and effective for sparse graphs. Eager Prim's with key-decrease using distance array: Tracks minimum known edge cost per node. Only pushes to heap when a better edge is found - reduces heap size significantly. Solve the Number of Islands problem in Python using DFS and BFS. Classic grid graph problem with full solutions and complexity analysis. Topics: graph, dfs, bfs, matrix Companies: amazon, google, meta, microsoft, bloomberg, airbnb Level: swe2, swe3 DFS with in-place marking: DFS from each unvisited land cell, mark all reachable land as visited in-place. Count DFS launches. BFS with queue: BFS from each unvisited land cell, mark visited immediately before enqueuing. Avoids deep recursion of DFS approach. Solve the Word Ladder problem using BFS in Python. Includes unidirectional and bidirectional BFS with full complexity analysis. Topics: graph, bfs, hash-map Companies: amazon, google, meta, microsoft, linkedin, uber Level: swe3, senior BFS with character substitution: BFS from beginWord, try all single-character mutations at each position. Return path length when endWord is found. Bidirectional BFS for large inputs: Bidirectional BFS simultaneously expands from both ends. Always expand the smaller frontier to minimize work. Drastically faster in practice. Solve the Alien Dictionary problem using topological sort in Python. BFS and DFS approaches with cycle detection. Topics: graph, topological-sort, bfs, dfs Companies: google, meta, amazon, airbnb, bloomberg, stripe Level: swe3, senior BFS topological sort (Kahn's) on character graph: Extract edges from adjacent word comparisons, then Kahn's BFS topological sort on character graph. Detect cycles via length check. DFS topological sort on character graph: Same graph construction, but uses three-color DFS postorder for topological sort and cycle detection. Find valid course ordering using topological sort in Python. BFS and DFS solutions for Course Schedule II with cycle detection. Topics: graph, topological-sort, bfs, dfs Companies: amazon, google, meta, microsoft, uber, bloomberg Level: swe2, swe3 Kahn's BFS topological sort: Build graph with edge from prereq to course. Kahn's BFS from zero-in-degree nodes gives valid ordering or detects cycle. DFS postorder topological sort: DFS with three-color state tracking. Postorder collection reversed gives topological order. Cycle makes output empty. Solve Network Delay Time in Python using Dijkstra's algorithm. Find maximum shortest path from source node with full analysis. Topics: graph, dijkstra, heap Companies: amazon, google, meta, uber, microsoft, oracle Level: swe2, swe3, senior Dijkstra's from source k: Dijkstra from k to all nodes. Answer is max shortest path; -1 if any node unreachable. Bellman-Ford alternative (handles edge case validation): Bellman-Ford as an alternative. Simpler to implement for small n; useful when asked to handle negative edges in follow-up questions. Find cheapest flights within K stops in Python using Bellman-Ford and Dijkstra. Full solutions with complexity analysis. Topics: graph, dynamic-programming, dijkstra, bfs Companies: amazon, google, meta, airbnb, uber, bloomberg Level: swe3, senior Modified Bellman-Ford (K+1 relaxations): Modified Bellman-Ford: relax all edges exactly K+1 times. Use a snapshot of distances each round to prevent within-round propagation. Dijkstra with stops constraint: Modified Dijkstra with stops as extra state. Prune states where stops exceed k or a better stop-count exists for same node. Solve Pacific Atlantic Water Flow using reverse BFS and DFS in Python. Full grid graph solution with complexity analysis. Topics: graph, bfs, dfs, matrix Companies: google, amazon, meta, microsoft, airbnb, linkedin Level: swe3, senior BFS from both ocean edges: Reverse BFS from ocean borders, allow uphill flow. Intersection of Pacific-reachable and Atlantic-reachable cells is the answer. DFS from both ocean edges: DFS from edge cells for each ocean. Uphill traversal (reversed flow) marks cells that can reach each ocean. Intersection is the answer. Solve Walls and Gates using multi-source BFS in Python. Fill rooms with minimum distance to nearest gate efficiently. Topics: graph, bfs, matrix Companies: google, meta, amazon, microsoft, bloomberg, linkedin Level: swe2, swe3 Multi-source BFS from all gates: Multi-source BFS: enqueue all gates at level 0 simultaneously. BFS naturally assigns minimum distances without revisiting. BFS with explicit distance tracking (cleaner for explanation): Same multi-source BFS with explicit distance in queue tuple - slightly more readable and easier to adapt for tracking paths. Solve Rotting Oranges using multi-source BFS in Python. Find minimum minutes for rot to spread with full complexity analysis. Topics: graph, bfs, matrix Companies: amazon, google, meta, microsoft, uber, stripe Level: swe2, swe3 Multi-source BFS with fresh orange counter: Multi-source BFS from all rotten oranges. Track fresh count and max time reached. Remaining fresh means impossible. Level-by-level BFS (minute tracking): Level-by-level BFS using queue size snapshot each minute. Clean separation between time steps, easier to reason about minute counting. Clone a graph using DFS with hash map in Python. Handles cycles using memoization. Includes BFS alternative. Topics: graph, dfs, bfs, hash-map Companies: google, meta, amazon, microsoft, linkedin, uber Level: swe2, swe3 DFS with hash map (recursive): DFS with memoization map. Create clone before recursing into neighbors to handle cycles. Return existing clone if already visited. BFS with hash map (iterative): BFS with map: create clone immediately when first encountered. Process neighbors level by level, linking clones as we go. Avoids recursion limit. Learn how to merge accounts with shared emails using Union-Find and DFS in Python. Detailed solutions with time and space complexity analysis. Topics: union-find, graph, hash-map Companies: google, amazon, meta, microsoft, linkedin, airbnb Level: swe2, swe3, senior Union-Find: Assign each email a unique ID. For each account, union all emails together. Then group emails by their root representative and reconstruct merged accounts. DFS / BFS Graph: Build an adjacency list where emails in the same account are connected. Then run DFS from each unvisited email to collect all emails in the same connected component. Find the redundant edge in an undirected graph using Union-Find and DFS cycle detection. Python solutions with complexity analysis. Topics: union-find, graph Companies: amazon, google, bloomberg, microsoft, uber, meta Level: swe2, swe3, senior Union-Find with Path Compression: Use Union-Find. For each edge, if both nodes share the same root, they are already connected - this edge is redundant. Otherwise, union them. DFS Cycle Detection: Build adjacency list incrementally. Before adding each edge, run DFS to check if a path already exists between the two endpoints. If yes, the current edge is redundant. Solve the longest consecutive sequence problem in O(n) time using a hash set. Two Python approaches with detailed complexity analysis. Topics: array, hash-map Companies: google, amazon, meta, microsoft, uber, linkedin Level: swe2, swe3, senior Hash Set O(n): Add all numbers to a set. For each number that is a sequence start (no num-1 in set), count consecutive numbers forward. Track the maximum. Hash Map with Sequence Lengths: Use a dict to store the length of consecutive sequence each number belongs to. When inserting a number, check left and right neighbors and merge sequences. Find the maximum area island in a binary grid using DFS and BFS in Python. Complete solutions with time and space complexity. Topics: graph, array Companies: amazon, google, meta, airbnb, uber, bloomberg Level: swe2, swe3, senior DFS with In-place Marking: Iterate over every cell. When a land cell is found, run DFS to count the island area and mark visited cells as 0. Track the maximum area seen. BFS Iterative: Use a queue to explore islands iteratively. For each land cell, add it to a queue and expand in four directions, counting cells until the queue is empty. Solve the swim in rising water problem using Dijkstra min-heap and binary search with BFS. Python solutions with full complexity analysis. Topics: graph, heap, greedy Companies: google, amazon, meta, stripe, microsoft, uber Level: swe3, senior Min-Heap (Dijkstra): Use a min-heap where each entry is (max_elevation_seen, row, col). Greedily pick the path that minimizes the maximum elevation encountered. This is Dijkstra with a modified cost function. Binary Search + BFS: Binary search on the answer t. For each t, run BFS to check if there is a valid path from (0,0) to (n-1,n-1) using only cells with elevation <= t. Solve coin change with minimum coins using bottom-up dynamic programming and top-down memoization in Python. Interview-ready solutions. Topics: dynamic-programming, memoization Companies: amazon, google, meta, microsoft, airbnb, stripe Level: swe2, swe3, senior Bottom-up DP: Build a dp array where dp[i] is the min coins for amount i. Initialize with infinity, set dp[0]=0, then fill from 1 to amount using all coin denominations. Top-down Memoization: Recursively compute minimum coins for each amount, caching results to avoid recomputation. For each amount, try subtracting every coin and recurse. Count the number of coin combinations that make up an amount using dynamic programming in Python. Two DP approaches explained. Topics: dynamic-programming Companies: amazon, google, bloomberg, meta, microsoft, oracle Level: swe2, swe3, senior 1D DP - Combinations Count: Use a 1D dp array. Outer loop over coins, inner loop over amounts. This ordering ensures each coin is processed once per amount, counting combinations not permutations. 2D DP - Explicit States: Use a 2D dp table where dp[i][j] = number of ways to make amount j using first i coin types. This makes the state transitions more explicit and easier to reason about. Solve the climbing stairs problem using Fibonacci dynamic programming in Python. Iterative and memoization approaches with O(1) space solution. Topics: dynamic-programming, memoization Companies: amazon, google, meta, microsoft, bloomberg, oracle Level: swe2, swe3 Iterative Fibonacci O(1) Space: Track only the last two values. At each step, the new value is the sum of the previous two. This reduces space from O(n) to O(1). Top-down Memoization: Recursively compute climbStairs(n) = climbStairs(n-1) + climbStairs(n-2) with memoization to avoid exponential recomputation. Maximize robbery amount without robbing adjacent houses using dynamic programming. O(1) space Python solution with detailed explanation. Topics: dynamic-programming Companies: amazon, google, meta, microsoft, airbnb, linkedin Level: swe2, swe3 O(1) Space DP: Track only two variables: the best result excluding the previous house and the best result including it. Update in a single pass. Bottom-up DP Array: Build a dp array where dp[i] is the max rob amount up to house i. Fill forward using the recurrence dp[i] = max(dp[i-1], dp[i-2] + nums[i]). Solve the circular house robber problem by splitting into two linear subproblems. Python DP solution with O(1) space. Topics: dynamic-programming Companies: amazon, google, meta, microsoft, bloomberg, uber Level: swe2, swe3, senior Two-pass Linear DP: Run the standard House Robber DP on two subarrays: nums[:-1] and nums[1:]. The answer is max of both results. Handle n=1 as an edge case. Explicit DP with Two Arrays: Compute dp1 for range [0, n-2] and dp2 for range [1, n-1] using full DP arrays for clarity. The explicit arrays make the logic easier to trace and debug. Solve house robber on a binary tree using tree DP with pair return values. Efficient O(n) Python solution with detailed explanation. Topics: dynamic-programming, graph Companies: amazon, google, meta, microsoft, uber, stripe Level: swe3, senior Tree DP with Pair Return: Post-order DFS returning (rob_node, skip_node) for each subtree. Compute the max at each level using children results. No memoization needed. Memoized DFS: Two separate recursive functions: one for robbing a node, one for skipping. Cache results with a dict to avoid recomputing the same subtree twice. Count unique paths in a grid using dynamic programming and combinatorics in Python. Two solutions with O(1) and O(n) space. Topics: dynamic-programming Companies: amazon, google, microsoft, meta, bloomberg, oracle Level: swe2, swe3 1D DP O(n) Space: Use a single row of length n. For each row, update each cell by adding the value from the left (same row). The top-row equivalent is already in the array. Math Combinatorics: Total moves = m+n-2. Choose m-1 of them to be downward moves. Answer is C(m+n-2, m-1) using math.comb for clean O(1) space solution. Find the minimum path sum in a grid using dynamic programming in Python. In-place and 1D DP solutions with complexity analysis. Topics: dynamic-programming Companies: amazon, google, meta, microsoft, airbnb, stripe Level: swe2, swe3 In-place DP: Modify the grid in place. Fill first row and first column as cumulative sums. For remaining cells, add the minimum of the cell above and the cell to the left. 1D DP Array: Use a 1D dp array of size n. Process row by row, updating dp[j] to represent the minimum path sum to reach current cell (i, j). Compute the minimum edit distance between two strings using dynamic programming in Python. 2D and space-optimized 1D DP solutions. Topics: dynamic-programming Companies: google, amazon, meta, microsoft, linkedin, airbnb Level: swe3, senior Bottom-up 2D DP: Build a (m+1) x (n+1) DP table. Row 0 and column 0 represent empty string conversions. Fill using the Levenshtein recurrence. Space-optimized 1D DP: Use two 1D arrays (previous row and current row) instead of the full 2D table, reducing space from O(m*n) to O(n). Find the longest common subsequence of two strings using dynamic programming in Python. 2D DP and space-optimized O(n) solutions. Topics: dynamic-programming Companies: google, amazon, meta, microsoft, linkedin, bloomberg Level: swe2, swe3, senior Bottom-up 2D DP: Build a (m+1) x (n+1) table. For matching characters extend the diagonal, otherwise take max of skipping one character from either string. Space-optimized 1D DP: Use two rows only (prev and curr) to reduce space. Track the diagonal value separately before overwriting. Solve the longest increasing subsequence problem in O(n log n) with patience sorting and binary search in Python. Topics: dynamic-programming, greedy Companies: google, amazon, meta, microsoft, bloomberg, stripe Level: swe2, swe3, senior O(n log n) Patience Sorting: Maintain a tails array. For each number, binary search for the leftmost position in tails that is >= num. Replace that position or extend tails. The length of tails is the LIS length. O(n^2) DP: For each index i, compute dp[i] = max of dp[j]+1 for all j < i where nums[j] < nums[i]. Track the global maximum. Find the longest palindromic subsequence using interval DP and LCS techniques in Python. Two O(n^2) solutions explained. Topics: dynamic-programming Companies: amazon, google, meta, microsoft, bloomberg, oracle Level: swe2, swe3, senior Interval DP: dp[i][j] is the LPS length in s[i..j]. If s[i]==s[j], extend from dp[i+1][j-1]+2. Otherwise take max of dp[i+1][j] and dp[i][j-1]. LCS with Reversed String: The longest palindromic subsequence of s equals the LCS of s and its reverse. Reuse the LCS algorithm directly. Count all palindromic substrings using expand-around-center and DP table in Python. O(n^2) solutions with O(1) space option. Topics: dynamic-programming, array Companies: amazon, google, meta, microsoft, airbnb, stripe Level: swe2, swe3 Expand Around Center: For each character and each pair of adjacent characters, expand outward while characters match. Each valid expansion contributes one palindromic substring. DP Table: Build a boolean dp[i][j] = True if s[i..j] is a palindrome. Fill diagonally by substring length. Count all True entries. Solve the word break problem using bottom-up DP and memoized DFS in Python. Complete solutions with complexity analysis. Topics: dynamic-programming, memoization, hash-map Companies: amazon, google, meta, microsoft, bloomberg, linkedin Level: swe2, swe3, senior Bottom-up DP: Use a boolean dp array of size n+1. dp[i] indicates if s[:i] can be broken. For each i, iterate over all j < i and check dp[j] and s[j:i] in word set. Top-down Memoization (DFS): Recursively check if s[start:] can be segmented. Memoize results for each start index. Try all dictionary words as prefixes at the current position. Find all valid word break sentences using backtracking and memoization in Python. Two complete solutions for this hard DP problem. Topics: dynamic-programming, memoization Companies: google, amazon, meta, microsoft, uber, airbnb Level: swe3, senior Backtracking with Memoization: DFS from each index, trying all words as prefixes. Cache results (list of valid sentence suffixes) per start index. Combine current word with memoized suffixes. Iterative DP + Reconstruction: First build dp[i] = list of words that end at position i and are valid. Then reconstruct all paths from the end back to the start using these dp lists. Solve the interleaving string problem using 2D dynamic programming. Learn the dp[i][j] transition and space-optimized 1D DP approach with Python examples. Topics: dynamic-programming, string Companies: google, amazon, meta, microsoft, bloomberg, adobe Level: senior, staff 2D DP Table: Build a 2D DP table where dp[i][j] indicates whether s3[:i+j] is a valid interleaving of s1[:i] and s2[:j]. Fill row by row using transitions from the top and left cells. Space-Optimized 1D DP: Compress the 2D DP table to a single row by iterating row by row and updating dp[j] in-place, reducing space from O(m*n) to O(n). Count the number of ways to decode a digit string using dynamic programming. Covers bottom-up DP and space-optimized two-variable approach in Python. Topics: dynamic-programming, string Companies: amazon, meta, microsoft, google, bloomberg, stripe Level: swe3, senior Bottom-Up DP: Use a DP array where dp[i] counts decodings for the first i characters. At each step consider single-digit and two-digit decodings, guarding against zeros. Space-Optimized Two Variables: Since each dp[i] depends only on dp[i-1] and dp[i-2], maintain two rolling variables instead of the full array, achieving constant space. Count distinct subsequences of s equal to t using 2D and space-optimized 1D dynamic programming. Detailed Python solutions with complexity analysis. Topics: dynamic-programming, string Companies: google, amazon, meta, apple, goldman-sachs, bloomberg Level: senior, staff 2D DP: Build a 2D DP table. For each cell, the count is the number of ways skipping the current character in s plus, when characters match, the ways using it. 1D Space-Optimized DP: Compress the DP table to one row. Iterate j from right to left to prevent using updated values from the current row, mimicking the prev-row semantics. Implement regex matching with . and * using 2D DP and memoization. Google interview classic with full Python solutions and complexity analysis. Topics: dynamic-programming, string Companies: google, meta, amazon, microsoft, apple, stripe Level: senior, staff 2D Bottom-Up DP: Build a 2D DP table handling three cases: literal match or dot, star with zero occurrences, and star with one-or-more occurrences. Initialize first row for star-patterns matching empty string. Recursive Memoization: Use top-down recursion with memoization on indices (i, j). At each step, handle the star lookahead case first, then plain character or dot match. Solve wildcard pattern matching with ? and * using 2D DP or greedy two-pointer. Full Python solutions with time and space complexity breakdown. Topics: dynamic-programming, string Companies: amazon, google, meta, microsoft, bloomberg, adobe Level: senior, staff 2D DP: A 2D DP where * transitions come from consuming one char in s (dp[i-1][j]) or matching nothing (dp[i][j-1]). Initialize first row for leading stars. Two-Pointer Greedy: Greedy two-pointer: advance both pointers on match or question-mark. On *, save position and try matching zero characters first, backtracking to match one more each time matching fails. Maximize coins from bursting balloons using interval dynamic programming. Learn the "last burst" insight with bottom-up and top-down memoization in Python. Topics: dynamic-programming, array Companies: google, meta, amazon, apple, goldman-sachs, stripe Level: staff Interval DP (Bottom-Up): Enumerate all intervals by increasing length. For each interval [left, right], try every balloon k as the last to burst, accumulating coins from sub-intervals. Top-Down Memoization: Recursive interval DP with memoization. For each open interval (left, right), enumerate the last balloon k to burst, caching results with lru_cache. Solve Stone Game I with the O(1) math insight and the general interval DP approach. Full Python solutions with explanations for coding interviews. Topics: dynamic-programming, array Companies: amazon, meta, google, bloomberg, microsoft, goldman-sachs Level: swe3, senior Math Observation O(1): With an even number of piles and odd total, Alice can always guarantee she picks the larger half (all odd or all even indexed piles). She always wins. Interval DP General Solution: Build interval DP where dp[i][j] stores the score advantage for the current player. At each step, pick whichever end maximizes advantage minus the opponent's optimal play. Partition array into two equal-sum subsets using 0/1 knapsack DP and Python bitset trick. Full solutions with complexity analysis for coding interviews. Topics: dynamic-programming, array Companies: amazon, google, meta, microsoft, apple, netflix Level: swe3, senior 0/1 Knapsack DP: Standard 0/1 knapsack: iterate each number, update dp array from right to left to avoid reusing the same number. Check dp[target] at the end. Bitset (Python int as bitmask): Use a Python integer as a bitset where bit s is set if sum s is achievable. For each number, shift the bitset left by num and OR it in. Check if bit target is set. Count ways to assign +/- to reach a target sum using subset sum DP reduction and DFS memoization. Python solutions with math derivation explained. Topics: dynamic-programming, array Companies: amazon, google, meta, bloomberg, stripe, microsoft Level: swe3, senior Subset Sum DP Reduction: Reduce to counting subsets summing to (total + target) // 2 using 0/1 knapsack counting DP. Each dp[s] holds the number of ways to achieve sum s. DFS with Memoization: Recursive DFS tries both + and - at each index. Memoize on (index, remaining) to avoid recomputation. Straightforward but uses more memory than the DP reduction. Simulate stone smashing using a max-heap in Python. Learn negation trick for max-heap with heapq, with time and space complexity analysis. Topics: heap, greedy, array Companies: amazon, google, bloomberg, microsoft, meta, apple Level: swe3 Max-Heap Simulation: Negate all values to use Python's min-heap as a max-heap. Repeatedly pop two largest values, push the difference back if non-zero, until one or zero stones remain. Sorted List Simulation: Maintain a sorted list, popping the two largest and binary-searching to re-insert the difference. Simpler to understand but O(n^2) due to list insertions. Find minimum CPU intervals for task scheduling with cooldown using the math formula and max-heap simulation. Python solutions with full complexity analysis. Topics: greedy, heap, array Companies: amazon, google, meta, microsoft, bloomberg, netflix Level: swe3, senior Math Formula O(1): The most frequent task creates frames of size n+1. Total frames = max_freq - 1, each with n+1 slots, plus the final group of max-freq tasks. Take max with len(tasks) for the dense case. Greedy Max-Heap Simulation: Max-heap simulation: each unit of time, pop the highest-frequency task, decrement its count, and put it in a cooldown queue. When cooldown expires, push back to heap. Count idle time implicitly. Determine if you can reach the last index using greedy forward and backward scan. O(n) Python solutions with clear explanation for coding interviews. Topics: greedy, array Companies: amazon, google, meta, microsoft, bloomberg, apple Level: swe3, senior Greedy Forward Scan: Single pass greedy: maintain the farthest reachable index. If the current index exceeds it, the last index is unreachable. Otherwise update the reach and continue. Greedy Backward Scan: Scan from right to left, updating the goal to the leftmost index that can reach the current goal. If goal reaches index 0, the start can reach the end. Find minimum jumps to reach the last index using greedy BFS-level approach and DP. O(n) Python solutions explained step by step for coding interviews. Topics: greedy, array Companies: amazon, google, meta, microsoft, bloomberg, stripe Level: swe3, senior Greedy BFS Level Approach: Scan left to right maintaining farthest reachable. When reaching the end of the current jump range, increment jump count and extend the range to farthest. Stop early once last index is reachable. DP Approach (for reference): For each index, update the minimum jumps needed to reach all positions within its range. Less optimal than greedy but easier to reason about correctness initially. Find the valid starting gas station for a circular route using O(n) greedy and prefix sum approaches. Python solutions with detailed explanation. Topics: greedy, array Companies: amazon, google, meta, microsoft, bloomberg, goldman-sachs Level: swe3, senior Greedy O(n): Check feasibility with total gas vs cost. Then scan: accumulate net gas, and whenever tank drops negative reset start to next station. The remaining candidate is the answer. Two-Pass Verification: Compute prefix sums of net gas. The optimal start is just after the position of the minimum prefix sum - this ensures the tank never goes negative when starting there. Solve the candy distribution problem using two-pass greedy and one-pass slope tracking. O(n) Python solutions with explanation for coding interviews. Topics: greedy, array Companies: amazon, google, meta, apple, bloomberg, microsoft Level: senior, staff Two-Pass Greedy: Left pass ensures each child with higher rating than left neighbor gets more candy. Right pass ensures the same for right neighbors. Taking max satisfies both constraints simultaneously. One-Pass with Slope Tracking: Track ascending and descending slopes. When descending, if the valley is longer than the peak, the peak child needs an extra candy. Complex but O(1) space. Determine if one person can attend all meetings by checking for overlapping intervals after sorting. Easy Python solutions for coding interviews. Topics: greedy, array Companies: amazon, google, meta, microsoft, bloomberg, stripe Level: swe3 Sort and Check: Sort by start time, then verify each meeting starts at or after the previous meeting ends. O(n log n) for sorting, O(n) for the linear scan. Using all() with zip: Pythonic one-liner using zip to pair consecutive sorted intervals and all() to verify no overlap. Same complexity as the explicit loop but more concise. Find the minimum number of conference rooms using heap and sweep line approaches. O(n log n) Python solutions with step-by-step explanation. Topics: greedy, heap, array Companies: amazon, google, meta, microsoft, bloomberg, apple Level: swe3, senior Min-Heap of End Times: Sort by start time. Maintain a min-heap of end times. For each meeting, if the earliest-ending room is free (end <= start), reuse it; otherwise add a new room. Sweep Line Two-Pointer: Sort starts and ends separately. Sweep through start events; if an end event precedes a start, a room is freed. Track peak concurrent rooms. Find minimum intervals to remove for non-overlapping set using greedy sort-by-end and DP approaches. O(n log n) Python solutions explained. Topics: greedy, array Companies: google, amazon, meta, microsoft, bloomberg, goldman-sachs Level: swe3, senior Greedy Sort by End Time: Sort by end time (activity selection). Greedily include intervals whose start >= last kept end. The number of removals = total - kept (maximum non-overlapping set). DP Approach (LIS-style): Patience sorting variant: maintain a list of smallest end times for chains of length k. Binary search to extend the longest non-overlapping chain. Analogous to LIS with binary search. Merge overlapping intervals using sort and linear scan. Two clean Python solutions with O(n log n) complexity, ideal for coding interviews. Topics: greedy, array Companies: amazon, google, meta, microsoft, bloomberg, stripe Level: swe3, senior Sort and Linear Merge: Sort by start time. Walk through intervals: if the current interval starts before the last merged interval ends, merge by extending the end. Otherwise start a new merged interval. In-place Merge (stack-style): Use a stack to track merged intervals. For each sorted interval, either extend the top of the stack (overlap) or push a new interval. Clean and interview-friendly framing. Insert a new interval into a sorted non-overlapping list and merge as needed. Three-phase linear scan and binary search Python solutions with complexity analysis. Topics: greedy, array Companies: google, amazon, meta, microsoft, bloomberg, apple Level: swe3, senior Three-Phase Linear Scan: Three clean phases: skip non-overlapping before, merge all overlapping by expanding newInterval bounds, then append non-overlapping after. No sorting needed since input is pre-sorted. Binary Search + Merge: Use binary search on the sorted ends and starts arrays to find the overlap range in O(log n). Merge the overlapping block into one interval. List slicing still costs O(n) overall. Learn to implement Lomuto and Hoare quicksort partition schemes in Python. Covers in-place partitioning, pivot selection, and recursion for coding interviews. Topics: sorting, divide-and-conquer, array Companies: google, amazon, microsoft, meta, bloomberg, adobe Level: swe2, swe3 Lomuto Partition Scheme: Lomuto scheme picks last element as pivot, maintains a boundary index i for elements smaller than pivot, and scans left to right placing qualifying elements before the boundary. Hoare Partition Scheme: Hoare scheme uses two converging pointers from both ends and swaps elements that are on the wrong side of the pivot. It performs roughly 3x fewer swaps than Lomuto on average. Count array inversions in O(n log n) using merge sort in Python. Essential divide and conquer technique for coding interviews at Google, Amazon, and Goldman Sachs. Topics: sorting, divide-and-conquer, array Companies: google, amazon, microsoft, goldman-sachs, stripe, bloomberg Level: swe3, senior Merge Sort with Inversion Count: Augment merge sort to count inversions during the merge step. When an element from the right subarray is placed before remaining left elements, those left elements all form inversions with it. In-place Merge Sort with Count: Index-based merge sort that operates on a shared temp array to avoid repeated list slicing, reducing constant factor overhead while maintaining the same inversion counting logic. Implement counting sort in Python for bounded integer arrays. Learn the frequency table approach and stable variant used in radix sort for coding interviews. Topics: sorting, array, hash-map Companies: amazon, microsoft, adobe, bloomberg, google, meta Level: swe2, swe3 Standard Counting Sort: Build a frequency table indexed by value offset from minimum, then reconstruct the sorted output by iterating the count table and appending each value the corresponding number of times. Stable Counting Sort (Cumulative Prefix): Stable variant uses a cumulative prefix sum on the count array to determine exact output positions, then fills the output array in reverse to preserve relative order of equal elements - critical when sorting compound objects by a key. Implement LSD radix sort in Python for large integers. Learn digit-by-digit stable sorting with counting sort subroutine for coding interviews. Topics: sorting, array Companies: google, amazon, microsoft, stripe, bloomberg, netflix Level: swe2, swe3 LSD Radix Sort with Counting Sort Subroutine: For each digit position (ones, tens, hundreds, ...), apply a stable counting sort keyed on that digit. LSD processes least significant digit first, and stability ensures earlier-pass orderings are preserved in later passes. Radix Sort with Base 256 for Speed: Use base 256 (byte-level) instead of base 10 to reduce the number of passes from ~10 to exactly 4 for 32-bit integers, significantly improving the constant factor through better cache utilization. Implement bucket sort in Python for uniformly distributed floats. Learn O(n) average case sorting for coding interviews at top tech companies. Topics: sorting, array, hash-map Companies: amazon, google, meta, microsoft, apple, stripe Level: swe2, swe3 Standard Bucket Sort: Map each element to a bucket using the formula int(x * n), sort each bucket independently, then concatenate. The average O(1) elements per bucket with uniform input makes inner sorts negligible. Generalized Bucket Sort for Arbitrary Range: Generalize by computing min and max to normalize any range into [0, num_buckets). The bucket index formula (num - min) / bucket_range scales elements into the bucket space, making this work for arbitrary floating-point ranges. Find the kth largest element using quickselect O(n) and min-heap O(n log k) in Python. Classic coding interview question at Google, Amazon, and Meta. Topics: sorting, divide-and-conquer, array, heap Companies: google, amazon, meta, microsoft, apple, netflix Level: swe2, swe3 Quickselect (Average O(n)): Quickselect uses Lomuto partition scheme with random pivot. After each partition, we know the exact sorted position of the pivot. If it equals our target index we are done; otherwise we recurse only into the relevant half. Min-Heap of Size K (Guaranteed O(n log k)): Maintain a min-heap of size k. For each element, push it and pop the minimum if the heap exceeds size k. The heap root always holds the kth largest seen so far. Preferred when k is small relative to n or when the array is a stream. Solve Sort Colors using Dutch National Flag three-way partition in Python. Single-pass O(n) O(1) space solution for coding interviews. Topics: sorting, two-pointers, array Companies: amazon, google, meta, microsoft, bloomberg, apple Level: swe2, swe3 Dutch National Flag - One Pass Three Pointers: Dutch National Flag algorithm maintains three regions: [0..low-1] contains all 0s, [low..mid-1] contains all 1s, [high+1..n-1] contains all 2s. The mid pointer scans through the unknown region [mid..high] making decisions based on the current value. Two-Pass Counting Approach: Count occurrences of 0, 1, and 2, then overwrite the array in order. Simpler to implement but requires two passes over the array. The interviewer usually wants the single-pass DNF solution. Rearrange an array into wiggle order in O(n) using greedy swaps in Python. In-place alternating valley-peak pattern for coding interviews. Topics: sorting, greedy, array, two-pointers Companies: amazon, google, microsoft, meta, bloomberg, stripe Level: swe2, swe3 Greedy One-Pass O(n): Single left-to-right pass: at even indices ensure current <= next (swap if not), at odd indices ensure current >= next (swap if not). The local correction never invalidates the previous position's invariant because the swap only affects adjacent elements. Sort Then Interleave: Sort the array first, then swap every pair of adjacent elements at odd positions. After sorting, consecutive equal elements are adjacent, and the pairwise swaps create the alternating pattern without violating the wiggle property. Design a MedianFinder using two heaps in Python. O(log n) insertion and O(1) median query for streaming data. Classic hard interview question at FAANG. Topics: heap, sorting, two-pointers Companies: google, amazon, meta, microsoft, apple, netflix Level: swe3, senior Two Heaps - Max-Heap Lower + Min-Heap Upper: Maintain two heaps where lower (max-heap) holds the smaller half and upper (min-heap) holds the larger half. After each insertion, rebalance heap sizes to differ by at most 1, ensuring the median is always at the heap tops. Two Heaps with Cleaner Rebalance Logic: Always route new elements through small first to small->large to guarantee the ordering invariant. The rebalance step then simply checks sizes and moves one element if needed. This two-step approach eliminates the need for an explicit comparison check. Find top K frequent elements in O(n) using bucket sort in Python. Compare with heap approach O(n log k) for coding interview preparation. Topics: sorting, hash-map, heap, array Companies: amazon, google, meta, microsoft, bloomberg, stripe Level: swe2, swe3 Bucket Sort O(n): Count frequencies with a hash map, then use bucket sort where bucket index equals frequency. Since frequencies range from 1 to n, bucket indices never exceed n. Scan buckets right-to-left (highest to lowest frequency) to collect the top k elements. Min-Heap of Size K: Count frequencies with a hash map, then use heapq.nlargest to extract the k elements with the highest frequency. The heap internally maintains a size-k structure giving O(n log k) total time - worse than bucket sort but cleaner to write. Sort string characters by frequency in O(n) using bucket sort or Counter sort in Python. Classic interview question testing frequency counting and sorting. Topics: sorting, hash-map, heap, array Companies: amazon, google, meta, microsoft, adobe, bloomberg Level: swe2, swe3 Counter + Sorted: Count frequencies with Counter, sort unique characters by descending frequency, then reconstruct the string by repeating each character its frequency count times. Since k <= 128 for ASCII, sorting k characters is effectively O(1). Bucket Sort O(n): Use bucket sort where bucket[i] collects all characters with frequency i. Scan buckets from high to low frequency and append each character repeated by its bucket index. Avoids the log factor from sorting. Form the largest number from an array of integers using custom comparator sort in Python. Greedy string comparison technique for coding interviews. Topics: sorting, greedy, array Companies: amazon, google, meta, microsoft, bloomberg, stripe Level: swe2, swe3 Custom Comparator Sort: Define a custom comparator that concatenates two strings both ways and picks the order that yields the larger concatenation. Apply this with cmp_to_key, sort descending, then join. This total order is consistent and transitive by the properties of string lexicographic ordering. Using Bubble Sort with Custom Compare: Bubble sort using the same concatenation comparison. O(n^2) but illustrates the comparator clearly. Only use this for interview explanation - use the cmp_to_key approach in production. Find minimum arrows to burst all balloons using greedy interval scheduling in Python. Sort by end coordinate for optimal arrow placement. Topics: sorting, greedy, array Companies: amazon, google, meta, microsoft, bloomberg, apple Level: swe2, swe3 Greedy Sort by End: Sort by end coordinate, shoot the first arrow at the end of the first balloon. For each subsequent balloon, if the current arrow position falls within its range we skip it (already burst); otherwise we must fire a new arrow at the end of this balloon, maximizing the chance to catch future overlapping balloons. Track Minimum End of Overlapping Group: Sort by start coordinate, track the minimum end seen in the current overlapping group. When a new balloon's start exceeds the tracked minimum end, the group is complete and we fire an arrow, starting a new group with the current balloon. Reconstruct a queue by height using greedy sort and insert in Python. Classic O(n^2) greedy problem for coding interviews at Google and Amazon. Topics: sorting, greedy, array Companies: google, amazon, meta, microsoft, bloomberg, netflix Level: swe2, swe3 Sort + Insert at Index K: Sort descending by height (ascending by k for ties). For each person in this sorted order, list.insert(k, person) places them correctly. Because all previously inserted people are taller or equal, the insertion index k directly counts exactly the right number of people ahead. BIT/Segment Tree for O(n log n): Instead of list.insert (which shifts elements), maintain a result array and find the k-th empty slot for each person. With a Binary Indexed Tree tracking empty slots, this becomes O(n log n). The linear scan version shown here has the same O(n^2) complexity as insert but avoids repeated memory copies. Determine if cards can be arranged into consecutive groups of size W in Python. Greedy frequency map approach for coding interviews. Topics: sorting, greedy, hash-map, array Companies: amazon, google, meta, microsoft, stripe, apple Level: swe2, swe3 Greedy with Sorted Counter: Count card frequencies, sort unique cards, and greedily form groups starting from the smallest available card. The frequency of the smallest card tells us how many groups must start there. We reduce all W consecutive cards by that amount and check none go negative. Heap-based Greedy: Use a min-heap to always access the smallest remaining card. For each group starting card, attempt to extend W-1 times. Pop cards from the heap only when their count reaches zero. Validate heap front matches expected card when popping. Rearrange array A to maximize wins against array B using greedy pairing in Python. Two-pointer and bisect approaches for coding interviews. Topics: sorting, greedy, two-pointers, array Companies: google, amazon, microsoft, meta, bloomberg, stripe Level: swe2, swe3 Greedy with Sorted A and Indexed B: Sort A and B's indices by B values. Use two pointers on B's sorted indices (lo=easiest, hi=hardest). For each A element (smallest first): if it beats the easiest B, assign it there; otherwise waste it on the hardest B. This is the "weakest horse strategy" from Chinese horse racing folklore. Greedy with SortedList (Bisect): For each B value in descending order, use binary search to find the smallest A that beats it. If found, assign and remove it; otherwise assign the smallest remaining A. Conceptually cleaner but list.pop is O(n); use sortedcontainers.SortedList for O(log n) removal. Find maximum XOR of two array elements using trie or bitwise greedy in Python. O(n) solution with bit-by-bit construction for coding interviews. Topics: bit-manipulation, divide-and-conquer, hash-map, array Companies: google, amazon, meta, microsoft, apple, stripe Level: swe3, senior Trie-based O(32n): Build a binary trie from MSB to LSB. For each number, traverse the trie greedily choosing the child whose bit is the complement of the current number's bit (maximizing XOR at each position). The XOR accumulates one bit at a time from the most to least significant. Bitwise Greedy with Sets O(32n): Build the answer bit by bit from MSB. At each step, compute the set of all numbers' prefixes up to the current bit. Try to set the current bit in the result (candidate). Using XOR property a^b=c <=> a^c=b, check if any two prefixes XOR to the candidate. If so, the bit is achievable. Compute bitwise AND of all numbers in a range in O(log n) using common prefix trick in Python. Brian Kernighan bit strip for coding interviews. Topics: bit-manipulation, array Companies: amazon, google, microsoft, meta, bloomberg, goldman-sachs Level: swe2, swe3 Right Shift Until Equal (Common Prefix): Shift both left and right right until they are equal. At this point they share the same bit prefix, and all lower bits get zeroed by the AND. Shift the common value back left by the number of shifts to restore magnitude. Maximum 32 iterations for 32-bit integers. Brian Kernighan Bit Strip: Use the bit trick x & (x-1) which clears the lowest set bit of x. Repeatedly apply this to right until right <= left. At that point, right holds the common prefix of all numbers in [left, right] because all bits that would differ across the range have been stripped. Count set bits using Hamming weight in Python. Brian Kernighan trick, bit shift, and SWAR parallel counting for coding interviews at FAANG. Topics: bit-manipulation, array Companies: amazon, google, microsoft, meta, apple, bloomberg Level: swe2, swe3 Brian Kernighan - Clear Lowest Set Bit: Brian Kernighan's trick: n & (n-1) always clears the lowest set bit (LSB). For example 12 (1100) & 11 (1011) = 8 (1000). Loop until n becomes 0, counting iterations. Runs in O(popcount) iterations - faster than 32 iterations when few bits are set. Bit Shift + Mask: Three methods: (1) right-shift and check LSB each iteration - always 32 iterations; (2) Python built-in bin().count("1") - fine in interviews but know how it works; (3) SWAR (SIMD Within A Register) parallel counting that processes all 32 bits simultaneously using bitmask arithmetic - used in hardware popcount instructions. Check if a number is a power of two using O(1) bit trick in Python. n & (n-1) == 0 explained with power of four extension for coding interviews. Topics: bit-manipulation, array Companies: amazon, google, microsoft, meta, adobe, bloomberg Level: swe2 Bit Trick O(1): n & (n-1) clears the lowest set bit. A power of two has exactly one set bit, so after clearing it the result is zero. Combined with n > 0 to exclude zero and negatives, this gives a one-line O(1) solution. The negative check is necessary in Python/Java because negative numbers in two's complement can satisfy n & (n-1) == 0. Multiple Approaches + Power of 4 Extension: Three approaches: (1) repeated division by 2 until odd - checks if remainder is 1; (2) the elegant bit trick n > 0 and n & (n-1) == 0; (3) floating-point log2 check. Bonus: power of four check requires the single set bit to be at an even position, enforced by masking with 0x55555555 (alternating 1s at even positions). Implement a producer-consumer bounded queue using threading.Condition in Python. Common in system design interviews at Google, Uber, Stripe. Topics: concurrency, queue, design Companies: google, amazon, uber, stripe, datadog, snowflake, linkedin Level: senior, staff threading.Condition Solution: Use a single Condition wrapping one lock. Producers wait while full; consumers wait while empty. notify_all wakes the other side after each operation. Two-Condition Solution: Use separate not_full and not_empty Condition objects sharing one lock for clearer semantic signaling between producers and consumers. Implement a concurrent LRU cache with a readers-writer lock in Python. Covers OrderedDict, threading, and cache eviction for senior engineering interviews. Topics: concurrency, caching, hash-table, linked-list, design Companies: facebook, google, netflix, airbnb, stripe, datadog, linkedin Level: senior, staff RWLock with OrderedDict: Implement a readers-writer lock using a counter and two locks. Readers increment a counter; only the first reader acquires the write lock. Writers acquire exclusively. threading.RLock Simple Version: Use a single reentrant lock for simplicity. Suitable when the read/write ratio does not justify the complexity of a full RW lock. Build an asyncio coroutine task manager with per-task timeouts and graceful cancellation in Python. Essential for senior backend and async systems interviews. Topics: async-await, concurrency, design Companies: stripe, datadog, cloudflare, netflix, uber, twitter, snowflake Level: senior, staff asyncio.gather with per-task timeout: Wrap each coroutine in asyncio.wait_for with its timeout. Use gather(return_exceptions=True) to collect results and exceptions without stopping on first failure. asyncio.create_task with cancellation: Create named Task objects so they can be individually cancelled. Use asyncio.wait with FIRST_EXCEPTION or ALL_COMPLETED to control collection behavior. Implement async HTTP request batching with error handling and retries using asyncio in Python. Common in Stripe, Cloudflare, and Datadog engineering interviews. Topics: async-await, concurrency, design, rate-limiting Companies: stripe, cloudflare, datadog, netflix, twitter, uber, adobe Level: senior, staff Chunked asyncio.gather: Split URL list into chunks of batch_size. For each chunk, use asyncio.gather with return_exceptions=True. Flatten results in order. Semaphore-controlled concurrency: Use asyncio.Semaphore to cap total concurrent requests rather than strict batches. All requests are submitted at once but semaphore throttles execution. Build a semaphore-based async connection pool in Python with timeout support and context manager protocol. Common in Snowflake, Databricks, and Stripe interviews. Topics: async-await, concurrency, design, queue Companies: snowflake, databricks, stripe, datadog, palantir, airbnb, netflix Level: senior, staff asyncio.Queue pool: Pre-create connections and place them in an asyncio.Queue. Acquire pops from the queue (blocks if empty), release pushes back. asynccontextmanager ensures cleanup. Semaphore + list pool: Use asyncio.Semaphore to gate the number of concurrent users; maintain a list of connections with a lock for thread-safe borrowing. Implement a thread-safe token bucket rate limiter in Python with per-key support. Used in Stripe, Cloudflare, and Twitter API gateway interviews. Topics: rate-limiting, design, concurrency, object-design Companies: stripe, cloudflare, twitter, uber, datadog, linkedin, apple Level: swe3, senior, staff Time-based refill with lock: Store last_time and current_tokens. On each consume, compute elapsed time, add rate*elapsed tokens (capped at capacity), then check if enough tokens exist. Async token bucket: Same algorithm but using asyncio.Lock for use in async services. Suitable for FastAPI middleware or aiohttp rate limiting. Implement a sliding window rate limiter with deque-based timestamp tracking in Python. Key algorithm for Cloudflare, Stripe, and Twitter API design interviews. Topics: rate-limiting, design, queue, hash-table Companies: cloudflare, stripe, twitter, uber, linkedin, datadog, snowflake Level: swe3, senior, staff Per-key deque of timestamps: Store request timestamps per key in a deque. On each request, remove timestamps older than window, then check if count < limit. Thread-safe with per-key locks. Sliding window with sorted list: Use a sorted list and bisect to efficiently find the cutoff index for the window start. Implement a fixed window rate limiter with atomic counter reset in Python. Simple and widely deployed in internal APIs at LinkedIn, Adobe, and Twitter. Topics: rate-limiting, design, hash-table, concurrency Companies: linkedin, apple, adobe, splunk, twitter, uber, stripe Level: swe3, senior Window ID + counter dict: Compute window ID as int(time() // window). If the window ID changed since last request, reset counter. Increment and compare against limit. Per-key RLock with window reset: Use per-key reentrant locks for finer granularity. Useful when many independent keys need concurrent access without contending on a single global lock. Implement a Redis-backed distributed sliding window rate limiter in Python. Critical for Cloudflare, Stripe, and Datadog distributed systems interviews. Topics: rate-limiting, design, system-design-coding, concurrency Companies: cloudflare, stripe, datadog, snowflake, palantir, netflix, uber Level: senior, staff Sorted set simulation: FakeRedis implements ZADD, ZREMRANGEBYSCORE, ZCARD as atomic operations under a lock. DistributedRateLimiter uses pipeline: expire old, add new, count, conditionally remove. Implement write-through and write-behind cache strategies in Python. Covers consistency trade-offs critical for Netflix, Airbnb, and Databricks system design interviews. Topics: caching, design, concurrency, object-design Companies: netflix, airbnb, stripe, databricks, palantir, datadog, snowflake Level: senior, staff Strategy pattern with background flusher: Write-through calls db immediately in put(). Write-behind adds key to dirty set and a background thread periodically flushes dirty keys to db. Implement TTL, LRU, and event-based cache invalidation in Python. Covers the hardest problem in distributed systems for Netflix, Cloudflare, and Stripe interviews. Topics: caching, design, hash-table, object-design Companies: netflix, cloudflare, airbnb, stripe, datadog, twitter, linkedin Level: senior, staff Combined TTL + LRU + event invalidation: Store (value, expiry) in OrderedDict. On get(), check TTL first. On put(), enforce LRU capacity. invalidate() removes immediately and triggers callbacks for event subscribers. Implement a read-through cache with thundering herd protection using per-key locks in Python. Essential for Airbnb, Netflix, and Stripe senior engineering interviews. Topics: caching, concurrency, design, hash-table Companies: airbnb, netflix, stripe, datadog, uber, linkedin, snowflake Level: senior, staff Per-key locks with double-checked locking: Check cache first. On miss, acquire per-key lock and check again (double-check). Only if still missing, call loader. Other threads for same key wait and then read from cache. Implement the cache-aside pattern in Python with explicit get, set, and invalidate operations. Used at Uber, Twitter, and LinkedIn for scalable caching. Topics: caching, design, hash-table, object-design Companies: uber, twitter, linkedin, adobe, splunk, airbnb, datadog Level: swe3, senior CacheAsideClient with loader callback: get() checks cache, calls loader(key) on miss, stores result. set() writes directly to cache. invalidate() removes entry. Pattern keeps DB and cache logic decoupled. Build a JSON serializer for datetime, Decimal, Enum, and UUID in Python. Critical for Stripe, Palantir, and Datadog API serialization interview questions. Topics: serialization, design, oop, object-design Companies: stripe, datadog, palantir, adobe, splunk, airbnb, linkedin Level: swe3, senior JSONEncoder subclass with type dispatch: Override default() in JSONEncoder to dispatch on type. Use json.loads() with object_hook for deserialization with type hints embedded in the JSON. Implement a Protocol Buffer encoder and decoder in Python using varint encoding. Covers binary serialization fundamentals for Google, Netflix, and Uber interviews. Topics: serialization, design, object-design, system-design-coding Companies: google, netflix, uber, datadog, palantir, stripe, cloudflare Level: senior, staff Varint + length-delimited encoding: Wire type 0 for int/bool (varint encoding: 7 bits per byte), wire type 2 for str (length + UTF-8 bytes). Tag = (field_num << 3) | wire_type. Simulate Avro schema evolution with backward and forward compatibility checks in Python. Essential for Databricks, Snowflake, and LinkedIn data engineering interviews. Topics: serialization, design, system-design-coding, object-design Companies: databricks, snowflake, palantir, linkedin, splunk, datadog, netflix Level: senior, staff Schema compatibility checker with projection: Parse field lists into dicts. Check backward: all old required fields exist in new. Check forward: all new required fields exist in old. Deserialize by projecting writer data onto reader schema with defaults. Implement an async observer pattern event bus in Python with concurrent dispatch and error isolation. Used at Stripe, Datadog, and Netflix for event-driven systems. Topics: design-patterns, async-await, design, object-design Companies: stripe, datadog, airbnb, netflix, twitter, uber, adobe Level: swe3, senior, staff Async EventBus with concurrent dispatch: Store callbacks in a dict of sets. emit() calls all subscribers concurrently via asyncio.gather. Sync callbacks are wrapped in run_in_executor. Errors are caught and logged per-subscriber. Implement the Command pattern for undo/redo in Python. Core design pattern for Adobe, Apple, and collaborative editor system design interviews. Topics: design-patterns, design, object-design, oop Companies: adobe, apple, netflix, twitter, linkedin, google, stripe Level: swe3, senior Stack-based command history: CommandHistory maintains undo_stack and redo_stack. execute() runs command, pushes to undo_stack, clears redo_stack. undo() pops from undo_stack, calls undo(), pushes to redo_stack. Implement the Strategy pattern with QuickSort, MergeSort, and HeapSort in Python. Classic OOP design pattern interview at Google, Apple, and LinkedIn. Topics: design-patterns, sorting, oop, object-design Companies: google, apple, linkedin, adobe, twitter, uber, stripe Level: swe3, senior Strategy pattern with multiple implementations: Define SortStrategy ABC. Implement QuickSort, MergeSort, HeapSort as concrete strategies. Sorter delegates to current strategy and allows runtime switching. Implement the Chain of Responsibility pattern for HTTP request processing in Python. Used in Netflix, Stripe, and Cloudflare middleware pipeline design interviews. Topics: design-patterns, design, object-design, oop Companies: netflix, stripe, uber, cloudflare, adobe, datadog, twitter Level: swe3, senior Linked handler chain: Each Handler holds a _next reference. set_next() enables fluent builder pattern. Concrete handlers check their condition; if passing, call _next.handle() or return True at end of chain. Implement a fluent SQL query builder using the Builder pattern in Python. Core ORM design question at Databricks, Snowflake, and Palantir engineering interviews. Topics: design-patterns, object-design, oop, design Companies: databricks, snowflake, palantir, stripe, linkedin, google, airbnb Level: swe3, senior Fluent builder with clause accumulation: Each method appends to internal clause lists and returns self. build() validates required clauses then joins them in correct SQL order with collected parameters. Implement the Flyweight pattern for shared object state in Python. Covers memory optimization at Apple, Adobe, and Google for game engine and text rendering systems. Topics: design-patterns, object-design, oop, hash-table Companies: google, apple, adobe, netflix, twitter, linkedin, stripe Level: swe3, senior Factory with shared state pool: FlyweightFactory maintains a dict of Flyweight instances keyed by frozen shared state. get_flyweight() creates new only if not present. Clients call operation() with extrinsic state each time. Implement virtual, caching, and protection proxies in Python. Common design pattern interview at Netflix, Airbnb, and Stripe for deferred loading and access control. Topics: design-patterns, object-design, caching, oop Companies: netflix, airbnb, stripe, palantir, uber, apple, adobe Level: swe3, senior Virtual + caching proxy: LazyImageProxy holds filename but not RealImage. On first display(), creates RealImage (expensive) and caches result. Subsequent calls return cached value. AuthProxy wraps another proxy for access control. Implement the Composite pattern for a file system tree in Python. Classic design interview at Apple, Google, and Dropbox covering recursive tree operations. Topics: design-patterns, graph, object-design, oop Companies: apple, google, adobe, dropbox, linkedin, netflix, airbnb Level: swe3, senior Composite with recursive operations: File is a leaf with fixed size. Directory is composite holding children list. size() recursively sums children. search() does DFS. display() shows tree with indentation. Implement the Visitor pattern for AST traversal with type checker and code generator in Python. Advanced design pattern interview at Google, Palantir, and Databricks. Topics: design-patterns, graph, object-design, oop Companies: google, palantir, databricks, apple, stripe, cloudflare, adobe Level: senior, staff Double-dispatch visitor with type checker and code gen: Each ASTNode.accept() calls visitor.visit_ClassName(self). TypeChecker returns type strings. CodeGenerator returns Python bytecode-like string. New operations add new Visitor subclass only. Design a job scheduler with priorities, dependencies, and recurring jobs in Python. Core system design interview at Airbnb, Stripe, and LinkedIn. Topics: system-design-coding, heap, graph, design, concurrency Companies: airbnb, uber, stripe, linkedin, datadog, palantir, snowflake Level: senior, staff Heap + dependency graph scheduler: Maintain dependency graph and count of unresolved deps per job. When a job completes, decrement dep counts of dependents and enqueue newly ready jobs. Use heapq for priority ordering. Implement a pub/sub message broker with retry logic and dead letter queue in Python. Core distributed systems interview at Google, Stripe, and Netflix. Topics: system-design-coding, queue, design, concurrency Companies: google, stripe, datadog, netflix, uber, cloudflare, linkedin Level: senior, staff Async broker with retry and DLQ: Each subscription has independent delivery state. publish() dispatches to all subs concurrently. Failed deliveries retry with backoff. After max_retries, message moved to DLQ. Implement the circuit breaker pattern with closed, open, and half-open states in Python. Core resilience pattern interview at Netflix, Uber, and Stripe. Topics: system-design-coding, design, design-patterns, concurrency Companies: netflix, uber, stripe, cloudflare, datadog, airbnb, twitter Level: senior, staff State machine circuit breaker: Track failure count and last_failure_time. CLOSED->OPEN on threshold. OPEN rejects immediately. After timeout, OPEN->HALF_OPEN allows one probe. Probe success: CLOSED; probe failure: OPEN. Build an API gateway with authentication, rate limiting, and route-based proxying in Python. Advanced system design coding interview at Cloudflare, Stripe, and Netflix. Topics: system-design-coding, design, rate-limiting, design-patterns Companies: cloudflare, stripe, netflix, uber, datadog, airbnb, twitter Level: senior, staff Middleware pipeline gateway: Chain auth, rate limiter, and router as middleware. Each middleware returns Response on error or calls next(). Router matches path prefix to registered backend handlers. Implement a G-Counter CRDT for distributed eventual consistency in Python. Core distributed systems interview at Twitter, LinkedIn, and Datadog. Topics: system-design-coding, design, concurrency, hash-table Companies: twitter, linkedin, facebook, datadog, snowflake, stripe, cloudflare Level: senior, staff G-Counter CRDT: Each node maintains its own count in a dict keyed by node_id. value() returns sum of all entries. merge() takes per-node maximum, making it commutative, associative, and idempotent. Implement a real-time leaderboard with O(log n) rank queries in Python using SortedList. Common system design interview at Twitter, LinkedIn, and Apple. Topics: system-design-coding, heap, hash-table, design Companies: twitter, linkedin, apple, google, adobe, netflix, uber Level: senior, staff SortedList leaderboard: Maintain sorted list of (-score, player_id) tuples for desc order. player_scores dict for O(1) score lookup. update removes old entry, inserts new. rank = bisect position + 1. Build a multi-channel notification service with deduplication and retry in Python. Common system design coding interview at Stripe, Airbnb, and Uber. Topics: system-design-coding, design, concurrency, async-await Companies: stripe, airbnb, uber, linkedin, datadog, netflix, twitter Level: senior, staff Async multi-channel with dedup and retry: Hash-based dedup cache with TTL. Per-channel sender classes implementing common interface. asyncio.gather dispatches to all channels concurrently. Exponential backoff retry per channel. Implement a feature flag system with percentage rollout and segment targeting in Python. Used at LinkedIn, Airbnb, and Stripe for safe feature releases. Topics: system-design-coding, design, hash-table, object-design Companies: linkedin, airbnb, twitter, stripe, datadog, netflix, uber Level: senior, staff Rule-based evaluator with hash bucketing: Sort rules by priority descending. Each rule type: whitelist checks membership, percentage uses stable hash bucket, segment checks user_attrs. First matching rule wins. Build a versioned config management service with compare-and-swap and hot-reload watchers in Python. Used at Palantir, Stripe, and Datadog for dynamic configuration. Topics: system-design-coding, design, hash-table, object-design Companies: palantir, stripe, datadog, airbnb, snowflake, linkedin, uber Level: senior, staff Versioned store with watcher notification: Each key maps to a list of (version, value, timestamp) entries. set() checks expected_version for CAS, appends new entry, notifies watchers. get() returns specific version or latest. Implement optimistic and pessimistic locking patterns in Python with TTL and CAS semantics. Core distributed systems interview at Stripe, Airbnb, and Snowflake. Topics: concurrency, system-design-coding, design, hash-table Companies: stripe, airbnb, uber, snowflake, palantir, databricks, netflix Level: senior, staff Combined pessimistic + optimistic lock managers: Pessimistic: per-resource threading.Lock with TTL stored alongside. Lock acquisition spins until available or timeout. Optimistic: version dict with CAS write that raises ConflictError on mismatch. Build a DAG-based workflow engine with parallel execution and cycle detection in Python. Core system design interview at Airbnb, Databricks, and Stripe. Topics: system-design-coding, graph, concurrency, design Companies: airbnb, stripe, databricks, palantir, linkedin, uber, datadog Level: senior, staff Kahn topological + thread pool execution: Build adjacency list and in-degree map. Queue tasks with zero in-degree. Worker threads execute tasks and decrement in-degree of dependents, enqueuing newly ready tasks. Build a metrics collection system with counter, gauge, histogram, and percentile computation in Python. Core APM design interview at Datadog, Splunk, and Netflix. Topics: system-design-coding, design, heap, sorting Companies: datadog, splunk, netflix, stripe, cloudflare, uber, linkedin Level: senior, staff Registry with reservoir sampling histogram: Counter: atomic increment. Gauge: latest value. Histogram: reservoir sampling (random replacement after reservoir full). Percentile: sort reservoir and index. Thread-safe throughout. Build an immutable audit log with cryptographic hash chaining in Python. Critical compliance system design at Stripe, Goldman Sachs, and Palantir. Topics: system-design-coding, design, hash-table, object-design Companies: stripe, palantir, goldman-sachs, snowflake, datadog, linkedin, airbnb Level: senior, staff Hash-chained append-only log: Each entry includes prev_hash computed from previous entry. Entries stored in list (append-only). Query filters applied in Python with pagination. verify() recomputes chain from start. Implement a thread pool with Future and graceful shutdown in Python from scratch. Essential concurrency interview at Google, Uber, Netflix, and Stripe. Topics: concurrency, design, queue, object-design Companies: google, amazon, uber, stripe, netflix, datadog, linkedin Level: senior, staff Queue-based thread pool with Future: Worker threads loop on queue.get(). Submit wraps callable in (fn, args, future) tuple. Future uses threading.Event for blocking result(). Sentinel None signals each worker to exit. Master Python's multiprocessing Pool with map, starmap, and apply_async for CPU-bound parallelism. Key interview topic at Databricks, Snowflake, and Google. Topics: concurrency, design, queue Companies: databricks, snowflake, palantir, netflix, google, uber, stripe Level: senior, staff Multiprocessing Pool patterns: Demonstrate map, starmap, apply_async, imap. Use context manager for cleanup. Show error handling with error_callback. Compare with threading for CPU vs I/O bound tasks. Build an async priority task queue with worker coroutines and graceful shutdown in Python. Used at Stripe, Cloudflare, and Netflix for priority-based task dispatch. Topics: async-await, concurrency, queue, heap Companies: stripe, datadog, cloudflare, netflix, uber, twitter, airbnb Level: senior, staff asyncio.PriorityQueue with worker coroutines: PriorityQueue stores (priority, seq, fn, args). Worker coroutines loop on get(). Shutdown enqueues sentinel per worker. Results tracked via asyncio.Event per task. Implement the Banker's Algorithm for deadlock detection and prevention in Python. Core OS and concurrency interview at Google, Uber, and Databricks. Topics: concurrency, graph, design, system-design-coding Companies: google, uber, databricks, palantir, snowflake, stripe, netflix Level: senior, staff Safety check with need matrix: Compute need = max - allocation. Safety: find process whose need <= work (available). Simulate completion: add allocation to work. If all processes finish, safe. request_resources() tentatively allocates then checks safety. Solve the dining philosophers problem without deadlock using fork ordering in Python. Classic concurrency interview at Google, Uber, and Stripe. Topics: concurrency, design, object-design Companies: google, amazon, uber, stripe, netflix, apple, datadog Level: senior, staff Fork ordering solution: Each philosopher picks up forks in order min(left,right) first. This breaks the circular wait condition. Even-numbered philosophers pick left first, odd pick right first - equivalent. Implement the readers-writers problem with writer-preference fairness in Python. Classic synchronization interview at Google, Netflix, and Datadog. Topics: concurrency, design, queue Companies: google, netflix, datadog, stripe, uber, linkedin, apple Level: senior, staff Fair RW lock with writer preference: Track active_readers, active_writer, waiting_writers. New readers block if waiting_writers > 0 (writer preference). Writers block while active_readers > 0 or active_writer. Release notifies all blocked parties. Implement producer-consumer with asyncio bounded queue backpressure in Python. Critical streaming system pattern at Stripe, Netflix, and Cloudflare. Topics: async-await, concurrency, queue, design Companies: stripe, datadog, cloudflare, netflix, uber, twitter, linkedin Level: senior, staff Bounded queue async pipeline: Producer is async generator yielding items; feeder coroutine puts into bounded queue. Consumers loop on queue.get() with task_done(). queue.join() waits for all items processed before shutdown. Master Python's concurrent.futures with parallel_map, race, callbacks, and chaining. Essential concurrency patterns for Google, Stripe, and Netflix interviews. Topics: concurrency, async-await, design Companies: google, stripe, netflix, datadog, uber, airbnb, linkedin Level: senior, staff concurrent.futures patterns: parallel_map uses ThreadPoolExecutor with as_completed for ordered results with per-task timeout. race() submits all, returns first completed. Callbacks for non-blocking notification. Simulate and compare LRU, LFU, FIFO, and random cache eviction policies in Python. Practical cache design interview at Netflix, Cloudflare, and Datadog. Topics: caching, design, hash-table, sorting Companies: netflix, cloudflare, datadog, airbnb, linkedin, stripe, uber Level: senior, staff Multi-policy cache simulator: Each policy implemented as standalone function. LRU=OrderedDict, LFU=heap+counter, FIFO=deque, Random=set. compare_policies() runs all and returns comparison dict. Implement a Bloom filter with optimal sizing and double hashing in Python. Used at Google BigTable, Cloudflare, and Netflix for efficient membership testing. Topics: design, hash-table, system-design-coding, object-design Companies: google, cloudflare, netflix, datadog, databricks, linkedin, stripe Level: senior, staff Bit array bloom filter with double hashing: Compute optimal size m and hash count k from n and p. Use double hashing (h1 + i*h2) for k positions. Bit array stored as bytearray for memory efficiency. Thread-safe with lock. Build a time-series store with downsampling and retention in Python. Core data engineering interview at Datadog, Splunk, and Snowflake. Topics: system-design-coding, design, sorting, hash-table Companies: datadog, splunk, netflix, cloudflare, stripe, snowflake, databricks Level: senior, staff Sorted list store with downsampling: Store (timestamp, value) sorted by timestamp using bisect for O(log n) insertion. query() slices by time range. downsample groups by interval floor and computes aggregates. Retention: remove on write. Implement event sourcing with immutable event log and projections in Python. Advanced system design interview at Stripe, Palantir, and LinkedIn. Topics: system-design-coding, design, object-design, hash-table Companies: stripe, palantir, airbnb, linkedin, netflix, databricks, uber Level: senior, staff Event store with projection registry: Event store appends with auto-incrementing version. Aggregates expose apply(event) for each event type. Projections are registered callbacks updated on every append. rebuild() replays from version 0. Implement CQRS with separate read and write models and eventual consistency in Python. Advanced system design interview at Stripe, Airbnb, and LinkedIn. Topics: system-design-coding, design, object-design, hash-table Companies: stripe, airbnb, linkedin, palantir, databricks, netflix, uber Level: senior, staff Command/Query buses with projections: CommandBus dispatches commands to handlers that validate, mutate write model, emit events. QueryBus reads from projection dict. Event bus links write side to projection updates maintaining eventual consistency. Implement the Saga pattern with compensating transactions in Python. Core distributed systems interview at Stripe, Airbnb, and Uber for multi-service orchestration. Topics: system-design-coding, design, design-patterns, object-design Companies: stripe, airbnb, uber, linkedin, netflix, palantir, datadog Level: senior, staff Orchestration-based saga with compensation stack: Execute steps sequentially. Push each successful step onto compensation stack. On failure, pop and execute compensations in reverse order. Track state machine transitions. Build a minimal ORM mapping Python classes to SQLite tables with CRUD operations. Advanced Python metaclass and SQL generation interview at Palantir, Stripe, and Airbnb. Topics: design, object-design, oop, design-patterns Companies: palantir, stripe, airbnb, databricks, linkedin, google, netflix Level: senior, staff Metaclass ORM with SQLite backend: ModelMeta collects Field instances from class body into _fields dict. Model.create() generates INSERT. Model.filter() generates SELECT WHERE. Model.save() generates UPDATE. Uses sqlite3 for actual execution. Implement TCP connection multiplexing with stream IDs in Python. Models HTTP/2 and gRPC internals for Cloudflare, Netflix, and Stripe system design interviews. Topics: system-design-coding, design, concurrency, queue Companies: cloudflare, stripe, netflix, uber, datadog, palantir, google Level: senior, staff Header-based stream multiplexer: Assign stream_id per send() call. Frame = struct.pack('!II', stream_id, len) + payload. Background reader parses frames and routes to per-stream asyncio.Queue. send() awaits its queue for the response. Implement request deduplication with idempotency keys in Python. Critical API safety pattern at Stripe, Airbnb, and Uber for payment and booking systems. Topics: system-design-coding, design, hash-table, caching Companies: stripe, airbnb, uber, linkedin, netflix, cloudflare, datadog Level: swe3, senior, staff Per-key lock with response cache: Check if key exists and not expired: return cached response. If in-flight, wait using per-key Event. If new, execute fn(), store result with expiry, signal waiters. Thread-safe. Simulate a 3-tier CDN with origin, regional, and leaf nodes in Python. Core content delivery interview at Cloudflare, Netflix, and Apple. Topics: system-design-coding, caching, design, graph Companies: cloudflare, netflix, akamai, stripe, datadog, apple, uber Level: senior, staff 3-tier CDN simulation with LRU + TTL: CacheNode holds LRU cache with TTL. get() checks local, then parent recursively. On parent hit, populate local cache. Origin always has the content. Stats track hits and misses per node. Build an async task dependency executor with parallel execution and result passing in Python. Core system design at Airbnb Airflow, Databricks, and Stripe. Topics: graph, concurrency, async-await, system-design-coding Companies: airbnb, databricks, stripe, palantir, uber, linkedin, snowflake Level: senior, staff Async topological executor with result passing: Build adjacency list and dep count map. Use asyncio.Queue of ready tasks. Worker coroutine executes task with dep_results dict, decrements dep counts of dependents, enqueues newly ready ones. Build a versioned key-value store with MVCC and snapshot isolation in Python. Core database internals interview at Palantir, Snowflake, and Google. Topics: system-design-coding, design, hash-table, sorting Companies: palantir, snowflake, databricks, stripe, google, linkedin, datadog Level: senior, staff MVCC versioned store with snapshot transactions: Global version counter incremented on each put. Per-key list of (version, value) sorted by version. Binary search for point-in-time reads. Transaction holds snapshot version; reads see only versions <= snapshot. Build a shopping cart with inventory reservation and discount codes in Python. System design interview at Amazon, Stripe, and Airbnb covering concurrency and checkout logic. Topics: system-design-coding, design, object-design, oop Companies: amazon, stripe, airbnb, apple, linkedin, uber, adobe Level: swe3, senior Cart with optimistic inventory checkout: Cart holds items list and applied discount. checkout() validates discount, checks inventory atomically for all items, decrements on success or rolls back on partial failure. Returns detailed order. Build a collaborative filtering recommendation engine with cosine similarity in Python. Core ML systems interview at Netflix, Spotify, and LinkedIn. Topics: system-design-coding, design, hash-table, sorting Companies: netflix, spotify, linkedin, amazon, twitter, airbnb, uber Level: senior, staff User-user collaborative filtering with cosine similarity: Store sparse ratings as dict of dicts. Cosine similarity between users based on co-rated items. For target user, find K most similar users, aggregate their ratings on unseen items (weighted by similarity). Solve Trapping Rain Water in Python with two-pointer O(1) space and monotonic stack O(n) approaches. Hard Google/Amazon interview question with full solutions. Topics: two-pointers, monotonic-stack, array Companies: google, amazon, meta, microsoft, bloomberg, adobe, uber Level: senior, staff Two Pointers O(1) Space: Two pointers converge inward. Always process the side with the smaller max because the other side guarantees at least that much water can be held. Track running left_max and right_max and accumulate water when current height is below the running max. Monotonic Stack: Maintain a monotonic decreasing stack of indices. When a taller bar is found, pop the stack top as a valley floor, compute the water layer between the new bar and the new stack top as left wall, accumulate width * bounded_height. Prefix/Suffix Max Arrays: Precompute left_max[i] and right_max[i] arrays in two passes. For each position, water trapped = min(left_max, right_max) - height[i]. Simple and intuitive but uses O(n) extra space. Find the largest rectangle in a histogram using monotonic stack O(n) in Python. Classic hard interview question for Google, Amazon, Meta with complete solutions. Topics: monotonic-stack, array, divide-and-conquer Companies: amazon, google, meta, microsoft, bloomberg, uber, adobe Level: senior, staff Monotonic Stack: Maintain a monotonically increasing stack of indices. When a shorter bar is found, pop taller bars and compute the rectangle they could form: width spans from current position back to the new stack top. Sentinel 0 ensures all bars are processed. Divide and Conquer: Recursively split on the minimum-height bar. The minimum bar constrains the full-width rectangle. Recurse left and right of it for potentially taller but narrower rectangles. Use a sparse table for O(1) range minimum queries to achieve guaranteed O(n log n). Find the maximal rectangle of 1s in a binary matrix using histogram and monotonic stack approach in Python. Hard interview question with O(m*n) solution. Topics: monotonic-stack, dynamic-programming, array Companies: google, amazon, microsoft, meta, bloomberg, apple, linkedin Level: senior, staff Histogram per Row with Monotonic Stack: For each row, update a heights array: increment if cell is "1", reset to 0 if "0". Run the largest rectangle in histogram algorithm on heights after each row. Overall time is O(m*n) since each histogram scan is O(n). DP with Left, Right, Height Arrays: Track height, left boundary, and right boundary for each column. Left is the leftmost column that can extend a rectangle of current height; right is the rightmost. Area = height * (right - left). Update all three arrays in O(n) per row. Count distinct ways to reach n stairs taking 1, 2, or 3 steps in Python. Tribonacci DP with O(1) space optimization. Classic interview question. Topics: dynamic-programming, math, array Companies: amazon, microsoft, google, apple, adobe, oracle, shopify Level: swe3, senior Bottom-Up DP O(n) Space: Standard tribonacci DP. dp[i] = number of ways to reach stair i. Recurrence: dp[i] = dp[i-1] + dp[i-2] + dp[i-3] because last step was 1, 2, or 3. Space-Optimized O(1): Keep only the last three values. Roll them forward: new_c = a + b + c, then shift a=b, b=c, c=new_c. Avoids the full DP array while maintaining correctness. Memoized Recursion: Top-down memoized recursion. Each subproblem computed once. The lru_cache handles memoization automatically. Clean and easy to reason about correctness. Count distinct subsequences of string s matching string t using 2D and space-optimized DP in Python. Hard Google/Meta interview question. Topics: dynamic-programming, string Companies: google, amazon, meta, microsoft, bloomberg, goldman-sachs, stripe Level: senior, staff 2D DP: dp[i][j] = number of ways to form t[:j] from s[:i]. Base: dp[i][0]=1 (empty t always matched). Transition: always carry forward dp[i-1][j]; if characters match, also add dp[i-1][j-1] for using s[i-1]. Space-Optimized 1D DP: Compress DP to 1D by processing s character by character. Iterate j right-to-left to ensure each s[i] is only used once per position. dp[j] accumulates ways to form t[:j]. Solve minimum cost to cut a stick using interval DP in Python. Hard Google/Amazon interview question similar to matrix chain multiplication. Topics: dynamic-programming, divide-and-conquer, array Companies: google, amazon, meta, microsoft, stripe, bloomberg, airbnb Level: senior, staff Interval DP Bottom-Up: Sort cuts with 0 and n as boundaries. dp[i][j] = minimum cost to perform all cuts strictly between cuts[i] and cuts[j]. For each interval length, try every internal cut point k. Cost = sub-interval costs + current stick length (cuts[j] - cuts[i]). Memoized Top-Down: Top-down with memoization. dp(i, j) computes minimum cost for cuts strictly between positions cuts[i] and cuts[j]. Base case: adjacent boundaries need no cuts. Try all internal splits and pick minimum. Solve Strange Printer minimum turns using interval DP in Python. Hard Google/Amazon interview question with O(n^3) solution explained. Topics: dynamic-programming, string Companies: google, amazon, meta, microsoft, bloomberg, apple, stripe Level: senior, staff Interval DP: dp[i][j] = min turns to print s[i..j]. Start with printing s[i] separately (+1). When s[k] == s[i] for k > i, we can extend the first print to cover position k for free, merging dp[i+1][k] (middle) + dp[k][j] (right part including k). Memoized Recursion: Top-down memoized recursion. For interval [i, j], default is dp(i+1, j)+1. When s[k]==s[i], we handle positions i and k in the same print turn, reducing total turns. Cache ensures each subproblem is solved once. Count all arithmetic subsequences using DP with hash maps in Python. Hard Google interview question with O(n^2) solution using difference dictionary. Topics: dynamic-programming, array, math Companies: google, amazon, meta, bloomberg, stripe, microsoft, linkedin Level: senior, staff DP with Hash Maps: For each pair (j, i), compute difference d. dp[i][d] counts arithmetic subsequences of length >= 2 ending at index i with difference d. Adding dp[j][d] to answer counts the new length-3+ subsequences formed by appending nums[i]. +1 accounts for the new pair (j, i) as a length-2 sequence. Brute Force O(n^3) for Verification: Brute force triple loop checks all (i, j, k) triplets. This only counts length-3 arithmetic subsequences correctly. For subsequences of all lengths >= 3, the DP with hash maps approach is required. This solution is shown for illustration of the counting principle. Count palindromic subsequences of length 5 using DP with prefix character pair counts in Python. Hard interview question with modular arithmetic. Topics: dynamic-programming, string, math Companies: google, amazon, meta, microsoft, goldman-sachs, bloomberg, stripe Level: senior, staff DP with Prefix Character Pair Counts: For each middle position k, compute 2-character subsequence counts for the left part (pairs ab where a < b < k) and right part (pairs ab where k < a < b, reversed as ba). Multiply matching outer/inner pairs and sum over all character combinations. Works because length-5 palindrome = outer pair + inner pair + middle. Brute Force O(n^5): Enumerate all 5-index subsequences (i,j,k,l,m) in order and check the palindrome condition: s[i]==s[m] and s[j]==s[l] (center k is unconstrained). Correct but too slow for large inputs. Shown to validate the prefix-DP approach for small test cases. Find the k-th symbol in grammar using recursion and bit manipulation in Python. Medium Google interview question with O(1) bit-count solution. Topics: math, divide-and-conquer, bit-manipulation Companies: google, amazon, meta, microsoft, apple, adobe, shopify Level: swe3, senior Recursive Bit Flip: The k-th element of row n is generated from the ceil(k/2)-th element of row n-1. If k is odd, same value as parent. If k is even, flipped value. Recurse until row 1 which is always 0. Bit Count in k-1: Mathematical insight: the k-th symbol (0-indexed k-1) equals the number of 1-bits in k-1 modulo 2. This follows from the fractal structure where each flip corresponds to a 1-bit in the binary representation of the position. Solve the 24 Game by backtracking all number pairs and operations in Python. Hard Google/Meta interview question with floating-point handling. Topics: backtracking, math, divide-and-conquer Companies: google, amazon, meta, microsoft, apple, bloomberg, uber Level: senior, staff Backtracking on Number Pairs: At each step, pick any two numbers, apply an operation, and recurse on the resulting list of 3 numbers. This implicitly handles all parenthesizations. Try all ordered pairs and all 4 operations. Use epsilon comparison for floating-point results. Brute Force All Permutations and Operators: Enumerate all 24 permutations of cards and all 64 operator combinations. Evaluate left-to-right and with alternative groupings. The recursive pair approach is more complete for all parenthesizations; this shows the explicit enumeration approach. Add operators to a number string to reach target using backtracking in Python. Hard Google/Amazon interview question with multiplication precedence tracking. Topics: backtracking, math, string Companies: google, amazon, meta, microsoft, bloomberg, stripe, uber Level: senior, staff Backtracking with Mult Tracking: Backtrack by trying each possible number from current position. Track cur_val (accumulated value) and last_val (the last multiplied operand). For multiplication, undo the last addition/subtraction and apply: cur - last + last * n. This handles operator precedence without expression tree parsing. Backtracking with String Building: Alternative implementation using explicit dfs function with cleaner parameter names. Same algorithm: track path (expression string), value (current evaluated result), and last (last multiplication operand for precedence handling). The last parameter enables O(1) undoing of the last addition when multiplying. Find minimum palindrome partition cuts using DP in Python. Hard Google/Amazon interview question with O(n^2) time and O(n) space solution. Topics: dynamic-programming, string Companies: google, amazon, meta, microsoft, bloomberg, goldman-sachs, apple Level: senior, staff DP with Palindrome Precomputation: Precompute is_pal[i][j] for all substrings using DP. Then compute dp[i] = min cuts for s[0..i]. If s[0..i] is itself a palindrome, dp[i]=0. Otherwise try all splits j where s[j..i] is a palindrome: dp[i] = min(dp[j-1]+1). Expand Around Centers O(n^2) One Pass: Expand palindromes around each center. For each palindrome s[l..r] found, update dp[r+1] = min(dp[r+1], dp[l]+1). This uses a 1D dp array with sentinel dp[0]=-1, achieving O(n) space while remaining O(n^2) time. Determine if one string is a scramble of another using memoized recursion and 3D DP in Python. Hard Google/Amazon interview question. Topics: dynamic-programming, string, divide-and-conquer Companies: google, amazon, meta, microsoft, bloomberg, apple, adobe Level: senior, staff Memoized Recursion: Memoize on pairs of substrings. For each split point k, check both no-swap and swap cases. Prune early with Counter comparison which is O(26). The string-keyed cache stores O(n^2) pairs each of length up to n, giving O(n^4) total states. 3D DP Bottom-Up: Bottom-up 3D DP. dp[len][i][j] = True if s1[i:i+len] is a scramble of s2[j:j+len]. Fill by increasing length. For each split k, check no-swap and swap variants using precomputed shorter subproblem answers. Solve Zuma game minimum moves using DFS with memoization in Python. Hard Google interview question with string compression and state caching. Topics: dynamic-programming, string, divide-and-conquer Companies: google, amazon, meta, microsoft, bloomberg, apple, stripe Level: senior, staff DFS with Memoization and String Compression: Compress board into runs. For each run, try completing it to 3 using hand balls. Use memoization on (board_state, hand_counts). After removing a completed group, recursively clean cascading removals. The state space is bounded by the small board/hand sizes. BFS State Exploration: BFS over (board_state, available_hand) states. Enqueue initial state and explore all valid insertions level by level. First time we reach empty board gives minimum moves. Visited set prevents reprocessing the same (board, hand) configuration. Equivalent to DFS+memoization but explores breadth-first. Determine if a color grid is printable using topological sort of color dependencies in Python. Hard Google interview question. Topics: graph, dynamic-programming, array Companies: google, amazon, meta, microsoft, bloomberg, stripe, linkedin Level: senior, staff Bounding Box + Topological Sort: Find the bounding rectangle of each color. Within each color's bounding box, any cell of a different color creates a dependency: the outer color must be printed first, then the inner color on top. Build a directed graph of these dependencies and check for cycles using Kahn's topological sort. DFS Cycle Detection: Same bounding box and dependency graph construction, but cycle detection uses DFS coloring (WHITE/GRAY/BLACK) instead of Kahn's BFS. GRAY marks nodes currently in the recursion stack; finding a GRAY neighbor indicates a back edge (cycle). Returns False if any cycle is found. Solve Cat and Mouse game using backward induction BFS minimax in Python. Hard Google staff-level interview question with game state graph. Topics: dynamic-programming, graph, math Companies: google, amazon, meta, microsoft, bloomberg, apple, stripe Level: staff Backward Induction BFS: Backward induction on the game state graph (mouse_pos, cat_pos, turn). Initialize terminal states (mouse at 0 = mouse wins, cat at mouse = cat wins). Propagate backward: a state is winning for the current player if any successor is winning; it is losing if all successors are losing (tracked via degree countdown). Unresolved states are draws. Forward DP with Iterative Relaxation: Alternative formulation of the same backward induction: identifies the moving player at each parent state and checks whether the propagated result is a win for them (immediate coloring) or reduces their degree (all moves lead away from winning). Equivalent correctness to the first solution. Maximize score from pick-left or pick-right multiplications using interval DP in Python. Hard Amazon/Google interview question with O(m^2) solution. Topics: dynamic-programming, array Companies: amazon, google, meta, microsoft, bloomberg, stripe, airbnb Level: senior, staff Top-Down Memoized DP: State: (operation_index i, left_picks count). right_picks = i - left_picks. At each state, choose to pick from the left (nums[left]) or right (nums[n-1-right]). Maximize over both choices. The state space is O(m^2) since left <= i <= m. Bottom-Up DP: Fill DP table bottom-up from operation m-1 down to 0. dp[i][left] stores max score starting at operation i with left elements taken from the left side. Process in reverse to avoid needing future values. Find minimum refueling stops using greedy max-heap and DP approaches in Python. Hard Amazon/Google interview question with two O(n log n) and O(n^2) solutions. Topics: dynamic-programming, greedy, heap Companies: amazon, google, meta, microsoft, bloomberg, uber, airbnb Level: senior, staff Greedy with Max Heap: Drive forward, adding each station's fuel to a max-heap as we pass it. When we run out of fuel, greedily take the largest available fuel from the heap (as if we had stopped there retroactively). Count stops taken. If heap is empty and still short, return -1. DP on Number of Stops: dp[k] = maximum distance reachable using exactly k refueling stops. For each station, if we can reach it (dp[k] >= pos), we can add its fuel: dp[k+1] = max(dp[k+1], dp[k]+fuel). Traverse k in reverse to prevent using the same station twice. Return the first k where dp[k] >= target. Minimize the largest subarray sum by splitting into k parts using binary search in Python. Hard Google/Amazon interview question with two solutions. Topics: binary-search, dynamic-programming, greedy Companies: google, amazon, meta, microsoft, bloomberg, stripe, linkedin Level: senior, staff Binary Search + Greedy Check: Binary search between max(nums) (minimum possible largest sum: all in one group) and sum(nums) (maximum: one group). For each mid, greedily check if we can form at most k subarrays where each sums at most mid. If yes, try smaller; if no, need larger. Dynamic Programming: dp[i][j] = minimum largest subarray sum when splitting nums[0..i-1] into j parts. For each split point p, the last subarray is nums[p..i-1] with sum prefix[i]-prefix[p]. Take max with dp[p][j-1] and minimize over all p. Find minimum initial health for dungeon game using reverse bottom-up DP in Python. Hard Amazon/Google interview question with space-optimized solution. Topics: dynamic-programming, array, divide-and-conquer Companies: amazon, google, meta, microsoft, bloomberg, apple, netflix Level: senior, staff Reverse DP from Bottom-Right: Fill DP table from bottom-right. dp[i][j] = minimum health needed entering cell (i,j) to guarantee reaching princess. From (i,j) you go right or down, so need = min(dp[i+1][j], dp[i][j+1]) - dungeon[i][j]. Take max with 1 since health can never be 0 or negative. Space-Optimized 1D DP: Compress DP to a single row by processing bottom to top, right to left. dp[j] represents the minimum health needed at column j for the current row, reusing the array in-place. Requires careful handling of the last row and column boundary conditions. Find the largest square of 1s in a binary matrix using DP in Python. Medium Amazon/Google interview question with O(mn) time and O(n) space solutions. Topics: dynamic-programming, array, math Companies: amazon, google, meta, microsoft, apple, bloomberg, adobe Level: swe3, senior 2D DP: dp[i][j] = side of largest all-1 square with bottom-right at (i,j). The minimum of three neighbors limits how large the square can be: the left, top, and diagonal constraint each independently bound the square size. The recurrence computes optimal side in O(1) per cell. Space-Optimized 1D DP: Use a 1D dp array and a prev variable to track the diagonal predecessor (dp[i-1][j-1]). Before updating dp[j], save it as the new prev for the next iteration. This reduces space from O(mn) to O(n) while maintaining correctness. Count all-ones submatrices using height DP and monotonic stack in Python. Medium Google/Amazon interview question with O(mn) optimal solution. Topics: dynamic-programming, array, monotonic-stack Companies: google, amazon, meta, microsoft, bloomberg, adobe, linkedin Level: swe3, senior Height Array + Row DP: For each row, compute height[j] = number of consecutive 1s above and including current row in column j. For each ending column j, scan left tracking the minimum height seen. Each minimum height value contributes that many submatrices ending at (i, j) with that height. Monotonic Stack O(mn): Use a monotonic stack to track (height, count) pairs as we scan each row's heights. When a shorter height is encountered, merge taller segments. Maintain row_sum = sum of contributions of all heights in the stack. After processing each column, add row_sum to answer. This gives O(n) per row. Maximize cherry pickup with two simultaneous robot traversals using 3D DP in Python. Hard Google/Amazon interview question with diagonal state compression. Topics: dynamic-programming, array, divide-and-conquer Companies: google, amazon, meta, microsoft, bloomberg, stripe, apple Level: senior, staff 3D DP Simultaneous Two Robots: Two robots move simultaneously from (0,0) toward (n-1,n-1). At each step, both are on the same diagonal (r1+c1 = r2+c2 = t), so the state is (r1, c1, r2) with c2 derived. Collect cherries from both cells (count once if same cell). Try all 4 move combinations and take max. Return 0 if no valid path exists. Bottom-Up 3D DP: Bottom-up DP iterating over diagonal steps t. At each step t, both robots are on the same diagonal (r+c=t). Iterate over all valid (r1, r2) pairs with r1 <= r2. Transition from all 4 combinations of previous (r1, r2) moves. Reduces top-down recursion to an iterative table fill. Count distinct phone numbers dialed by knight moves using DP in Python. Medium Google/Amazon interview question with O(n) and matrix exponentiation solutions. Topics: dynamic-programming, math, array Companies: google, amazon, meta, microsoft, bloomberg, apple, linkedin Level: swe3, senior DP with Adjacency List: Precompute which digits a knight can jump to from each digit. Start with dp[digit]=1 (one way to start at any digit). Each step, accumulate counts by propagating to reachable neighbors. After n-1 steps, sum all counts. Only O(1) space for the 10-element dp array. Matrix Exponentiation for Very Large n: Build a 10x10 transition matrix T where T[i][j]=1 if knight can jump from i to j. Raise T to the (n-1)th power using fast matrix exponentiation. Sum all entries of the resulting matrix for the total count. Useful when n is astronomically large. Calculate soup serving probability using DP with convergence optimization in Python. Medium Google interview question with mathematical insight. Topics: dynamic-programming, math Companies: google, amazon, meta, microsoft, bloomberg, stripe, goldman-sachs Level: senior, staff Scaled DP with Early Convergence: Scale all quantities by 25 to reduce state space. Use memoized recursion where dp(a,b) returns probability A empties first or 0.5 for simultaneous. Operations become (4,0), (3,1), (2,2), (1,3) in scaled units. For n >= 4800, return 1.0 as probability converges due to A being consumed faster on average. Bottom-Up DP with Scaling: Forward DP propagating probabilities from (m, m) downward. For each state (a, b) with probability p, distribute p/4 to each of the 4 resulting states. When a state empties A (a=0), accumulate to result with weight 1.0 (or 0.5 if both zero). Equivalent to the memoized recursion but computed forward. Determine if a frog can cross a river using DP with hash map in Python. Hard Amazon/Google interview question with jump constraint tracking. Topics: dynamic-programming, array, binary-search Companies: amazon, google, meta, microsoft, bloomberg, apple, stripe Level: senior, staff DP with Hash Map: Create a dictionary mapping each stone to the set of jump sizes that can land on it. Start at stone 0 with jump 0. For each stone and each reachable jump size k, try jumps of k-1, k, k+1 to extend the path. The last stone is reachable if its jump set is non-empty. BFS with Visited Set: BFS over states (position, last_jump). Explore k-1, k, k+1 jumps from each position. Use visited set to avoid reprocessing same states. Returns True if target stone is reached. Maximize product of integer parts using DP and greedy math in Python. Medium Google/Amazon interview question with O(1) mathematical solution. Topics: dynamic-programming, math, greedy Companies: google, amazon, microsoft, meta, apple, bloomberg, adobe Level: swe3, senior Dynamic Programming: dp[i] = max product from breaking integer i. For each i, try all splits j and (i-j). The right part (i-j) can either stay as is (for product j*(i-j)) or be further broken (j*dp[i-j]). Take the max over all splits. Greedy Math O(1): Mathematical insight: breaking into 3s is always optimal (3/3 > 2/2 > 1/1 in terms of product per unit). Avoid 1s. Handle remainder: if n%3==0, all 3s; if n%3==1, replace one 3 with two 2s (3+1 -> 2+2 is better productwise 4 vs 3); if n%3==2, append one 2. Find maximum Russian doll envelope nesting using 2D LIS and patience sort in Python. Hard Google/Amazon interview question with O(n log n) solution. Topics: dynamic-programming, binary-search, divide-and-conquer Companies: google, amazon, meta, microsoft, bloomberg, apple, uber Level: senior, staff Sort + LIS with Binary Search O(n log n): Sort envelopes by width ascending; for equal widths, sort by height descending. This ensures that among envelopes of the same width, only one can appear in the LIS (since heights are decreasing for same width). Apply patience-sort LIS on heights only using binary search. The result is the longest chain of nested envelopes. DP O(n^2): Standard LIS DP on sorted envelopes. dp[i] = longest chain ending at envelope i. For each i, check all j < i where both dimensions are strictly smaller. O(n^2) - works for smaller inputs but TLEs for n=10^5. Find minimum replacements to make array strictly increasing using DP with binary search in Python. Hard Google interview question with dict-based state. Topics: dynamic-programming, binary-search, array Companies: google, amazon, meta, microsoft, bloomberg, stripe, apple Level: senior, staff DP with Dict and Binary Search: DP where state is a dictionary mapping the last value placed to the minimum operations. For each element in arr1, either keep it (if it maintains strictly increasing) or replace it with the smallest valid element from sorted arr2 using binary search. Propagate the minimum operation count for each reachable last value. DP with Sorted Array and Index Tracking: Same DP with dictionary but with cleaner variable naming and explicit sorting + deduplication of arr2 upfront. For each element in arr1, maintain a dictionary of {last_value: min_ops}. Use bisect to find optimal replacement value in O(log m). This formulation is easier to reason about correctness for interviews. Find minimum typing distance with two fingers on keyboard using DP in Python. Hard Google interview question with O(n) space-optimized solution. Topics: dynamic-programming, string, math Companies: google, amazon, meta, microsoft, bloomberg, apple, linkedin Level: senior, staff DP Tracking Other Finger Position: State: after typing word[i], one finger is at word[i] (current) and the other can be anywhere (tracked). At each step, either move the current finger to the next char (other stays put) or move the other finger to the next char (current becomes the "other"). Transition costs are Manhattan distances. 3D DP Explicit: Explicit 27-element DP array where index represents the position of the non-active finger (26 = not yet placed). For each character, transition by moving either the active or inactive finger. Manhattan distance on 2x13 grid. O(n) time with O(1) space for the DP array. Minimize XOR sum of two arrays using bitmask DP in Python. Hard Google/Amazon interview question with O(n * 2^n) solution for n <= 14. Topics: dynamic-programming, bit-manipulation, array Companies: google, amazon, meta, microsoft, bloomberg, stripe, goldman-sachs Level: senior, staff Bitmask DP: dp[mask] = minimum XOR sum when mask indicates which elements of nums2 have been assigned. The number of set bits in mask tells us the current position in nums1. For each unset bit j, try assigning nums2[j] to nums1[i] and update dp[mask | (1<<j)]. Answer is dp[(1<<n)-1]. Top-Down Memoized Bitmask DP: Top-down memoized DP where dp(i, mask) returns minimum XOR sum for nums1[i:] with nums2 elements indicated by mask already used. For each position i, try all unused nums2 elements (bit j not set in mask), recurse, and take minimum. Count ways to paint a fence with k colors and no 3 adjacent same-color posts using DP in Python. Medium Google interview question with O(n) solution. Topics: dynamic-programming, math Companies: google, amazon, meta, microsoft, bloomberg, apple, adobe Level: swe3, senior DP Same/Different Tracking: Track same = ways where last two posts have the same color, diff = ways where they differ. Recurrence: new same = old diff (can only have same if the post before the last two was different); new diff = (old same + old diff) * (k-1) colors to pick differently. Roll forward without extra space. Closed Form: Alternative recurrence: total(n) = (k-1) * (total(n-1) + total(n-2)). The (k-1) factor comes from choosing a different color for the new post, and the sum represents adding either a same or different previous pair. This collapses same and diff into total. Generate all valid IP addresses from a digit string using backtracking in Python. Medium Amazon/Google interview question with bounded O(1) complexity. Topics: backtracking, string Companies: amazon, google, meta, microsoft, bloomberg, apple, uber Level: swe3, senior Backtracking: Backtrack by trying segments of length 1, 2, or 3. Validate each segment for leading zeros and value <= 255. When 4 segments are formed and the entire string is consumed, add the IP to results. The search space is bounded at 3^4 since each of 4 segments can be 1-3 chars. Iterative Three Loops: Use three nested loops to place three dots at positions i, j, k. Validate all four resulting segments. Since each segment is at most 3 chars, loops are bounded making this effectively O(1). Clean and non-recursive alternative to backtracking. Find minimum stickers to spell a word using bitmask DP in Python. Hard Google/Amazon interview question with O(2^n * S * n) solution. Topics: dynamic-programming, bit-manipulation, backtracking Companies: google, amazon, meta, microsoft, bloomberg, stripe, apple Level: senior, staff Bitmask DP: dp[mask] = min stickers to cover target characters indicated by mask bits. For each mask, find the first uncovered character and only try stickers that cover it (pruning). Apply sticker greedily to cover as many uncovered characters as possible, compute new_mask, and minimize dp[new_mask]. BFS over Bitmask States: BFS over bitmask states guarantees minimum stickers (BFS gives shortest path in unweighted graph). Start from mask=0, expand by applying each sticker to the first uncovered character position. Use dist array for visited tracking. BFS level = number of stickers used. Find shortest path visiting all graph nodes using BFS with bitmask in Python. Hard Google/Amazon interview question with O(n * 2^n) solution. Topics: graph, bit-manipulation, dynamic-programming Companies: google, amazon, meta, microsoft, bloomberg, uber, stripe Level: senior, staff BFS with Bitmask State: BFS over states (node, visited_mask). Initialize all n nodes as starting states. Level-by-level BFS ensures minimum distance. Use a visited set of (node, mask) pairs to prevent redundant exploration. When visited_mask equals full_mask (all nodes visited), return current distance. DP with Bitmask: DP table dp[node][mask] = minimum steps to be at node with visited set = mask. Initialize all starting positions with 0 steps. Process using BFS-like updates. When full_mask is reached for any node, that distance is optimal. Equivalent to BFS but stored in DP table. Find minimum character replacements to make two strings anagrams using frequency counting in Python. Medium Amazon/Google interview question. Topics: string, math, greedy Companies: amazon, google, meta, microsoft, bloomberg, apple, shopify Level: swe3, senior Frequency Count: Count character frequencies in both strings. For each character that appears more in t than s, the excess must be replaced. Sum all excess counts. This equals the minimum changes since each replacement converts one excess char to a needed char. Array Count: Use a 26-element difference array. Increment for each character in s, decrement for t. Positive values in diff represent characters s needs more of (t must replace something with these). Sum positives = minimum steps. Find minimum swaps to group binary array 1s using sliding window in Python. Medium Amazon/Google interview question with O(n) solution. Topics: sliding-window, array, greedy Companies: amazon, google, meta, microsoft, bloomberg, apple, adobe Level: swe3, senior Sliding Window: Window size = total count of 1s. Slide this window across the array, tracking the number of 1s inside. The window with the most 1s needs the fewest swaps. Swaps needed = (total_ones - max_ones_in_window) since each 0 in the optimal window needs one swap with a 1 outside. Count Zeros in Optimal Window: Equivalent formulation: count zeros in each window of size total_ones. Minimum zeros = minimum swaps needed (each zero in the window must swap with a one outside). Slide the window counting zeros using (1 - data[i]) as the zero indicator. Simpler than tracking ones. Find longest subarray with absolute difference at most limit using two monotonic deques in Python. Hard Google/Amazon interview question with O(n) solution. Topics: sliding-window, monotonic-stack, array Companies: google, amazon, meta, microsoft, bloomberg, stripe, airbnb Level: senior, staff Two Monotonic Deques: Maintain a sliding window [left, right]. Two deques track the maximum and minimum values in the window. When max-min > limit, advance left and remove stale deque entries. Each element enters and exits each deque at most once, giving amortized O(n) total. Sorted Container (SortedList): Use a sorted container (balanced BST / sorted list) to maintain window elements. O(log n) insert/remove. Check max (last) minus min (first) in O(1). Simpler to implement than the deque solution but O(n log n) instead of O(n). Requires the sortedcontainers library. Maximize events attended using greedy min-heap scheduling in Python. Medium Amazon/Google interview question with O(n log n) solution. Topics: greedy, heap, array Companies: amazon, google, meta, microsoft, bloomberg, airbnb, uber Level: swe3, senior Greedy with Min Heap: Sort events by start day. Simulate day by day. Each day, add all events that started by today to a min-heap (keyed by end day). Remove expired events. Greedily attend the event with earliest end day (to preserve future flexibility). Advance day and repeat. If heap empty, jump to next event start to avoid O(max_day) simulation. Greedy Sorted by Start and End: Iterate through each day from 1 to 100000. Add events starting on the current day to a min-heap. Remove expired events. If heap non-empty, pop the soonest-ending event and attend it. Simpler implementation but O(D log n) where D can be 10^5; effectively O(n log n) in practice since most days have no events. Count fence painting ways with no three consecutive same-color posts using DP. O(n) time O(1) space Python solution. Topics: dynamic-programming, recursion Companies: amazon, google, apple, linkedin, stripe, adobe, uber Level: swe2, swe3, senior DP same/diff state O(1) space: Track same (last two posts same color) and diff (different). At each step update both. Total = same + diff. Closed-form DP with total ways: total[i] = (k-1) * (total[i-1] + total[i-2]). First term: any of k-1 different colors from i-1. Second term: match i-2 with any of k-1 colors != i-1. Maximize stock profit with unlimited transactions and per-trade fee using DP states. O(n) Python solution. Topics: dynamic-programming, greedy, array Companies: amazon, google, goldman-sachs, stripe, coinbase, jane-street, visa Level: swe3, senior, staff DP with cash and hold states: cash = max profit without stock today. hold = max profit holding stock today. Update both each day. Answer is cash. Find minimum cost path in grid with blocked cells using DP with path reconstruction. Python solution. Topics: dynamic-programming, matrix, graph Companies: amazon, google, facebook, uber, stripe, linkedin, adobe Level: swe2, swe3, senior Grid DP with path reconstruction: Fill dp table: dp[i][j] = grid cost + min of top/left predecessor. Skip blocked (-1) cells. Backtrack from bottom-right to find path. Find minimum number of words to segment string using DP or BFS shortest path. Python solutions. Topics: dynamic-programming, hash-map, string, bfs Companies: amazon, google, facebook, apple, stripe, linkedin, databricks Level: senior, staff DP minimum word count: dp[i] = minimum words to segment s[:i]. For each i, try all j < i where s[j:i] in word_set. dp[i] = min(dp[j] + 1). Return dp[n] or -1. BFS shortest path: BFS from index 0. Level = number of words used. Add all positions reachable via a valid word from current position. First time we reach n is minimum words. Find minimum cuts for palindrome partitioning using DP with palindrome precomputation. O(n^2) Python solution. Topics: dynamic-programming, string, divide-and-conquer Companies: amazon, google, facebook, stripe, palantir, jane-street, netflix Level: senior, staff DP with palindrome precomputation: Precompute is_pal[i][j] using DP. Then cuts[i] = 0 if s[:i+1] is palindrome, else min(cuts[j]+1) for valid palindrome suffix s[j+1:i+1]. Find longest arithmetic subsequence using DP with per-index difference hash maps. O(n^2) Python solution. Topics: dynamic-programming, hash-map, array Companies: amazon, google, apple, linkedin, stripe, adobe, paypal Level: swe3, senior, staff DP with hash maps per index: For each index i, maintain dict dp[i] mapping common difference to LAS length ending at i. For all j < i, dp[i][diff] = dp[j].get(diff, 1) + 1. Determine Stone Game III winner using minimax DP. O(n) Python solution for optimal two-player strategy. Topics: dynamic-programming, greedy, array Companies: google, amazon, facebook, jane-street, palantir, stripe, coinbase Level: senior, staff DP from right to left: dp[i] = max score current player gets from index i onward. For each choice k (1,2,3), score = sum of chosen + remaining total - dp[i+k] (opponent gets dp[i+k]). Compare dp[0] with total/2. Solve weighted interval scheduling for maximum profit using DP and binary search. O(n log n) Python solution. Topics: dynamic-programming, binary-search, sorting, heap Companies: google, amazon, facebook, linkedin, stripe, databricks, palantir Level: senior, staff DP with binary search on end times: Sort by end time. dp[i] = max profit using first i jobs. For job i, binary search the latest job j with end[j] <= start[i]. dp[i] = max(dp[i-1], dp[j]+profit[i]). Group strings that are anagrams using sorted key or frequency tuple hash map. Python solutions with complexity analysis. Topics: hash-map, string, sorting Companies: amazon, google, facebook, apple, uber, linkedin, stripe Level: new-grad, swe2, swe3 Sorted string as key: For each string, sort its characters to get the canonical key. Append original string to the group for that key. Frequency tuple as key: Use a 26-element count tuple as key, avoiding sort. O(n*k) time. Solve Two Sum for sorted arrays with two pointers, BST with in-order, and streaming data with hash set. Python solutions. Topics: hash-map, two-pointers, binary-search, array Companies: amazon, google, apple, facebook, uber, stripe, paypal Level: new-grad, swe2, swe3 Three variants implemented: Sorted: two pointers. BST: in-order into list then two pointers. Stream: maintain hash set, check complement on each add. Find all duplicate elements using array index as hash with sign marking. O(n) time O(1) space Python solution. Topics: hash-map, array, sorting Companies: amazon, google, apple, linkedin, adobe, oracle, paypal Level: swe2, swe3, senior Index as hash with negation: For each num, check sign at index abs(num)-1. If negative, num is a duplicate; add to result. Otherwise, negate it to mark visited. Sorting approach: Sort the array, then scan for adjacent duplicates. O(n log n) time, O(1) extra space but modifies input. Compute product of array except each element without division using prefix-suffix passes. O(n) Python solution. Topics: array, prefix-sum, two-pointers Companies: amazon, google, facebook, apple, linkedin, stripe, uber Level: new-grad, swe2, swe3 Two-pass prefix and suffix products: Left pass: output[i] = product of nums[:i]. Right pass: multiply output[i] by running product of nums[i+1:] tracked as a variable. Find maximum product subarray tracking both max and min products to handle negatives. O(n) Python solution. Topics: dynamic-programming, array Companies: amazon, google, facebook, apple, nvidia, linkedin, adobe Level: swe2, swe3, senior Track max and min product: At each element, the new max is max(num, num*cur_max, num*cur_min) and min is the corresponding min. Update global result. Find minimum in rotated sorted array with duplicates using binary search with duplicate-safe shrinking. Python solution. Topics: array, binary-search, divide-and-conquer Companies: amazon, google, facebook, apple, stripe, linkedin, oracle Level: swe3, senior, staff Binary search with duplicate handling: Standard binary search but when nums[mid] == nums[right], decrement right (cannot determine half). When nums[mid] > nums[right], min is in right half; else left half. Count subarrays with sum in [lower, upper] using merge sort on prefix sums. O(n log n) Python solution. Topics: array, prefix-sum, divide-and-conquer, sorting Companies: google, amazon, stripe, palantir, jane-street, databricks, nvidia Level: senior, staff Merge sort on prefix sums: Build prefix sums. Use merge sort: during merge, for each element in right half count elements in left half within [lower+r, upper+r] range using two pointers. This is the key cross-half count. Implement Tower of Hanoi for 3 pegs recursively and minimize moves for 4 pegs using Frame-Stewart DP. Python solutions. Topics: recursion, divide-and-conquer Companies: amazon, google, apple, stripe, jane-street, palantir, discord Level: swe3, senior, staff Classic 3-peg recursive + 4-peg Frame-Stewart: Recursively solve 3-peg. For 4-peg, try all split points k and use DP: min_moves4[n] = min over k of 2*min_moves4[k] + 2^(n-k)-1. Generate all valid bracket sequences with k types of brackets using backtracking with nesting stack. Python solution. Topics: recursion, backtracking, string Companies: google, amazon, facebook, stripe, palantir, discord, databricks Level: senior, staff Backtracking with nesting stack: Backtrack with current string, open count, and stack of open brackets. At each step, add any open bracket (if open < n) or add the closing bracket matching stack top. Move even elements before odd using two-pointer in-place or stable filter. Python solutions with complexity analysis. Topics: two-pointers, array, sorting Companies: amazon, google, apple, adobe, oracle, paypal, visa Level: new-grad, swe2 Two-pointer in-place (unstable): Left pointer finds next odd, right pointer finds next even. Swap them. Continue until left >= right. Filter partition (stable): Concatenate even elements followed by odd elements, maintaining original relative order within each group. Find all intersections of two sorted interval lists using two-pointer sweep. O(m+n) Python solution. Topics: two-pointers, interval, array Companies: amazon, google, facebook, apple, stripe, linkedin, discord Level: swe2, swe3, senior Two-pointer sweep: Use pointers i and j into both lists. Compute intersection as [max(starts), min(ends)]. If valid (start <= end), add to result. Advance pointer with smaller end. Find minimum single-letter transformations from begin to end word using BFS and bidirectional BFS. Python solutions. Topics: bfs, hash-map, graph, string Companies: amazon, google, facebook, apple, linkedin, stripe, airbnb Level: swe3, senior, staff BFS with neighbor generation: BFS from beginWord. For each word, try replacing each position with all 26 letters. If result is in word_set, add to queue and remove from set (visited). Return level when endWord found. Bidirectional BFS: BFS simultaneously from beginWord and endWord. At each step expand the smaller frontier. When frontiers intersect, return total steps. Halves search depth on average. Implement Bellman-Ford to find shortest paths with negative edge weights and detect negative cycles. Python solution. Topics: graph, dynamic-programming Companies: amazon, google, microsoft, imc, optiver, hrt Level: swe3, senior Bellman-Ford: Initialize dist[src]=0, others=inf. Relax every edge V-1 times. On pass V, if any relaxation succeeds, return [] (negative cycle). O(V*E) time. Implement Floyd-Warshall algorithm to compute shortest paths between all pairs of vertices. Python O(V^3) solution. Topics: graph, dynamic-programming, matrix Companies: google, microsoft, amazon, renaissance, imc, optiver Level: swe3, senior Floyd-Warshall DP: For each intermediate vertex k from 0 to V-1, update dist[i][j] = min(dist[i][j], dist[i][k]+dist[k][j]) for all i,j. After V iterations all shortest paths are found. Implement Kruskal's algorithm with Union-Find path compression to find the Minimum Spanning Tree. Python solution. Topics: graph, union-find, greedy, sorting Companies: google, amazon, microsoft, hrt, virtu, optiver Level: swe2, swe3, senior Kruskal's + Union-Find: Sort edges by weight. Use Union-Find with path compression. For each edge (u,v,w) in sorted order, if find(u) != find(v), add to MST and union(u,v). Stop after V-1 edges. Find all Strongly Connected Components using Kosaraju's two-pass DFS algorithm. Python implementation. Topics: graph, dfs Companies: google, meta, amazon, deepmind, anthropic Level: swe3, senior, staff Kosaraju's Two-Pass DFS: Build adjacency lists for original and transposed graphs. Pass 1: DFS on original, push to finish stack. Pass 2: pop from stack, DFS on transposed graph collecting each component. Find all bridge edges in an undirected graph using DFS with discovery time and low arrays. Python solution. Topics: graph, dfs Companies: google, amazon, microsoft, cloudflare, openai Level: swe3, senior, staff Tarjan's Bridge Finding: DFS with disc[] and low[] arrays. For each DFS tree edge (u,v), low[u] = min(low[u], low[v]). For back edges to ancestor, low[u] = min(low[u], disc[neighbor]). Bridge condition: low[v] > disc[u]. Check if a graph is bipartite using BFS 2-coloring. Handles disconnected graphs. Python solution. Topics: graph, bfs, dfs Companies: amazon, google, microsoft, spotify, canva Level: swe2, swe3 BFS 2-Coloring: For each unvisited vertex, BFS and assign alternating colors 0/1. If any neighbor already colored same as current, return False. Works on disconnected graphs. Solve the burst balloons problem using interval dynamic programming. The key insight: think about which balloon to burst LAST. Topics: dynamic-programming, divide-and-conquer Companies: google, amazon, meta, anthropic, openai, deepmind Level: senior, staff Interval DP: Pad array with 1s on both ends. dp[i][j] = max coins from range (i, j) exclusive. For each subproblem, try every k as the LAST balloon burst between i and j. Solve TSP optimally for small n using Held-Karp bitmask dynamic programming. Python O(2^n * n^2) solution. Topics: dynamic-programming, bit-manipulation, graph Companies: google, renaissance, imc, optiver, jane-street, citadel Level: senior, staff Held-Karp Bitmask DP: dp[mask][i] = min cost to reach i visiting all cities in mask. Start at city 0. Iterate over all masks in increasing order. Final answer: min dp[full_mask][i] + dist[i][0]. Implement regex matching with '.' and '*' using bottom-up 2D DP. Python solution to the classic hard interview problem. Topics: dynamic-programming, strings, recursion Companies: google, amazon, meta, microsoft, apple Level: swe3, senior Bottom-up DP: Build dp[len(s)+1][len(p)+1]. Base: dp[0][0]=True, handle leading '*' patterns. Transition: single char match or '.' → dp[i][j] = dp[i-1][j-1]. '*' → zero occurrences dp[i][j-2], or one+ if char matches dp[i-1][j]. Implement an LFU cache with O(1) get and put using three hash maps and OrderedDict. Python solution to the classic system design coding problem. Topics: lfu-cache, hash-map, design-patterns, object-design Companies: amazon, google, meta, microsoft, netflix, databricks, snowflake Level: senior, staff Three Hash Maps + OrderedDict: key_val: key->value. key_freq: key->frequency. freq_keys: freq->OrderedDict (insertion-order = LRU). min_freq tracks eviction target. All ops O(1) amortized. Implement a token bucket rate limiter with lazy refill strategy. Used in API gateways and Cloudflare. Python O(1) solution. Topics: rate-limiting, design-patterns, system-design-coding Companies: amazon, google, cloudflare, stripe, twilio, plaid, brex, retool Level: swe2, swe3, senior Lazy Refill Token Bucket: On each request, compute tokens to add since last call (elapsed * rate), cap at capacity. Deduct requested tokens if available. O(1) per call with no background thread needed. Implement consistent hashing with virtual nodes using a sorted ring and bisect. The algorithm behind DynamoDB and Cassandra. Python solution. Topics: hash-map, system-design-coding, design-patterns Companies: amazon, google, meta, databricks, snowflake, cloudflare, discord, rippling Level: swe3, senior, staff Sorted Ring + Bisect: Hash each virtual node position using MD5. Keep sorted list for O(log n) lookup via bisect. add_node inserts replicas entries; remove_node deletes them; get_node bisects to find nearest clockwise node. Implement KMP string search with LPS failure function. Achieves O(n+m) vs naive O(n*m). Python solution. Topics: strings, string-matching Companies: google, amazon, microsoft, bloomberg, adobe, canva, spotify Level: swe2, swe3, senior KMP with LPS table: Build LPS array in O(m). Then scan text with two pointers i (text) and j (pattern). On match advance both; on mismatch at j>0, set j=lps[j-1]; on full match record i-m and set j=lps[j-1]. Find the longest palindromic substring in O(n) using Manacher's algorithm. Python implementation with transform trick. Topics: strings, string-matching Companies: google, amazon, microsoft, meta, openai, deepmind Level: senior, staff Manacher's O(n): Transform string with '#' separators. Maintain center c and right boundary r. For each i, initialize p[i] from mirror if inside current palindrome. Expand around i. Update c,r when palindrome extends past r. Expand Around Center O(n^2): For each center (and each gap between chars), expand outward while characters match. Track global max. Simpler to implement but O(n^2) — shown for contrast. Implement Rabin-Karp rolling hash for string pattern matching. O(n+m) average. Python solution with collision handling. Topics: strings, string-matching, hash-map Companies: google, amazon, microsoft, bloomberg, anthropic, spotify Level: swe2, swe3, senior Rolling Hash: Use polynomial rolling hash with a large prime modulus. Slide window: remove leading char * high power, shift remaining left, add new char. Verify on hash match to handle collisions. Average O(n+m). Implement the Z-algorithm for linear-time string matching. Easier to implement than KMP, same O(n+m) complexity. Python solution. Topics: strings, string-matching Companies: google, amazon, microsoft, bloomberg, openai, deepmind Level: swe2, swe3, senior Z-Function: Build Z-array for pattern+"$"+text in O(n+m). Maintain l,r pointers. When Z[i] == m, record i - m - 1 as a match position in original text. Solve 3D trapping rain water using min-heap BFS from boundary inward. Python O(mn log(m+n)) solution. Topics: heap, matrix, bfs Companies: google, amazon, meta, microsoft, optiver, imc, hrt Level: senior, staff Min-Heap BFS from boundary: Initialize heap with all border cells. Visited set tracks processed cells. Pop min-height cell; for each unvisited neighbor, trapped water = max(0, current_level - neighbor_height). Push neighbor at max(current_level, neighbor_height). Find median of two sorted arrays in O(log(min(m,n))) using binary search on partition. Python solution to the classic hard problem. Topics: binary-search, array, divide-and-conquer Companies: google, amazon, meta, microsoft, apple, bloomberg, jane-street, renaissance Level: swe3, senior Binary Search on Partition: Ensure nums1 is smaller. Binary search i in [0, m]. j = half - i. Find i where nums1[i-1] <= nums2[j] AND nums2[j-1] <= nums1[i]. Compute median from the four boundary values. Count smaller elements to the right using merge sort inversion counting or Fenwick Tree. Python O(n log n) solutions. Topics: divide-and-conquer, sorting, binary-search, fenwick-tree Companies: google, amazon, meta, bloomberg, citadel, imc, optiver Level: swe3, senior Modified Merge Sort: Carry (value, original_index) pairs through merge sort. During merge, when right element placed before left elements, add (remaining left count) to each left element's count. O(n log n). Fenwick Tree (BIT): Coordinate compress values. Scan right to left. For each element, query BIT for sum of elements smaller than current (prefix sum up to current-1). Update BIT at current position. Find minimum window substring containing all target characters using sliding window. Classic hard interview problem. Python O(n) solution. Topics: sliding-window, hash-map, strings Companies: amazon, google, meta, microsoft, bloomberg, linkedin, spotify, canva Level: swe2, swe3, senior Sliding Window: Two pointers l, r. Expand r adding chars to window dict. When window covers t (have==need), record window and shrink l. Update have when shrinking makes a char unsatisfied. Find all words on a board using Trie + DFS backtracking with pruning. Python solution to the classic hard Trie problem. Topics: trie, backtracking, dfs, matrix Companies: amazon, google, meta, microsoft, bloomberg, anthropic, openai Level: swe3, senior, staff Trie + DFS Backtracking: Insert all words into Trie. For each board cell (r,c), DFS walking the Trie. On word end, add to result and prune Trie node. Mark cell as visited during DFS and restore after. Find the largest rectangle in a histogram using a monotonic stack in O(n). Python solution to the classic hard problem. Topics: stack, monotonic-stack, array Companies: amazon, google, meta, microsoft, bloomberg, optiver, virtu Level: swe2, swe3, senior Monotonic Stack: Append sentinel 0. For each bar, while stack top is taller than current bar, pop and compute area: height = popped bar, width = current_index - new_top - 1. Track global max. Design serialize/deserialize for a binary tree using DFS pre-order with null markers. Python solution to the classic hard design problem. Topics: binary-tree, bfs, dfs, design-patterns Companies: amazon, google, meta, microsoft, linkedin, databricks, rippling Level: swe3, senior DFS Pre-order: Serialize: DFS pre-order, append "N" for None. Join with ",". Deserialize: split by ",", use index pointer. If "N", return None. Else create node, recurse left then right. Maximize stock trading profit with 1-day cooldown using a DP state machine (held/sold/rest). Python O(n) solution. Topics: dynamic-programming, array Companies: amazon, google, bloomberg, goldman-sachs, adyen, klarna, brex Level: swe2, swe3 DP State Machine: Three states: held (best profit while holding), sold (best profit after selling today, triggers cooldown), rest (best profit while resting). Transitions: held stays or buy from rest; sold = sell held; rest = max rest or come from sold cooldown. Solve dynamic island counting after each land addition using Union-Find with path compression. Python O(k*alpha(n)) solution. Topics: union-find, matrix, graph Companies: amazon, google, meta, microsoft, bloomberg, canva, n26, adyen Level: swe3, senior Union-Find (DSU): DSU with path compression and union by rank on flattened cells. land set tracks added cells. For each position: add 1, check 4 neighbors; if land and different root, union and subtract 1. Implement a thread-safe counter using threading.Lock in Python. Prevent race conditions when incrementing from multiple threads. Topics: concurrency Companies: google, amazon, microsoft, meta Level: swe2, swe3 threading.Lock: Wrap the read-modify-write operation in a Lock. The with statement guarantees release even if an exception occurs. Implement producer-consumer pattern with threading.Queue in Python. Learn sentinel shutdown and daemon threads. Topics: concurrency, queue Companies: amazon, google, microsoft, netflix Level: swe2, swe3 threading.Queue with sentinels: Use threading.Queue for safe inter-thread communication. Each consumer exits when it receives None. Producers put real items then one sentinel per consumer. Implement a bounded resource pool with threading.Semaphore in Python. Limit concurrent access to shared resources. Topics: concurrency Companies: google, amazon, stripe, microsoft Level: swe3, senior threading.Semaphore: Semaphore(n) counts down to 0 on acquire and blocks there, releasing when release() is called. This bounds concurrency to n. Use asyncio.gather to fetch multiple URLs concurrently in Python. Learn async/await and event loop basics. Topics: concurrency Companies: google, meta, netflix, airbnb Level: swe2, swe3 asyncio.gather: Schedule all coroutines with asyncio.gather which runs them on the event loop concurrently. Total time is the max of individual times, not the sum. Build an async producer-consumer pipeline with asyncio.Queue. Python coroutines, task_done, and gather. Topics: concurrency, queue Companies: google, netflix, amazon, uber Level: swe3, senior asyncio.Queue with task_done: asyncio.Queue provides coroutine-safe communication. Producers put items; consumers call task_done after processing. q.join() waits for all items. Use concurrent.futures.ThreadPoolExecutor.map for parallel task execution in Python. I/O-bound parallel processing. Topics: concurrency Companies: amazon, google, microsoft, salesforce Level: new-grad, swe2 ThreadPoolExecutor.map: ThreadPoolExecutor manages a pool of threads. map() submits all tasks immediately and returns results in input order, blocking only when results are consumed. Use concurrent.futures.ProcessPoolExecutor for CPU-bound parallel tasks in Python. Bypass GIL with multiprocessing. Topics: concurrency Companies: google, amazon, nvidia, intel Level: swe3, senior ProcessPoolExecutor.map: ProcessPoolExecutor spawns separate Python interpreter processes. Each process runs is_prime independently on a CPU core, giving true parallel speedup for CPU-bound work. Implement async context managers with __aenter__ and __aexit__ in Python. Manage async resources safely. Topics: concurrency, oop Companies: google, airbnb, stripe, netflix Level: swe3, senior __aenter__ / __aexit__: Define async __aenter__ for setup and async __aexit__ for teardown. The runtime calls these automatically with "async with", guaranteeing cleanup. Use threading.Event and Condition to signal between threads in Python. Start gun pattern for concurrent workers. Topics: concurrency Companies: google, microsoft, amazon, bloomberg Level: swe3, senior threading.Event: threading.Event has internal flag. wait() blocks until the flag is True. set() turns it True and wakes all blocked threads simultaneously. Detect deadlocks using cycle detection on a resource allocation graph in Python. DFS-based wait-for graph algorithm. Topics: concurrency, graph, dfs Companies: google, microsoft, oracle, ibm Level: senior, staff DFS cycle detection on wait-for graph: Build adjacency list from wait-for edges. Run DFS with coloring: WHITE=0 unvisited, GRAY=1 in current path, BLACK=2 done. A back edge to GRAY node means cycle. Implement thread-safe Singleton pattern in Python using __new__ and double-checked locking. Topics: oop, design-patterns Companies: amazon, microsoft, google, oracle Level: new-grad, swe2 __new__ override: Override __new__ to check if _instance already exists. If not, create it via super().__new__. Subsequent calls return the existing instance. Implement Observer pattern in Python with subscribe/notify. Event-driven architecture using subject and observers. Topics: oop, design-patterns Companies: microsoft, amazon, google, salesforce Level: swe2, swe3 Classic Observer: Subject holds a list of observers. When state changes (via property setter), it iterates the list calling update(). Observers implement update() to react. Implement Strategy design pattern in Python with interchangeable sort algorithms. ABC-based pluggable behaviors. Topics: oop, design-patterns Companies: amazon, google, microsoft, stripe Level: new-grad, swe2 Strategy via ABC: Define SortStrategy ABC. Each concrete strategy implements sort(). Sorter delegates to strategy.sort() and can swap strategy at runtime. Implement Command pattern with undo/redo stacks in Python. Text editor operations with full reversibility. Topics: oop, design-patterns, stack Companies: microsoft, adobe, google, apple Level: swe2, swe3 Command with undo/redo stacks: Encapsulate each edit as a Command. Invoker keeps undo_stack and redo_stack. execute() runs the command and saves it; undo() reverses it and moves to redo_stack. Implement Builder pattern with method chaining in Python. Fluent HTTP request builder with validation. Topics: oop, design-patterns Companies: stripe, google, amazon, netflix Level: new-grad, swe2 Fluent Builder: Each setter method stores data and returns self for chaining. build() validates and constructs the immutable result object. Implement logging and timing decorators in Python using functools.wraps. Stackable structural Decorator pattern. Topics: oop, design-patterns, decorators Companies: google, amazon, meta, netflix Level: new-grad, swe2 functools.wraps decorators: Each decorator is a function returning a wrapper. functools.wraps preserves the original function metadata. Stack with @timed @logged syntax. Implement Factory Method pattern in Python with a registry-based shape factory. Creational design pattern. Topics: oop, design-patterns Companies: amazon, microsoft, google, oracle Level: new-grad, swe2 Registry-based Factory: A registry dict maps type strings to classes. Factory.create looks up the class and calls it with **kwargs. Adding new shapes only requires updating the registry. Implement Abstract Factory pattern for cross-platform UI widgets in Python. ABC-based family of related objects. Topics: oop, design-patterns Companies: microsoft, apple, google, amazon Level: swe2, swe3 Abstract Factory with ABC: UIFactory ABC declares creation methods. Two concrete factories implement all methods returning platform widgets. Client only imports UIFactory - swapping factory changes entire widget family. Implement Template Method design pattern for a data pipeline in Python. Fix the algorithm skeleton in base class. Topics: oop, design-patterns Companies: amazon, google, databricks, snowflake Level: swe2, swe3 Template Method ABC: Base DataPipeline.run() calls abstract read(), optional transform(), abstract write() in sequence. Subclasses implement required abstract methods and optionally override transform(). Implement Flyweight pattern for shared glyph objects in Python. Separate intrinsic and extrinsic state. Topics: oop, design-patterns Companies: adobe, microsoft, google, apple Level: swe3, senior Flyweight with factory cache: GlyphFactory caches Glyph objects keyed by (char, font, size). Repeated get() calls return the same object. render() takes x,y extrinsic state without storing it. Implement Chain of Responsibility as HTTP middleware in Python. Linked handler chain with fluent API. Topics: oop, design-patterns Companies: amazon, google, stripe, netflix Level: swe2, swe3 Linked handler chain: Handler ABC with set_next for fluent linking. Each handler inspects the request and either processes it or calls self._next.handle(). Fluent chaining: auth.set_next(log).set_next(final). Implement Python iterator protocol with __iter__ and __next__. Custom range class and generator comparison. Topics: oop, generators Companies: google, amazon, microsoft, meta Level: new-grad, swe2 Iterator protocol + generator: __iter__ returns self. __next__ increments current and raises StopIteration at end. Generator version is cleaner: yield each value in a loop. Implement __enter__ and __exit__ for a database transaction context manager in Python. Commit/rollback pattern. Topics: oop, design-patterns Companies: stripe, amazon, google, microsoft Level: swe2, swe3 __enter__/__exit__ + contextmanager: __enter__ begins transaction and returns self. __exit__ checks exc_type: None means commit, non-None means rollback. contextmanager version splits on yield. Implement Python descriptor protocol with __get__, __set__, __set_name__ for validated attributes. Topics: oop, type-hints Companies: google, microsoft, amazon, stripe Level: swe3, senior Data Descriptor with __set_name__: __set_name__ captures attribute name automatically. __set__ validates and stores in instance.__dict__ under a private key. __get__ retrieves from the same private key. Use Python metaclass to auto-register subclasses. Plugin architecture with __init_subclass__ and RegistryMeta. Topics: oop Companies: google, stripe, amazon, deepmind Level: senior, staff Metaclass registry + __init_subclass__ alternative: RegistryMeta.__new__ adds each new class to registry dict, skipping the base. __init_subclass__ achieves the same without a metaclass and is preferred in modern Python. Build functools.lru_cache from scratch using OrderedDict in Python. LRU eviction, decorator pattern. Topics: functools, lru-cache, hash-map, design-patterns Companies: google, meta, amazon, microsoft Level: swe3, senior OrderedDict LRU: Wrap function in a closure with an OrderedDict. On hit: move to end (most recent). On miss: call function, add to end; if over capacity, popitem(last=False) removes LRU. Use functools.reduce for fold and scan operations in Python. Product, max, scan with accumulate. Topics: functools, recursion Companies: google, amazon, microsoft, jane-street Level: new-grad, swe2 functools.reduce examples: reduce applies binary function cumulatively. For scan, itertools.accumulate is the idiomatic choice. Use itertools.groupby to group consecutive elements in Python. Run-length encoding and key-based grouping. Topics: itertools, strings Companies: google, amazon, microsoft, bloomberg Level: new-grad, swe2 itertools.groupby: groupby yields (key, group_iterator) pairs. Consume group with list() immediately before next iteration. For RLE: key is char, group count gives run length. Use itertools.combinations and permutations for combinatorial enumeration in Python. Topics: itertools, combinatorics Companies: google, amazon, jane-street, two-sigma Level: new-grad, swe2 itertools combinatorics: itertools provides lazy generators for all combinatorial arrangements. Convert to list only when needed to avoid memory issues with large n. Use collections.Counter for top-K frequency, anagram detection, and grouping in Python. Topics: collections, hash-map, heap Companies: google, amazon, meta, microsoft Level: new-grad, swe2 collections.Counter: Counter is a dict subclass for frequency counting. most_common(k) uses heapq internally. Anagram check: Counter equality. Grouping: use sorted counter items as key. Use collections.defaultdict for nested dicts, adjacency lists, and frequency maps in Python. Topics: collections, hash-map Companies: amazon, google, microsoft, meta Level: new-grad, swe2 defaultdict variants: defaultdict avoids KeyError and if-key-not-in-dict boilerplate. Nest with lambdas for multi-level grouping. Implement LRU Cache with collections.OrderedDict in Python. O(1) get and put with move_to_end. Topics: collections, lru-cache, hash-map Companies: google, amazon, meta, microsoft Level: swe2, swe3 OrderedDict LRU: OrderedDict preserves insertion/access order. move_to_end() marks as recently used. popitem(last=False) removes LRU. Both ops are O(1). Use heapq.nlargest and nsmallest for top-K queries in Python. Streaming top-K with min-heap of size k. Topics: heap, collections Companies: google, amazon, meta, bloomberg Level: new-grad, swe2 heapq.nlargest + streaming min-heap: heapq.nlargest is convenient for batch. For streaming, maintain a min-heap of size k: push new element, pop if size exceeds k. Final heap contains k largest. Use Python bisect module for binary search on sorted lists. bisect_left, bisect_right, insort operations. Topics: binary-search, sorting Companies: google, amazon, microsoft, bloomberg Level: new-grad, swe2 bisect module operations: bisect provides O(log n) binary search. insort inserts while maintaining sort. rank = bisect_right gives count of elements <= val. Use Python dataclasses with __slots__ for memory-efficient record objects. Compare memory with and without slots. Topics: oop, type-hints Companies: google, amazon, stripe, databricks Level: swe2, swe3 dataclass + __slots__: Regular dataclass has __dict__ overhead. Adding __slots__ = ("x","y","z") eliminates it. Python 3.10+ @dataclass(slots=True) automates this. Implement AVL tree insertion with LL, RR, LR, RL rotations in Python. Self-balancing BST O(log n). Topics: tree, binary-tree, recursion Companies: google, amazon, microsoft, oracle Level: swe3, senior AVL rotations: Recursively insert, update height, check balance factor. Apply single or double rotation based on imbalance case. Return new subtree root after each rotation. Implement Red-Black Tree insertion with color flips and rotations in Python. RB tree invariants and fixup. Topics: tree, binary-tree Companies: google, microsoft, amazon, oracle Level: senior, staff RB Tree insertion with fixup: Insert as in BST with red color. Fix up: if uncle is red, recolor and move up. If uncle is black, rotate toward uncle then away. Set root black at end. Implement B-Tree search and insert in Python. Disk-friendly multi-way search tree for database indexes. Topics: tree, binary-search Companies: oracle, microsoft, amazon, databricks Level: senior, staff B-Tree search and insert: Search descends by finding insertion point in keys array. Insert splits full nodes proactively on the way down to keep tree balanced. Build a Segment Tree for range sum queries and point updates in Python. O(n) build, O(log n) operations. Topics: segment-tree, tree Companies: google, amazon, microsoft, two-sigma Level: swe3, senior Array-based Segment Tree: Store tree in array with 1-based indexing. Left child = 2*i, right = 2*i+1. Build bottom-up. Query splits range; update propagates changes up. Segment tree with lazy propagation for O(log n) range updates and range queries in Python. Topics: segment-tree, tree Companies: google, two-sigma, citadel, bloomberg Level: senior, staff Lazy Propagation Segment Tree: lazy[node] holds pending addition. Before recursing, push lazy down to children. On range update, if segment is fully covered, update tree and lazy without recursing. Implement Fenwick Tree (Binary Indexed Tree) for O(log n) point updates and prefix sum queries in Python. Topics: fenwick-tree, prefix-sum Companies: google, amazon, two-sigma, jane-street Level: swe3, senior Fenwick Tree LSB trick: BIT stores partial sums indexed by LSB ranges. Update propagates up by adding LSB. Query accumulates down by stripping LSB. Convert to 1-indexed internally. Implement 2D Fenwick Tree for O(log m log n) point updates and rectangle sum queries in Python. Topics: fenwick-tree, matrix, prefix-sum Companies: google, two-sigma, citadel, amazon Level: senior, staff 2D BIT: Nested BIT: outer BIT over rows, inner BIT over columns. Each update touches O(log m * log n) cells. Prefix sum uses double loop stripping LSB. Implement Trie with insert, search, and startsWith in Python. Prefix tree for string matching. Topics: trie, strings Companies: google, amazon, meta, microsoft Level: swe2, swe3 Dict-based Trie: Each node holds a dict mapping char to child TrieNode. insert builds path. search checks path exists AND is_end. startsWith only checks path exists. Implement Trie deletion with recursive pruning in Python. Remove nodes no longer needed after word deletion. Topics: trie, strings, recursion Companies: google, amazon, microsoft, meta Level: swe3, senior Post-order recursive delete: Recurse to end of word. Unmark is_end. On the way back, remove child reference if child has no children and is not a word end. Return True if current node is now deletable. Implement autocomplete with Trie and DFS in Python. Find all words with a prefix, ranked by frequency. Topics: trie, dfs, strings Companies: google, amazon, meta, linkedin Level: swe2, swe3 Trie DFS autocomplete: Insert with frequency. For suggest, navigate to prefix node. DFS collects all (freq, word) pairs below. Sort by (-freq, word) and return top k. Build a suffix array in O(n log^2 n) using prefix doubling in Python. Foundation for string matching algorithms. Topics: string-matching, sorting, divide-and-conquer Companies: google, amazon, bloomberg, two-sigma Level: senior, staff Prefix doubling O(n log^2 n): Assign initial ranks from chars. Repeatedly double the comparison window, sorting by (rank[i], rank[i+gap]). Reassign ranks. Stop when all unique. Build Sparse Table for O(1) range minimum queries after O(n log n) preprocessing in Python. Topics: divide-and-conquer, prefix-sum Companies: google, two-sigma, citadel, imc Level: senior, staff Sparse Table O(1) RMQ: Precompute table[k][i] = min of 2^k elements from i. Query uses k = log2(r-l+1); take min of two overlapping windows of that size. Build a Cartesian tree from an array in O(n) using a stack. Combines BST index property with min-heap value property. Topics: tree, binary-tree, stack Companies: google, two-sigma, citadel, bloomberg Level: senior, staff Stack-based O(n) construction: Maintain a stack of right-spine nodes. For each new element, pop nodes with larger values (they become left children). New node becomes right child of new top. Implement Splay Tree with zig, zig-zig, zig-zag rotations in Python. Amortized O(log n) self-adjusting BST. Topics: tree, binary-tree Companies: google, two-sigma, jane-street, renaissance Level: senior, staff Splay Tree with parent pointers: After every access, splay the accessed node to root. Three rotation cases handle all relative positions of node, parent, and grandparent. Implement Link-Cut Tree for dynamic tree operations in Python. Link, cut, and path queries in O(log n) amortized. Topics: tree, graph, union-find Companies: google, two-sigma, jane-street, deepmind Level: staff Link-Cut Tree with splay auxiliary trees: LCT decomposes dynamic forest into preferred paths represented by splay trees. access(v) makes a path from v to root preferred. Operations compose to O(log n) amortized. Solve the egg drop problem with optimized DP in Python. Find minimum trials with k eggs and n floors. Topics: dynamic-programming, binary-search Companies: google, amazon, microsoft, bloomberg Level: swe3, senior DP reformulation O(k log n): Reframe: dp[k][t] = max floors checkable with k eggs in t moves. Recurrence: dp[k][t] = dp[k-1][t-1] + dp[k][t-1] + 1. Find smallest t where dp[k][t] >= n. Find minimum cuts for palindrome partitioning using DP in Python. Precompute palindrome table and minimize cuts. Topics: dynamic-programming, string-matching Companies: google, amazon, microsoft, meta Level: swe3, senior DP with palindrome table: Precompute is_pal[i][j] by expanding from center. Then cuts[i] = min number of cuts for s[:i+1]. For each i, try all j: if s[j..i] is palindrome, cuts[i] = min(cuts[i], cuts[j-1]+1). Solve wildcard pattern matching with ? and * using DP in Python. O(mn) solution with 2D table. Topics: dynamic-programming, string-matching Companies: google, amazon, facebook, microsoft Level: swe3, senior DP O(mn): dp[i][j] means p[:j] matches s[:i]. For each cell: char match or ? gives dp[i-1][j-1]; * gives dp[i-1][j] (consume one s char) or dp[i][j-1] (use * as empty). Compute Levenshtein edit distance with DP and backtrack the edit operations in Python. Topics: dynamic-programming, string-matching Companies: google, amazon, microsoft, meta Level: swe2, swe3 DP + backtrack: Standard edit distance DP. For backtrack, start from dp[m][n] and trace back: if chars matched, go diagonal; else find which operation was cheapest. Find the longest common substring (contiguous) of two strings using DP in Python. O(mn) solution. Topics: dynamic-programming, strings Companies: google, amazon, microsoft, bloomberg Level: swe2, swe3 DP table O(mn): dp[i][j] = longest common substring ending at s1[i-1],s2[j-1]. Reset to 0 on mismatch. Track max and its position to extract the result. Find longest palindromic subsequence using interval DP in Python. LPS via LCS or direct DP. Topics: dynamic-programming, strings Companies: amazon, google, microsoft, meta Level: swe2, swe3 Interval DP: dp[i][j] = LPS length in s[i..j]. Base: dp[i][i]=1. If s[i]==s[j]: dp[i][j]=dp[i+1][j-1]+2. Else max(dp[i+1][j], dp[i][j-1]). Fill by increasing length. Count distinct subsequences of s equal to t using DP in Python. O(mn) solution. Topics: dynamic-programming, strings Companies: google, amazon, meta, microsoft Level: swe3, senior DP O(mn): dp[i][j] = ways to form t[:j] from s[:i]. On char match, we can either use s[i] (add dp[i-1][j-1]) or skip it (add dp[i-1][j]). On mismatch, only skip. Solve Stone Game with interval DP and mathematical insight in Python. Optimal play game theory. Topics: dynamic-programming, math Companies: google, amazon, jane-street, two-sigma Level: swe2, swe3 DP interval + math insight: Mathematical: Alice always wins (return True). DP proof: dp[i][j] = best score difference for current player over opponent. If dp[0][n-1] > 0, first player wins. Solve strange printer problem with interval DP in Python. Minimum printing operations. Topics: dynamic-programming Companies: google, amazon, microsoft, meta Level: senior, staff Interval DP: dp[i][j] = min turns to print s[i..j]. Start with 1 turn per character. If s[k]==s[j], we can merge the j-th char printing into the k-th range, saving a turn. Count valid music playlists with constraints using DP in Python. Song replay restriction with modular arithmetic. Topics: dynamic-programming, combinatorics Companies: google, amazon, spotify, netflix Level: swe3, senior DP with song count constraint: dp[i][j] = playlists of exactly i songs using j distinct songs. Transitions: add new song (n-j+1 choices) or replay old (max(j-k,0) choices since k songs blocked). Solve Cherry Pickup II with two robots using 3D DP in Python. Maximize cherries collected simultaneously. Topics: dynamic-programming, matrix Companies: google, amazon, microsoft, meta Level: senior, staff 3D DP row by row: dp[c1][c2] = max cherries when robots are at columns c1 and c2 at the current row. Process row by row, trying all 9 movement combinations. Solve painting the walls problem with knapsack DP in Python. Minimize cost with free painter credits. Topics: dynamic-programming Companies: google, amazon, microsoft, meta Level: swe3, senior Knapsack DP: dp[j] = min cost to cover exactly j walls. For each wall i, it covers time[i]+1 walls at cost[i]. Fill from right like 0/1 knapsack. Count good strings of given length range using DP with modular arithmetic in Python. Topics: dynamic-programming, math Companies: google, amazon, meta, microsoft Level: swe2, swe3 DP over lengths: dp[i] = number of ways to form a string of exactly length i. Add zero-block or one-block to shorter strings. Sum dp[low..high]. Solve minimum cost to cut a stick with interval DP in Python. Optimize cut order for minimum total cost. Topics: dynamic-programming, intervals Companies: google, amazon, microsoft, two-sigma Level: swe3, senior Interval DP: Add boundaries 0 and n. Sort cuts. dp[i][j] = min cost to cut all positions strictly between cuts[i] and cuts[j]. Try each cut k as the last cut in this interval. Solve maximum profit job scheduling with DP and binary search in Python. Weighted interval scheduling O(n log n). Topics: dynamic-programming, binary-search, intervals Companies: google, amazon, microsoft, bloomberg Level: swe3, senior DP + binary search: Sort jobs by endTime. dp[i] = max profit with first i jobs. For each job, binary search for latest non-overlapping job j (end[j] <= start[i]). dp[i] = max(dp[i-1], profit[i] + dp[j]). Implement Sieve of Eratosthenes to find all primes up to N in Python. O(n log log n) prime enumeration. Topics: math, number-theory Companies: google, amazon, microsoft, jane-street Level: new-grad, swe2 Sieve of Eratosthenes: Initialize all as prime. For each prime p, mark p^2, p^2+p, p^2+2p... as composite. Only iterate p up to sqrt(N). Implement prime factorization with trial division and smallest prime factor sieve in Python. Topics: math, number-theory Companies: google, amazon, jane-street, two-sigma Level: new-grad, swe2 Trial division + SPF sieve: Trial division: divide out 2 then odd numbers up to sqrt(n). If n>1 remains, it is prime. SPF sieve enables fast batch factorization. Implement Extended Euclidean Algorithm to find GCD and Bezout coefficients in Python. Topics: math, number-theory Companies: google, jane-street, two-sigma, imc Level: swe2, swe3 Extended Euclidean recursive: Recurse with extended_gcd(b, a%b). Unwind: x = y1, y = x1 - (a//b)*y1. Verify: a*x + b*y == gcd. Implement modular exponentiation using binary fast power in Python. O(log n) exponentiation. Topics: math, number-theory, bit-manipulation Companies: google, amazon, jane-street, two-sigma Level: new-grad, swe2 Binary exponentiation iterative: Process bits of exp from LSB to MSB. If bit is set, multiply result by current base. Square the base at each step. Compute modular inverse using Fermat little theorem and Extended GCD in Python. Topics: math, number-theory Companies: google, jane-street, two-sigma, imc Level: swe2, swe3 Fermat + Extended GCD: Fermat: a^(p-1) ≡ 1 (mod p) => a^(p-2) ≡ a^(-1) (mod p). ExtGCD: solve a*x + m*y = 1; x mod m is the inverse. Solve system of congruences using Chinese Remainder Theorem in Python. CRT implementation. Topics: math, number-theory Companies: jane-street, two-sigma, google, renaissance Level: senior, staff CRT construction: Compute M = product of all moduli. For each congruence i, compute Mi=M/mi and its inverse yi mod mi. Solution = sum(ri * Mi * yi) mod M. Compute Catalan numbers with DP and closed formula in Python. Count BSTs, parenthesizations. Topics: math, combinatorics, dynamic-programming Companies: google, amazon, jane-street, microsoft Level: swe2, swe3 DP + closed form: DP: C[n] = sum of C[i]*C[n-1-i]. Formula: C(n) = C(2n,n)/(n+1). Both give same result; formula is O(n) with big integer arithmetic. Compute C(n,r) mod prime p using factorial precomputation and Lucas theorem in Python. Topics: math, combinatorics, number-theory Companies: google, jane-street, two-sigma, renaissance Level: senior, staff Factorial precompute + Lucas: Precompute factorials and modular inverses up to MAXN. C(n,r) = fact[n] * inv_fact[r] * inv_fact[n-r] mod p. Lucas handles n >= p by recursing on digits base-p. Compute nth Fibonacci in O(log n) using matrix exponentiation in Python. Generalize to any linear recurrence. Topics: math, divide-and-conquer Companies: google, amazon, jane-street, two-sigma Level: swe3, senior Matrix exponentiation: Define matrix mult. Apply binary exponentiation to matrix [[1,1],[1,0]]. Extract F(n) from result[0][1]. Multiply polynomials in O(n log n) using FFT in Python. Cooley-Tukey recursive FFT implementation. Topics: math, divide-and-conquer Companies: google, jane-street, two-sigma, renaissance Level: staff Cooley-Tukey FFT: Recursive Cooley-Tukey: split into even/odd, recurse, combine with twiddle factors. Inverse FFT conjugates twiddle and divides by n. Pointwise multiply in frequency domain. Implement a Bloom filter with optimal parameters in Python. Space-efficient probabilistic data structure. Topics: system-design-coding, bit-manipulation, hash-map Companies: google, amazon, meta, databricks Level: senior, staff Bloom filter with optimal k and m: Compute optimal bit count m = -n*ln(p)/ln(2)^2 and hash count k = (m/n)*ln(2). Use k independent hash functions (seed variants of Python hash). Track bit array as bytearray. Implement Skip List with random levels for O(log n) search, insert, delete in Python. Topics: system-design-coding, design-patterns Companies: google, amazon, redis, databricks Level: senior, staff Skip list with random levels: Header node links at all levels. Search descends levels. Insert finds update[] pointers, generates random level, splices in node. Delete finds and removes node from all levels. Build trie-based autocomplete with per-node top-k frequency cache in Python. Production-ready design. Topics: trie, system-design-coding, heap Companies: google, amazon, meta, linkedin Level: swe3, senior Trie with per-node top-k cache: Each node caches top-k (freq, word) pairs sorted by freq. On insert, traverse and update each node's heap. Query just returns the prefix node's cached list. Implement Write-Ahead Log for crash recovery in Python. Append, checkpoint, and replay WAL entries. Topics: system-design-coding Companies: amazon, google, databricks, snowflake Level: senior, staff WAL with checkpoint and replay: Append log entries with monotonically increasing LSN. Checkpoint saves state snapshot and LSN. Recovery restores checkpoint state then replays all log entries after checkpoint LSN. Implement Merkle Tree for data integrity verification in Python. Build, proof generation, and verification. Topics: system-design-coding, tree Companies: amazon, google, stripe, databricks Level: senior, staff Bottom-up Merkle tree: Compute leaf hashes. Repeatedly hash adjacent pairs (duplicate last if odd) until one root. Store all levels for proof generation. Proof = sibling hashes from leaf to root. Build an inverted index and support AND/OR queries in Python. Foundation of search engines. Topics: system-design-coding, hash-map, strings Companies: google, amazon, elasticsearch, linkedin Level: swe3, senior Inverted index with merge-based AND/OR: Index maps term to sorted doc_id list. AND: intersect posting lists with two-pointer. OR: merge sorted lists with set. Start AND with smallest list for efficiency. Implement Count-Min Sketch for streaming top-K heavy hitters in Python. Probabilistic frequency estimation. Topics: system-design-coding, hash-map Companies: google, amazon, meta, twitter Level: senior, staff Count-Min Sketch + heap top-K: For each of d rows, hash item to column and increment. Query returns minimum across all rows (overcount is possible, undercount is not). Combine with a counter for exact top-K in small domains. Implement sliding window rate limiter with deque in Python. Accurate per-second request limiting. Topics: rate-limiting, system-design-coding, queue Companies: stripe, amazon, google, netflix Level: swe3, senior Deque-based sliding window: Deque stores timestamps of recent requests. On each request, evict timestamps outside the window. If remaining count < limit, allow and record; otherwise deny. Implement Twitter Snowflake 64-bit distributed ID generator in Python. Time-sortable unique IDs. Topics: system-design-coding, bit-manipulation Companies: twitter, amazon, meta, linkedin Level: senior, staff Snowflake 64-bit ID: Shift timestamp left by 22 bits, machine_id by 12 bits, OR with sequence. If same millisecond, increment sequence; overflow -> busy-wait for next ms. Implement event sourcing with append-only log, snapshot, and time-travel in Python. Topics: system-design-coding Companies: amazon, google, stripe, confluent Level: senior, staff Event sourcing with snapshots: Append-only event log. get_state replays all events or from last snapshot. Snapshot saves current state at event index. state_at replays events 0..t from nearest snapshot before t. Compute convex hull using Graham Scan in Python. O(n log n) algorithm with cross product and stack. Topics: geometry, sorting Companies: google, amazon, nvidia, deepmind Level: swe3, senior Graham Scan: Find lowest y (then leftmost x) point. Sort rest by polar angle. Maintain stack: pop while cross product <= 0 (right turn or collinear). Stack is the hull. Test if two line segments intersect using cross product orientation in Python. Handles collinear cases. Topics: geometry, math Companies: google, nvidia, amazon, deepmind Level: swe3, senior Orientation-based intersection test: Four orientation checks determine general intersection. Special cases: collinear points handled by on_segment check. Find closest pair of points in O(n log n) using divide and conquer in Python. Strip optimization. Topics: geometry, divide-and-conquer, sorting Companies: google, amazon, two-sigma, nvidia Level: senior, staff Divide and Conquer O(n log n): Sort by x. Divide at mid. Recurse on both halves. Get d = min(d_left, d_right). Check strip |x - mid_x| < d sorted by y; compare at most 7 forward neighbors. Find two single numbers in array using XOR partitioning in Python. O(n) O(1) bit manipulation. Topics: bit-manipulation Companies: google, amazon, microsoft, meta Level: swe2, swe3 XOR partition trick: XOR all to get a^b. Isolate LSB of a^b. Partition: numbers with that bit set vs not. XOR each partition to extract a and b. Reverse all 32 bits of an integer in Python. Bit-by-bit reversal with 32-bit mask. Topics: bit-manipulation Companies: apple, google, amazon, microsoft Level: new-grad, swe2 Bit-by-bit reversal: Loop 32 times. Each iteration: shift result left 1, OR in LSB of n, shift n right 1. Mask to 32 bits at end. Count set bits (Hamming weight) using Brian Kernighan trick in Python. O(k) where k is popcount. Topics: bit-manipulation Companies: apple, google, amazon, microsoft Level: new-grad, swe2 Brian Kernighan trick: Repeatedly clear the lowest set bit with n &= (n-1). Count iterations. This is O(k) where k is popcount, better than O(32) for sparse bits. Master bit manipulation tricks in Python: swap, LSB, power of 2, set/clear bits, missing number. Topics: bit-manipulation, math Companies: google, amazon, microsoft, apple Level: swe2, swe3 Bit manipulation toolkit: Collection of O(1) bit tricks. Each operation uses XOR, AND, OR, shift in a single expression. Implement XOR linked list with ctypes in Python. Memory-efficient doubly linked list using XOR pointers. Topics: bit-manipulation, linked-list Companies: google, amazon, microsoft, apple Level: senior, staff XOR linked list with ctypes: Store XOR of prev/next id in each node. Anchor nodes in a list to prevent GC. Use ctypes.cast to recover object from id. Traverse by XORing stored id with known prev id. Generate n-bit Gray codes using XOR formula in Python. Adjacent codes differ by exactly one bit. Topics: bit-manipulation, math Companies: apple, google, amazon, microsoft Level: swe2, swe3 Formula: i XOR (i>>1): Direct formula: gray(i) = i ^ (i >> 1). Generate all 2^n values. Verify adjacency property. Decode with running XOR from MSB. Enumerate all 2^n subsets using bitmask iteration in Python. O(n * 2^n) iterative approach. Topics: bit-manipulation, backtracking Companies: google, amazon, microsoft, meta Level: new-grad, swe2 Bitmask enumeration: For each mask in 0..2^n-1, include nums[i] if bit i is set. Result has 2^n subsets in consistent order. Find Eulerian path and circuit with Hierholzer's algorithm in Python. O(E) directed graph traversal. Topics: graph, dfs Companies: google, amazon, microsoft, bloomberg Level: swe3, senior Hierholzer's algorithm: Build adjacency list. Find start node (out > in or node 0 for circuit). Iterative DFS: push to stack, follow edges. When node has no more edges, pop to result. Reverse result. Find Hamiltonian path using backtracking with pruning in Python. NP-complete graph problem. Topics: graph, backtracking Companies: google, amazon, microsoft, two-sigma Level: senior, staff Backtracking with pruning: Build adjacency set. DFS from each start vertex. At each step try unvisited neighbors. Backtrack when no neighbors available and path is incomplete. Find maximum flow using Edmonds-Karp algorithm in Python. BFS-based Ford-Fulkerson O(VE^2). Topics: graph, bfs Companies: google, amazon, microsoft, two-sigma Level: senior, staff Edmonds-Karp BFS: Build residual graph. BFS to find shortest augmenting path. Augment by bottleneck. Repeat. Total flow = sum of augmentations. Implement Hungarian algorithm for minimum weight bipartite matching in Python. O(n^3) assignment problem. Topics: graph, dynamic-programming Companies: google, amazon, two-sigma, renaissance Level: staff Hungarian algorithm O(n^3): Use scipy for clean O(n^3) solution. Manual implementation uses potential arrays and augmenting paths. Both return same optimal assignment. Find articulation points using Tarjan low-link algorithm in Python. O(V+E) cut vertex detection. Topics: graph, dfs Companies: google, amazon, microsoft, bloomberg Level: senior, staff Tarjan low-link DFS: DFS assigns discovery times. low[u] = min reachable discovery time from subtree of u. Articulation point: root with 2+ DFS children, or non-root where any child v has low[v] >= disc[u].Reverse a String - Python Solution | Engineers of AI
Count Vowels in a String - Python Solution | Engineers of AI
Check Palindrome - Python Solution | Engineers of AI
FizzBuzz - Python Solution | Engineers of AI
Find Duplicates in a List - Python Solution | Engineers of AI
Flatten a Nested List - Python Solution | Engineers of AI
List Comprehension Filter and Transform - Python | Engineers of AI
Word Frequency Counter - Python Solution | Engineers of AI
Implement a Stack Using a List - Python Solution | Engineers of AI
Implement a Queue Using Deque - Python Solution | Engineers of AI
BankAccount Class - Python OOP Solution | Engineers of AI
Decorator: Timing Function - Python Solution | Engineers of AI
Fibonacci Generator - Python Solution | Engineers of AI
Context Manager for File Handling - Python Solution | Engineers of AI
Filter Evens with Lambda and Filter - Python Solution | Engineers of AI
Email Validator with Regex - Python Solution | Engineers of AI
String Formatting: Format a Receipt - Python Solution | Engineers of AI
Read and Count Lines from a File - Python Solution | Engineers of AI
Custom Exception Classes - Python Solution | Engineers of AI
Type-Hinted Stack Implementation - Python Solution | Engineers of AI
Zip and Enumerate Together - Python Solution | Engineers of AI
Default Mutable Argument Bug - Python Solution | Engineers of AI
*args and **kwargs Variadic Functions - Python Solution | Engineers of AI
Closure Counter - Python Solution | Engineers of AI
Inheritance: Shape Hierarchy - Python Solution | Engineers of AI
Abstract Base Class: Animal - Python Solution | Engineers of AI
Custom Iterator: Countdown - Python Solution | Engineers of AI
Property Decorator: Temperature Converter - Python Solution | Engineers of AI
Named Tuples: Point and Distance - Python Solution | Engineers of AI
Dataclass: Student Registry - Python Solution | Engineers of AI
Two Sum - Python Hash Map Solution | Engineers of AI
Best Time to Buy and Sell Stock - Greedy Python Solution | Engineers of AI
Contains Duplicate - Python Set Solution | Engineers of AI
Product of Array Except Self - Python Solution | Engineers of AI
Maximum Subarray - Kadane's Algorithm Python | Engineers of AI
Maximum Product Subarray - Python Solution | Engineers of AI
Find Minimum in Rotated Sorted Array - Python Solution | Engineers of AI
Search in Rotated Sorted Array - Python Solution | Engineers of AI
Three Sum - Python Two Pointers Solution | Engineers of AI
Container With Most Water - Python Two Pointers | Engineers of AI
Valid Anagram - Python Solution | Engineers of AI
Group Anagrams - Python Solution | Engineers of AI
Longest Common Prefix - Python Solution | Engineers of AI
Valid Parentheses - Python Stack Solution | Engineers of AI
Reverse Words in a String - Python Solution | Engineers of AI
String Compression - Python Solution | Engineers of AI
Rotate Array - Python Three Reverses Solution | Engineers of AI
Missing Number - Python Math and XOR Solutions | Engineers of AI
Single Number XOR Trick - Python Solution | Engineers of AI
Move Zeroes - Python Two Pointers Solution | Engineers of AI
Merge Intervals - Python Sort Solution | Engineers of AI
Insert Interval - Python Solution | Engineers of AI
Spiral Matrix - Python Boundary Simulation | Engineers of AI
Set Matrix Zeroes - Python O(1) Space Solution | Engineers of AI
Longest Substring Without Repeating Characters - Python | Engineers of AI
Minimum Window Substring - Python Sliding Window | Engineers of AI
Find All Anagrams in a String - Python Sliding Window | Engineers of AI
Subarray Sum Equals K - Python Prefix Sum Solution | Engineers of AI
Trapping Rain Water - Python Two Pointers Solution | Engineers of AI
Jump Game - Python Greedy Solution | Engineers of AI
Reverse Linked List - Python Iterative and Recursive | Engineers of AI
Detect Cycle in Linked List - Python Floyd's Algorithm | Engineers of AI
Find Middle of Linked List - Python Slow/Fast Pointers | Engineers of AI
Merge Two Sorted Lists - Python Solution | Engineers of AI
Remove Nth Node from End of List - Python Solution | Engineers of AI
Palindrome Linked List - Python Solution | Engineers of AI
Intersection of Two Linked Lists - Python Solution | Engineers of AI
Remove Duplicates from Sorted List - Python Solution | Engineers of AI
Insert into Circular Linked List - Python Solution | Engineers of AI
Delete Node in Linked List - Python Solution | Engineers of AI
Add Two Numbers Linked List - Python Solution | Engineers of AI
Reverse Nodes in k-Group - Python Solution | Engineers of AI
Copy List with Random Pointer - Python Solution | Engineers of AI
LRU Cache - Python Doubly Linked List Solution | Engineers of AI
Sort List (Merge Sort on Linked List) - Python Solution | Engineers of AI
Reorder List - Python Solution | Engineers of AI
Swap Nodes in Pairs - Python Solution | Engineers of AI
Partition List - Python Solution | Engineers of AI
Flatten Multilevel Doubly Linked List - Python Solution | Engineers of AI
Rotate List - Python Solution | Engineers of AI
Binary Tree Inorder Traversal - Python Recursive and Iterative | Engineers of AI
Binary Tree Level Order Traversal - Python BFS | Engineers of AI
Maximum Depth of Binary Tree - Python Solution | Engineers of AI
Symmetric Tree - Python Recursive Solution | Engineers of AI
Invert Binary Tree - Python Solution | Engineers of AI
Diameter of Binary Tree - Python DFS Solution | Engineers of AI
Path Sum - Python DFS Solution | Engineers of AI
Lowest Common Ancestor of BST - Python Solution | Engineers of AI
Validate Binary Search Tree - Python DFS with Bounds | Engineers of AI
Kth Smallest Element in BST - Python Inorder Solution | Engineers of AI
Convert Sorted Array to BST - Python Solution | Engineers of AI
Binary Tree Maximum Path Sum - Python DFS Solution | Engineers of AI
Serialize and Deserialize Binary Tree - Python Solution | Engineers of AI
Binary Tree Right Side View - Python BFS Solution | Engineers of AI
Sum Root to Leaf Numbers - Python DFS Solution | Engineers of AI
Subtree of Another Tree - Python DFS Solution | Engineers of AI
Balanced Binary Tree - Python Post-Order DFS | Engineers of AI
Implement Trie (Prefix Tree) - Python Solution | Engineers of AI
Flatten Binary Tree to Linked List - Python Solution | Engineers of AI
Construct Binary Tree from Preorder and Inorder - Python | Engineers of AI
Number of Islands - Python DFS BFS Solution | Engineers of AI
Clone Graph DFS BFS - Python | Engineers of AI
Course Schedule Topological Sort - Python | Engineers of AI
Pacific Atlantic Water Flow BFS - Python | Engineers of AI
Word Ladder BFS Shortest Path - Python | Engineers of AI
Graph Valid Tree Union Find DFS - Python | Engineers of AI
Number of Connected Components - Python Union Find | Engineers of AI
Alien Dictionary Topological Sort - Python | Engineers of AI
Shortest Path in Binary Matrix BFS - Python | Engineers of AI
Surrounded Regions DFS - Python | Engineers of AI
Rotting Oranges Multi-Source BFS - Python | Engineers of AI
Find if Path Exists in Graph - Python | Engineers of AI
Max Area of Island DFS - Python | Engineers of AI
Network Delay Time Dijkstra - Python | Engineers of AI
Find the Town Judge - Python | Engineers of AI
Is Graph Bipartite BFS 2-Coloring - Python | Engineers of AI
Kruskal's Minimum Spanning Tree - Python | Engineers of AI
Accounts Merge Union Find - Python | Engineers of AI
Redundant Connection Union Find - Python | Engineers of AI
Walls and Gates Multi-Source BFS - Python | Engineers of AI
Climbing Stairs DP - Python | Engineers of AI
House Robber DP - Python | Engineers of AI
House Robber II Circular DP - Python | Engineers of AI
Longest Increasing Subsequence DP Binary Search - Python | Engineers of AI
Coin Change DP - Python | Engineers of AI
Word Break DP - Python | Engineers of AI
Unique Paths DP - Python | Engineers of AI
Jump Game Greedy DP - Python | Engineers of AI
Jump Game II Minimum Jumps - Python | Engineers of AI
Longest Common Subsequence DP - Python | Engineers of AI
Edit Distance DP - Python | Engineers of AI
Partition Equal Subset Sum DP - Python | Engineers of AI
Target Sum DP DFS - Python | Engineers of AI
Decode Ways DP - Python | Engineers of AI
Best Time to Buy and Sell Stock III - Python | Engineers of AI
Palindrome Partitioning II Minimum Cuts - Python | Engineers of AI
Wildcard Matching DP - Python | Engineers of AI
Regular Expression Matching DP - Python | Engineers of AI
Maximum Product Subarray DP - Python | Engineers of AI
Triangle Minimum Path Sum DP - Python | Engineers of AI
Minimum Path Sum Grid DP - Python | Engineers of AI
Burst Balloons Interval DP - Python | Engineers of AI
0/1 Knapsack DP - Python | Engineers of AI
Rod Cutting DP - Python | Engineers of AI
Egg Drop Problem DP - Python | Engineers of AI
Merge Sort Implementation - Python | Engineers of AI
Quick Sort Implementation - Python | Engineers of AI
Heap Sort Implementation - Python | Engineers of AI
Find K-th Largest Element - Python Heap Quickselect | Engineers of AI
Sort Colors Dutch National Flag - Python | Engineers of AI
Merge Intervals - Python | Engineers of AI
Insert Interval - Python | Engineers of AI
Search in Rotated Sorted Array - Python | Engineers of AI
Find Peak Element Binary Search - Python | Engineers of AI
Search a 2D Matrix Binary Search - Python | Engineers of AI
Median of Two Sorted Arrays - Python | Engineers of AI
Find Minimum in Rotated Sorted Array - Python | Engineers of AI
H-Index - Python | Engineers of AI
Meeting Rooms II Min Heap - Python | Engineers of AI
Largest Number Custom Sort - Python | Engineers of AI
3Sum Two Pointers - Python | Engineers of AI
4Sum Two Pointers - Python | Engineers of AI
Container With Most Water Two Pointers - Python | Engineers of AI
Trapping Rain Water Two Pointers DP - Python | Engineers of AI
Minimum Window Substring Sliding Window - Python | Engineers of AI
Longest Substring Without Repeating - Python | Engineers of AI
Permutation in String Sliding Window - Python | Engineers of AI
Find All Anagrams in a String - Python | Engineers of AI
Longest Repeating Character Replacement - Python | Engineers of AI
Max Consecutive Ones III Sliding Window - Python | Engineers of AI
Fruit Into Baskets Sliding Window - Python | Engineers of AI
Subarrays with K Different Integers - Python | Engineers of AI
Minimum Size Subarray Sum Sliding Window - Python | Engineers of AI
Longest Subarray of 1s After Deleting One Element - Python | Engineers of AI
Count Nice Subarrays - Python | Engineers of AI
Valid Parentheses Stack - Python | Engineers of AI
Min Stack Design - Python | Engineers of AI
Evaluate Reverse Polish Notation Stack - Python | Engineers of AI
Daily Temperatures Monotonic Stack - Python | Engineers of AI
Largest Rectangle in Histogram Stack - Python | Engineers of AI
Implement Queue Using Stacks - Python | Engineers of AI
Implement Stack Using Queues - Python | Engineers of AI
Sliding Window Maximum Monotonic Deque - Python | Engineers of AI
Next Greater Element Monotonic Stack - Python | Engineers of AI
Basic Calculator II Stack - Python | Engineers of AI
Single Number XOR Bit Manipulation - Python | Engineers of AI
Number of 1 Bits Hamming Weight - Python | Engineers of AI
Reverse Bits - Python | Engineers of AI
Missing Number Math XOR - Python | Engineers of AI
Power of Two Bit Manipulation - Python | Engineers of AI
Counting Bits DP Bit Manipulation - Python | Engineers of AI
Sum of Two Integers Bit Manipulation - Python | Engineers of AI
Reverse Integer - Python | Engineers of AI
Palindrome Number - Python | Engineers of AI
Integer to Roman Numeral - Python | Engineers of AI
Roman to Integer - Python | Engineers of AI
Excel Sheet Column Number - Python | Engineers of AI
Happy Number Cycle Detection - Python | Engineers of AI
Sqrt(x) Binary Search - Python | Engineers of AI
Greatest Common Divisor of Strings - Python | Engineers of AI
Single Number - XOR Bit Manipulation Python | Engineers of AI
Single Number II - Bit Manipulation Every Element 3 Times | Engineers of AI
Single Number III - Two Unique Numbers XOR Python | Engineers of AI
Hamming Weight Number of 1 Bits Python | Engineers of AI
Reverse Bits 32-bit Integer Python | Engineers of AI
Missing Number XOR Gauss Formula Python | Engineers of AI
Power of Two Bit Manipulation Python | Engineers of AI
Counting Bits DP Python Solution | Engineers of AI
Sum of Two Integers Without Plus Operator Python | Engineers of AI
Reverse Integer Python with Overflow Check | Engineers of AI
Palindrome Number Python Without String | Engineers of AI
Integer to Roman Numeral Python | Engineers of AI
Roman to Integer Python Solution | Engineers of AI
Excel Sheet Column Number Python Base-26 | Engineers of AI
Happy Number Cycle Detection Python | Engineers of AI
Sqrt(x) Binary Search Newton Method Python | Engineers of AI
GCD LCM Euclidean Algorithm Python | Engineers of AI
Sieve of Eratosthenes Count Primes Python | Engineers of AI
Fast Power Exponentiation Python O(log n) | Engineers of AI
Multiply Strings Python Grade School Algorithm | Engineers of AI
Add Binary Strings Python | Engineers of AI
Add Two Numbers Strings Python Without int() | Engineers of AI
Count Digit 1 in Range 0 to N Python | Engineers of AI
Nth Ugly Number DP Three Pointers Python | Engineers of AI
Perfect Squares Minimum Count DP BFS Python | Engineers of AI
Merge Sort Python Implementation | Engineers of AI
Quick Sort Randomized Pivot Python | Engineers of AI
Heap Sort Python Implementation | Engineers of AI
Find Kth Largest Element Python - Heap and Quickselect | Engineers of AI
Sort Colors Dutch National Flag Python | Engineers of AI
Merge Intervals Python Solution | Engineers of AI
Insert Interval Python Solution | Engineers of AI
Search in Rotated Sorted Array Python | Engineers of AI
Find Peak Element Binary Search Python | Engineers of AI
Search 2D Matrix Binary Search Python | Engineers of AI
Median of Two Sorted Arrays Python O(log n) | Engineers of AI
Find Minimum Rotated Sorted Array Python | Engineers of AI
H-Index Python Solution | Engineers of AI
Meeting Rooms II Python Min Heap | Engineers of AI
Largest Number Custom Sort Python | Engineers of AI
Count Smaller Numbers After Self Python Merge Sort | Engineers of AI
Sort Linked List Merge Sort Python | Engineers of AI
Top K Frequent Elements Python Heap Bucket Sort | Engineers of AI
Top K Frequent Words Python Heap | Engineers of AI
Find K Closest Elements Binary Search Python | Engineers of AI
Kth Smallest in Sorted Matrix Python Heap Binary Search | Engineers of AI
Find K Pairs Smallest Sums Python Min Heap | Engineers of AI
Sort Characters By Frequency Python | Engineers of AI
Wiggle Sort II Python | Engineers of AI
Relative Ranks Python | Engineers of AI
3Sum Two Pointers Python | Engineers of AI
4Sum Python Two Pointers | Engineers of AI
Container With Most Water Two Pointers Python | Engineers of AI
Trapping Rain Water Python Two Pointers | Engineers of AI
Minimum Window Substring Python Sliding Window | Engineers of AI
Longest Substring Without Repeating Characters Python | Engineers of AI
Permutation in String Sliding Window Python | Engineers of AI
Find All Anagrams in String Python | Engineers of AI
Longest Repeating Character Replacement Python | Engineers of AI
Max Consecutive Ones III Sliding Window Python | Engineers of AI
Fruit Into Baskets Sliding Window Python | Engineers of AI
Subarrays with K Different Integers Python | Engineers of AI
Minimum Size Subarray Sum Python Sliding Window | Engineers of AI
Longest Subarray of 1s After Deleting One Element Python | Engineers of AI
Count Nice Subarrays with K Odd Numbers Python | Engineers of AI
Subarray Product Less Than K Sliding Window Python | Engineers of AI
Minimum Operations Reduce X to Zero Python | Engineers of AI
Maximum Erasure Value Sliding Window Python | Engineers of AI
Substrings Containing All Three Characters Python | Engineers of AI
Replace Substring for Balanced String Python | Engineers of AI
Sliding Window Median Python Two Heaps | Engineers of AI
Maximum Points from Cards Sliding Window Python | Engineers of AI
Longest Subarray Absolute Diff at Most Limit Python | Engineers of AI
Grumpy Bookstore Owner Sliding Window Python | Engineers of AI
Minimum K Consecutive Bit Flips Python | Engineers of AI
Valid Parentheses Stack Python | Engineers of AI
Min Stack Design Python O(1) | Engineers of AI
Evaluate Reverse Polish Notation Stack Python | Engineers of AI
Daily Temperatures Monotonic Stack Python | Engineers of AI
Largest Rectangle in Histogram Stack Python | Engineers of AI
Implement Queue Using Stacks Python | Engineers of AI
Implement Stack Using Queues Python | Engineers of AI
Sliding Window Maximum Monotonic Deque Python | Engineers of AI
Next Greater Element I Monotonic Stack Python | Engineers of AI
Next Greater Element II Circular Array Python | Engineers of AI
Basic Calculator Stack Python | Engineers of AI
Basic Calculator II Stack Python | Engineers of AI
Remove Duplicate Letters Greedy Stack Python | Engineers of AI
Remove K Digits Smallest Number Python | Engineers of AI
132 Pattern Monotonic Stack Python | Engineers of AI
Score of Parentheses Stack Python | Engineers of AI
Asteroid Collision Stack Python | Engineers of AI
Online Stock Span Monotonic Stack Python | Engineers of AI
Sum of Subarray Minimums Monotonic Stack Python | Engineers of AI
Maximal Rectangle Matrix Stack Python | Engineers of AI
Car Fleet Stack Python | Engineers of AI
Decode String Stack Python | Engineers of AI
Maximum Width Ramp Monotonic Stack Python | Engineers of AI
Number of Visible People in Queue Stack Python | Engineers of AI
Minimum Add Make Parentheses Valid Python | Engineers of AI
Kth Largest Element Heap Python | Engineers of AI
Find Median from Data Stream Two Heaps Python | Engineers of AI
Merge K Sorted Lists Heap Divide Conquer Python | Engineers of AI
Task Scheduler Greedy Heap Python | Engineers of AI
Reorganize String No Adjacent Duplicates Python | Engineers of AI
K Closest Points to Origin Heap Python | Engineers of AI
Smallest Range Covering K Lists Python | Engineers of AI
Ugly Number II DP Three Pointers Python | Engineers of AI
Super Ugly Number DP Python | Engineers of AI
IPO Maximize Capital Two Heaps Python | Engineers of AI
Furthest Building Reach Greedy Heap Python | Engineers of AI
Single Threaded CPU Heap Simulation Python | Engineers of AI
Skyline Problem Heap Python | Engineers of AI
Employee Free Time Intervals Python | Engineers of AI
Minimum Cost Hire K Workers Python | Engineers of AI
Seat Reservation Manager Min Heap Python | Engineers of AI
Maximum Subsequence Score Greedy Heap Python | Engineers of AI
Minimum Refueling Stops Greedy Heap Python | Engineers of AI
Kth Smallest Prime Fraction Heap Python | Engineers of AI
Minimize Deviation in Array Heap Python | Engineers of AI
Maximum Performance of Team Heap Sort Python | Engineers of AI
Kth Largest in Stream Min Heap Python | Engineers of AI
Top K Frequent from Stream Design Python | Engineers of AI
Process Tasks Using Servers Two Heaps Python | Engineers of AI
Swim in Rising Water Dijkstra Binary Search Python | Engineers of AI
LRU Cache OrderedDict Python | Engineers of AI
LFU Cache O(1) Python Implementation | Engineers of AI
Thread-Safe Singleton Metaclass Python | Engineers of AI
Observer Pattern Python OOP | Engineers of AI
Python Iterator Protocol __iter__ __next__ | Engineers of AI
Python Context Manager __enter__ __exit__ | Engineers of AI
Python Retry Decorator Exponential Backoff | Engineers of AI
Memoization Decorator LRU Python | Engineers of AI
Python flatten Generator Nested Lists | Engineers of AI
Python Lazy Property Descriptor | Engineers of AI
Python Dataclass Validation __post_init__ | Engineers of AI
Abstract Base Class Payment System Python | Engineers of AI
Python __getattr__ __setattr__ Tracking | Engineers of AI
Python Protocol Comparable Structural Typing | Engineers of AI
Asyncio Producer Consumer Queue Python | Engineers of AI
asyncio gather Semaphore Python | Engineers of AI
Token Bucket Rate Limiter Python | Engineers of AI
Python ThreadPoolExecutor concurrent.futures | Engineers of AI
Custom defaultdict Python __missing__ | Engineers of AI
Trie Python Implementation with Autocomplete | Engineers of AI
Graph Class BFS DFS Topological Sort Python | Engineers of AI
MinHeap from Scratch Python | Engineers of AI
Circular Buffer Ring Buffer Python | Engineers of AI
Bloom Filter Python Implementation | Engineers of AI
Consistent Hash Ring Python | Engineers of AI
Design LRU Cache O(1) Python | Engineers of AI
Design LFU Cache Python O(1) | Engineers of AI
Design Hit Counter Last 5 Minutes Python | Engineers of AI
Design Rate Limiter Sliding Window Python | Engineers of AI
Design Twitter Post Tweet News Feed Python | Engineers of AI
Design File System In-Memory Python | Engineers of AI
Key-Value Store with TTL Python | Engineers of AI
Design In-Memory Database Python | Engineers of AI
Design URL Shortener Python Base62 | Engineers of AI
Design Leaderboard Top K Python | Engineers of AI
Design Parking Lot OOP Python | Engineers of AI
Vending Machine State Pattern Python | Engineers of AI
Design Elevator System SCAN Algorithm Python | Engineers of AI
Library Management System OOP Python | Engineers of AI
Restaurant Reservation System Python OOP | Engineers of AI
Movie Ticket Booking System Python OOP | Engineers of AI
Design Chat System Python OOP | Engineers of AI
Autocomplete System Trie Python | Engineers of AI
Log Aggregator K-Way Merge Python | Engineers of AI
Priority Task Scheduler Python | Engineers of AI
Design Pub/Sub Message Queue Python | Engineers of AI
Event Sourcing System Python | Engineers of AI
Circuit Breaker Pattern Python | Engineers of AI
API Gateway Design Python Middleware | Engineers of AI
Search Suggestions Trie Binary Search Python | Engineers of AI
KMP String Search Algorithm Python | Engineers of AI
Rabin-Karp Rolling Hash Python | Engineers of AI
Z-Algorithm Pattern Matching Python | Engineers of AI
Longest Palindromic Substring Manacher's Python | Engineers of AI
Palindrome Partitioning Backtracking Python | Engineers of AI
Merge Intervals - Python Solution | EngineersOfAI
Insert Interval - Python Solution | EngineersOfAI
Non-overlapping Intervals - Python Greedy | EngineersOfAI
Meeting Rooms I - Python Solution | EngineersOfAI
Meeting Rooms II - Python Min-Heap Solution | EngineersOfAI
Employee Free Time - Python Solution | EngineersOfAI
Interval List Intersections - Python Two Pointers | EngineersOfAI
Remove Covered Intervals - Python Sorting | EngineersOfAI
Video Stitching - Python Greedy Solution | EngineersOfAI
Minimum Arrows to Burst Balloons - Python Greedy | EngineersOfAI
My Calendar I - Python Binary Search | EngineersOfAI
My Calendar II - Python Double Booking | EngineersOfAI
My Calendar III - Python Difference Array | EngineersOfAI
Data Stream as Disjoint Intervals - Python | EngineersOfAI
Range Module - Python Interval Design | EngineersOfAI
Count of Range Sum - Python Merge Sort | EngineersOfAI
Falling Squares - Python Interval Heights | EngineersOfAI
Rectangle Area II - Python Sweep Line | EngineersOfAI
Minimum Interval to Include Each Query - Python Heap | EngineersOfAI
Number of Flowers in Full Bloom - Python Binary Search | EngineersOfAI
Find Right Interval - Python Binary Search | EngineersOfAI
Partition Labels - Python Greedy Solution | EngineersOfAI
Task Scheduler - Python Greedy & Math | EngineersOfAI
Car Fleet - Python Monotonic Stack Solution | EngineersOfAI
Jump Game VII - Python Prefix Sum | EngineersOfAI
Koko Eating Bananas - Python Binary Search | EngineersOfAI
Capacity to Ship Packages Within D Days - Python Binary Search | EngineersOfAI
Minimum Days to Make m Bouquets - Python Binary Search | EngineersOfAI
Split Array Largest Sum - Python Binary Search | EngineersOfAI
Magnetic Force Between Two Balls - Python Binary Search | EngineersOfAI
Find in Mountain Array - Python Binary Search | EngineersOfAI
Search in Rotated Sorted Array II - Python | EngineersOfAI
Find the Duplicate Number - Python Floyd Cycle | EngineersOfAI
First Bad Version - Python Binary Search | EngineersOfAI
Find Smallest Letter Greater Than Target - Python | EngineersOfAI
Count Negative Numbers in Sorted Matrix - Python | EngineersOfAI
Kth Smallest Element in Sorted Matrix - Python Binary Search | EngineersOfAI
Find Kth Smallest Pair Distance - Python Binary Search | EngineersOfAI
Kth Smallest in Multiplication Table - Python Binary Search | EngineersOfAI
Random Pick with Weight - Python Binary Search | EngineersOfAI
Time Based Key-Value Store - Python Binary Search Design | EngineersOfAI
Online Election - Python Binary Search | EngineersOfAI
Peak Index in Mountain Array - Python Binary Search | EngineersOfAI
Search a 2D Matrix II - Python Staircase | EngineersOfAI
Sqrt(x) - Python Binary Search | EngineersOfAI
H-Index II - Python Binary Search | EngineersOfAI
Minimum Speed to Arrive on Time - Python Binary Search | EngineersOfAI
Minimum Time to Complete Trips - Python Binary Search | EngineersOfAI
Maximum Candies Allocated to K Children - Python Binary Search | EngineersOfAI
Minimum Limit of Balls in a Bag - Python Binary Search | EngineersOfAI
Binary Tree Maximum Path Sum - Python DFS | EngineersOfAI
Binary Tree Cameras - Python Greedy DFS | EngineersOfAI
Distribute Coins in Binary Tree - Python DFS | EngineersOfAI
Maximum Width of Binary Tree - Python BFS | EngineersOfAI
Count Complete Tree Nodes - Python O(log^2 n) | EngineersOfAI
Sum Root to Leaf Numbers - Python DFS | EngineersOfAI
Path Sum III - Python Prefix Sum Hash Map | EngineersOfAI
Flatten Binary Tree to Linked List - Python O(1) Space | EngineersOfAI
Binary Tree Right Side View - Python BFS | EngineersOfAI
Find Duplicate Subtrees - Python Serialization | EngineersOfAI
LRU Cache Python - O(1) OrderedDict & Doubly Linked List Solution
LFU Cache Python - O(1) Least Frequently Used Cache Implementation
Design Twitter Python - News Feed with Heap Merge Solution
Design Snake Game Python - Deque and Set Solution
Design Hit Counter Python - Circular Buffer and Queue Solutions
Design Phone Directory Python - Set and Queue Solutions
Design In-Memory File System Python - Trie Solution
Implement Trie Prefix Tree Python - Insert Search StartsWith
Add and Search Word Python - Trie with Wildcard Dot Support
Word Search II Python - Trie + DFS Backtracking Solution
Implement Stack Using Queues Python - One and Two Queue Solutions
Implement Queue Using Stacks Python - Amortized O(1) Solution
Min Stack Python - O(1) getMin with Auxiliary Stack Solution
Max Stack Python - O(log n) Solution with Heap and Lazy Deletion
Sliding Window Maximum Python - Monotonic Deque O(n) Solution
Sliding Window Minimum Python - Monotonic Deque O(n) Solution
First Unique Character in Stream Python - OrderedDict and Deque Solutions
Design HashMap Python - Separate Chaining and Direct Address Solutions
Design HashSet Python - Chaining and Bitset Solutions
Iterator for Combination Python - Lazy Generator and Bitmask Solutions
N-ary Tree Level Order Traversal - Python BFS Solution
Maximum Depth of N-ary Tree - Python DFS and BFS Solutions
Diameter of Binary Tree - Python DFS Solution with Examples
Lowest Common Ancestor of Deepest Leaves - Python DFS Solution
Check Completeness of a Binary Tree - Python BFS Solution
Cousins in Binary Tree II - Python BFS Solution
Even Odd Tree - Python BFS Level Validation Solution
Step-By-Step Directions From a Binary Tree Node to Another - Python
Pseudo-Palindromic Paths in a Binary Tree - Python Bitmask DFS
Sum of Nodes with Even-Valued Grandparent - Python DFS Solution
Create Binary Tree From Descriptions - Python Hash Map Solution
Count Nodes Equal to Average of Subtree - Python DFS Solution
Maximum Level Sum of Binary Tree - Python BFS Solution
Reverse Odd Levels of Binary Tree - Python BFS and DFS Solutions
Count Good Nodes in Binary Tree - Python DFS Solution
Trapping Rain Water II - Python Min-Heap BFS Solution
Maximal Square - Python DP Solution with O(n) Space Optimization
Maximal Rectangle - Python Monotonic Stack and DP Solutions
Longest Consecutive Sequence - Python O(n) Hash Set Solution
First Missing Positive - Python Cyclic Sort O(n) O(1) Solution
Text Justification - Python Greedy String Simulation Solution
Jump Game VI - Python Deque DP Sliding Window Solution
Minimum Cost to Cut a Stick - Python Interval DP Solution
Largest Color Value in a Directed Graph - Python Topological DP
Parallel Courses III - Python Topological Sort Critical Path
Count Vowels Permutation - Python DP and Matrix Exponentiation
Strange Printer - Python Interval DP Solution
Minimum Number of Days to Disconnect Island - Python DFS
Minimum Total Distance Traveled - Python DP Robot Factory Solution
Minimize the Maximum Difference of Pairs - Python Binary Search
Count Palindromic Substrings - Python Expand Center and Manacher
Shortest Palindrome - Python KMP O(n) Solution
Wildcard Matching - Python DP and Greedy Solutions
Regular Expression Matching - Python DP and Recursion Solutions
Edit Distance - Python DP Levenshtein Distance Solution
Word Break II - Python Backtracking with Memoization Solution
Concatenated Words - Python DP and Trie DFS Solutions
Distinct Subsequences - Python DP Solution with Space Optimization
Interleaving String - Python DP Solution with Space Optimization
Word Ladder II - Python BFS Backtrack All Shortest Paths
Extract Email Addresses with Named Regex Groups | Python Interview Q501
Parse Structured Log Lines with Regex | Python Interview Q502
Validate and Normalize Phone Numbers with Regex | Python Q503
Nested List Comprehension Multi-Condition Filter | Python Q504
Dict Comprehension Invert and Aggregate Duplicates | Python Q505
Set Comprehension Symmetric Difference Analysis | Python Q506
Infinite Fibonacci Generator with send() Reset | Python Q507
Lazy ETL Generator Pipeline Read Filter Transform Batch | Python Q508
Retry Decorator with Exponential Backoff | Python Interview Q509
Rate Limiting Decorator with Token Bucket | Python Interview Q510
Type-Annotated Generic Stack Using TypeVar and Generic | Python Q511
Protocol for Comparable Objects and top_k | Python Interview Q512
Retry Decorator with Exponential Backoff | Python Interview Q513
Memoize Decorator with functools.wraps | Python Interview Q514
Timer Decorator Measuring Execution Time | Python Interview Q515
Rate Limiter Decorator N Calls Per Second | Python Interview Q516
Class Decorator Adding __repr__ and __eq__ | Python Interview Q517
Infinite Fibonacci Generator with take(n) | Python Interview Q518
Generator Pipeline Read Filter Transform | Python Interview Q519
Coroutine Data Pipeline Using send() | Python Interview Q520
Async Generator for Paginated API Results | Python Interview Q521
Context Manager for Database Transaction | Python Interview Q522
Context Manager with contextlib.contextmanager | Python Interview Q523
Reentrant Context Manager with Nesting Depth | Python Interview Q524
Descriptor for Validated Typed Attributes | Python Interview Q525
Lazy Property Descriptor Python | Python Interview Q526
Read-Only Descriptor Raising AttributeError | Python Interview Q527
Metaclass Auto-Registering Subclasses | Python Interview Q528
Metaclass Enforcing snake_case Method Names | Python Interview Q529
Singleton Pattern Using Metaclass | Python Interview Q530
Abstract Base Class with __init_subclass__ | Python Interview Q531
__slots__ vs Regular Class Memory Comparison | Python Interview Q532
Flexible Config Object with __getattr__ and __setattr__ | Python Interview Q533
__missing__ in Dict Subclass for Auto-Default | Python Interview Q534
Custom Range with __iter__ and __next__ | Python Interview Q535
Sorted Collection __len__ __getitem__ __contains__ | Python Interview Q536
Vector Class with __add__ and __mul__ | Python Interview Q537
Sync and Async Context Manager for Resource | Python Interview Q538
Dataclass with __post_init__ Validation and __hash__ | Python Interview Q539
Dataclass field() Defaults and Computed Fields | Python Interview Q540
NamedTuple with Methods and Default Values | Python Interview Q541
TypedDict for Structured Dicts with Optional Keys | Python Interview Q542
Generic Class with Bounded TypeVar | Python Interview Q543
Protocol Class for Structural Subtyping | Python Interview Q544
Implement functools.partial from Scratch | Python Interview Q545
Implement functools.reduce from Scratch | Python Interview Q546
Implement itertools.groupby from Scratch | Python Interview Q547
Implement itertools.chain from Scratch | Python Interview Q548
Implement itertools.islice from Scratch | Python Interview Q549
Implement itertools.product Cartesian Product | Python Interview Q550
Closure Loop Variable Capture Gotcha | Python Interview Q551
Event Emitter with on/emit/off in Python | Python Interview Q552
Weak References with weakref to Avoid Memory Leaks | Python Interview Q553
copy and deepcopy with __copy__ and __deepcopy__ | Python Interview Q554
Pickle-Aware Class with __getstate__ and __setstate__ | Python Interview Q555
Extract Emails from Text Using Regex Named Groups | Python Interview Q556
Parse Log Lines with Named Regex Groups | Python Interview Q557
Validate and Parse ISO 8601 Datetime Strings | Python Interview Q558
Exception Chaining raise X from Y and __cause__ vs __context__ | Python Interview Q559
Custom Exception Hierarchy with Error Codes | Python Interview Q560
Doubly Linked List with Sentinel Nodes | Python Interview Q561
Circular Doubly Linked List Rotate Insert Delete | Python Q562
Doubly Linked List as Deque O(1) All Operations | Python Q563
Flatten Multilevel Doubly Linked List | Python Interview Q564
Reverse Doubly Linked List in Groups of K | Python Q565
Segment Tree Range Sum Query Point Update | Python Q566
Segment Tree Range Minimum Query | Python Interview Q567
Lazy Propagation Segment Tree Range Add Sum | Python Q568
Fenwick Tree BIT Prefix Sums Count Inversions | Python Q569
2D Fenwick Tree Rectangle Sum Queries | Python Interview Q570
BST Floor and Ceiling Operations | Python Interview Q571
BST Rank and Select with Augmented Subtree Sizes | Python Q572
BST In-Order Successor Predecessor Parent Pointers | Python Q573
AVL Tree Balanced BST with Rotations | Python Interview Q574
BST Serialization and Deserialization | Python Interview Q575
Trie with Wildcard Search Single Character Pattern | Python Q576
Trie Autocomplete with Frequency Ranking Top-K | Python Q577
Compressed Patricia Trie Implementation | Python Interview Q578
Trie for IP Routing Longest Prefix Match | Python Q579
Aho-Corasick Automaton Multi-Pattern String Matching | Python Q580
Deque Sliding Window Sum | Python Interview Q581
Sliding Window Median Sorted List | Python Interview Q582
Monotonic Deque Jump Game Minimum Jumps | Python Q583
LRU Cache with TTL Expiration | Python Interview Q584
Thread-Safe LRU Cache with threading.Lock | Python Q585
LFU Cache O(1) All Operations | Python Interview Q586
LFU Cache with Frequency Aging | Python Interview Q587
SortedList Order Statistics Insert Delete Rank | Python Q588
Skip List Probabilistic Data Structure | Python Interview Q589
K-Way Merge Sorted Arrays Min-Heap | Python Q590
External Sort Merge Phase K-Way Heap | Python Q591
Median of Two Sorted Arrays O(log min m n) | Python Q592
Streaming Median with Two Heaps | Python Interview Q593
Sliding Window Median Two Heaps Lazy Deletion | Python Q594
Union-Find Path Compression Union by Rank | Python Q595
Union-Find Dynamic Connectivity Arbitrary Keys | Python Q596
Kruskal's MST with Union-Find | Python Interview Q597
Persistent Union-Find with Rollback | Python Interview Q598
Circular Queue Ring Buffer Implementation | Python Interview Q599
Queue from Two Stacks O(1) Amortized | Python Interview Q600
BFS Shortest Path in Unweighted Graph - Python Interview Question
Count Connected Components in Graph - Python DFS and Union-Find
Topological Sort Kahn's Algorithm Python - BFS Approach
Topological Sort DFS Postorder Python - Iterative and Recursive
Detect Cycle in Directed Graph Using DFS Colors - Python
Detect Cycle in Undirected Graph Using Union-Find - Python
Dijkstra's Shortest Path Algorithm Python - Min-Heap Implementation
Bellman-Ford Algorithm Python - Negative Edges and Cycle Detection
Floyd-Warshall All-Pairs Shortest Path Python - Full DP Solution
Prim's MST Algorithm Python - Min-Heap Implementation
Number of Islands Python - DFS and BFS Grid Solutions
Word Ladder BFS Python - Minimum Transformations Solution
Alien Dictionary Problem Python - Topological Sort Solution
Course Schedule II Python - Topological Sort Order Solution
Network Delay Time Python - Dijkstra's Algorithm Solution
Cheapest Flights Within K Stops Python - Bellman-Ford and Dijkstra
Pacific Atlantic Water Flow Python - BFS from Edges Solution
Walls and Gates Multi-Source BFS Python - Grid Distance Problem
Rotting Oranges BFS Python - Multi-Source Grid Propagation
Clone Graph Python - DFS and BFS with Hash Map Solutions
Accounts Merge - Union-Find Graph Problem | Python Solution
Redundant Connection - Cycle Detection with Union-Find | Python
Longest Consecutive Sequence O(n) - Hash Set Solution | Python
Max Area of Island - DFS BFS Grid Problem | Python Solution
Swim in Rising Water - Min-Heap and Binary Search | Python
Coin Change DP - Bottom-up and Memoization Solutions | Python
Coin Change II - Count Combinations DP | Python Solution
Climbing Stairs - Fibonacci DP Solution | Python
House Robber - Linear DP No Adjacent Selection | Python
House Robber II - Circular DP Problem | Python Solution
House Robber III - Binary Tree DP | Python Solution
Unique Paths - Grid DP and Combinatorics | Python Solution
Minimum Path Sum - Grid DP Solution | Python
Edit Distance (Levenshtein) - DP Solution | Python
Longest Common Subsequence - DP Solution | Python
Longest Increasing Subsequence O(n log n) | Python Solution
Longest Palindromic Subsequence - Interval DP | Python
Palindromic Substrings Count - Expand Around Center | Python
Word Break DP - Dictionary Segmentation | Python Solution
Word Break II - Backtracking with Memoization | Python
Interleaving String - 2D DP Solution | Python
Decode Ways - Count Encodings DP | Python
Distinct Subsequences - DP Count | Python
Regular Expression Matching DP | Python
Wildcard Matching DP and Greedy | Python
Burst Balloons - Interval DP | Python
Stone Game I - DP and Math Proof | Python
Partition Equal Subset Sum - 0/1 Knapsack | Python
Target Sum - DP and DFS Memoization | Python
Last Stone Weight - Max-Heap Greedy | Python
Task Scheduler - Greedy and Heap | Python
Jump Game I - Greedy Reachability | Python
Jump Game II - Minimum Jumps Greedy | Python
Gas Station - Circular Greedy | Python
Candy Distribution - Two-Pass Greedy | Python
Meeting Rooms I - Can Attend All | Python
Meeting Rooms II - Minimum Rooms Heap | Python
Non-overlapping Intervals - Remove Minimum | Python
Merge Intervals - Sort and Merge | Python
Insert Interval - Binary Search and Merge | Python
Quicksort Partition In-Place | Python Sorting Interview Question
Merge Sort Counting Inversions | Python Divide and Conquer Interview
Counting Sort for Bounded Integers | Python Sorting Interview Question
Radix Sort for Large Integers | Python Sorting Interview Question
Bucket Sort for Uniform Distribution | Python Sorting Interview
Kth Largest Element Quickselect | Python Interview Question
Sort Colors Dutch National Flag | Python Two Pointers Interview
Wiggle Sort Alternating Array | Python Greedy Interview Question
Find Median from Data Stream | Python Two Heaps Interview Question
Top K Frequent Elements Bucket Sort O(n) | Python Interview
Sort Characters by Frequency | Python Hash Map Interview Question
Largest Number from Array of Integers | Python Sorting Interview
Minimum Arrows to Burst Balloons | Python Greedy Interval Interview
Queue Reconstruction by Height | Python Greedy Sort Interview
Hand of Straights Consecutive Groups | Python Greedy Interview
Advantage Shuffle Greedy Pairing | Python Sorting Interview
Maximum XOR of Two Numbers Trie | Python Bit Manipulation Interview
Bitwise AND of Numbers Range | Python Bit Manipulation Interview
Number of 1 Bits Hamming Weight | Python Bit Manipulation Interview
Power of Two Bit Check | Python Bit Manipulation Interview Question
Thread-Safe Bounded Queue | Python Concurrency Interview
Thread-Safe LRU Cache Python | Read-Write Lock Interview
asyncio Task Manager Python | Coroutine Cancellation Interview
async HTTP Request Batching Python | asyncio Interview Question
Async Connection Pool Python | asyncio Semaphore Interview
Token Bucket Rate Limiter Python | System Design Interview
Sliding Window Rate Limiter Python | API Rate Limiting Interview
Fixed Window Rate Limiter Python | Rate Limiting Interview
Distributed Rate Limiter Redis Python | System Design Interview
Write-Through vs Write-Behind Cache Python | System Design
Cache Invalidation TTL LRU Event Python | System Design Interview
Read-Through Cache Stampede Protection Python | Interview
Cache-Aside Pattern Python | Caching Interview Question
Custom JSON Serializer Python | datetime Decimal Enum Interview
Protocol Buffer Encoder Decoder Python | Binary Serialization Interview
Avro Schema Evolution Python | Schema Compatibility Interview
Observer Pattern Async Python | Event System Design Interview
Command Pattern Undo Redo Python | Design Pattern Interview
Strategy Pattern Sort Algorithms Python | Design Pattern Interview
Chain of Responsibility Pattern Python | Middleware Pipeline Interview
Builder Pattern SQL Query Builder Python | Design Pattern Interview
Flyweight Pattern Python | Memory Optimization Design Interview
Proxy Pattern Lazy Loading Python | Design Pattern Interview
Composite Pattern File System Python | Design Pattern Interview
Visitor Pattern AST Traversal Python | Compiler Design Interview
Job Scheduler Python | Priority Queue Dependency Graph Interview
Pub/Sub Message Broker Dead Letter Queue Python | System Design
Circuit Breaker Pattern Python | Resilience System Design Interview
API Gateway Python | Auth Rate Limiting Routing System Design
Distributed Counter CRDT Python | Eventual Consistency Interview
Real-Time Leaderboard Python | Sorted Data Structure Interview
Notification Service Python | Multi-Channel Dedup Retry Interview
Feature Flag System Python | Gradual Rollout A/B Testing Interview
Config Management Service Python | Versioned CAS Watcher Interview
Distributed Lock Python | Optimistic Pessimistic Locking Interview
Workflow Engine DAG Python | Airflow Task Scheduling Interview
Metrics Collection System Python | Counter Gauge Histogram Interview
Audit Log System Python | Hash Chain Tamper-Evident Interview
Thread Pool Implementation Python | Future Graceful Shutdown Interview
Python Process Pool CPU-Bound | multiprocessing Interview
Async Priority Queue Python | asyncio PriorityQueue Interview
Banker's Algorithm Python | Deadlock Detection Interview
Dining Philosophers Python | Deadlock Prevention Concurrency Interview
Readers-Writers Problem Python | Fair RW Lock Interview
asyncio Producer Consumer Backpressure Python | Streaming Interview
concurrent.futures Python | Futures Promises Interview Patterns
Cache Eviction Policy Simulator Python | LRU LFU FIFO Interview
Bloom Filter Python | Probabilistic Data Structure Interview
Time-Series Storage Python | Downsampling Retention Interview
Event Sourcing Python | CQRS Projections System Design Interview
CQRS Python | Command Query Segregation System Design Interview
Saga Pattern Python | Distributed Transaction Compensation Interview
Simple ORM Python | SQLite Metaclass Object-Relational Mapper Interview
Connection Multiplexer Python | HTTP2 gRPC Stream Multiplexing Interview
Idempotency Keys Python | Request Deduplication API Safety Interview
CDN Cache Hierarchy Python | Multi-Tier Caching System Design Interview
Task Dependency Graph Executor Python | DAG Parallel Execution Interview
Versioned Key-Value Store Python | MVCC Snapshot Isolation Interview
Shopping Cart Service Python | Inventory Discount Checkout Interview
Recommendation Engine Python | Collaborative Filtering Cosine Similarity Interview
Trapping Rain Water - Two Pointers + Stack | Python Q741
Largest Rectangle in Histogram - Monotonic Stack | Python Q742
Maximal Rectangle Binary Matrix - Histogram DP | Python Q743
Count Ways to Climb N Stairs with 1 2 3 Steps | Python Q744
Count Distinct Subsequences of S in T | Python Q745
Minimum Cost to Cut a Stick - Interval DP | Python Q746
Strange Printer Minimum Turns - Interval DP | Python Q747
Arithmetic Slices II Subsequence DP | Python Q748
Count Palindromic Subsequences of Length 5 | Python Q749
K-th Symbol in Grammar - Recursive Bit Trick | Python Q750
24 Game Backtracking All Combinations | Python Q751
Expression Add Operators Backtracking | Python Q752
Palindrome Partitioning II Minimum Cuts DP | Python Q753
Scramble String Memoized DP | Python Q754
Zuma Game Minimum Moves Interval DP | Python Q755
Strange Printer II Color Dependencies Topological Sort | Python Q756
Cat and Mouse Game Minimax DP | Python Q757
Maximum Score from Multiplications DP | Python Q758
Minimum Refueling Stops Greedy Heap DP | Python Q759
Split Array Largest Sum Binary Search DP | Python Q760
Dungeon Game Reverse DP Minimum Health | Python Q761
Maximal Square DP Binary Matrix | Python Q762
Count Submatrices with All Ones DP | Python Q763
Cherry Pickup Two-Robot Simultaneous DP | Python Q764
Knight Dialer DP Phone Pad Paths | Python Q765
Soup Servings Probability DP | Python Q766
Frog Jump River Cross DP | Python Q767
Integer Break DP Maximize Product | Python Q768
Russian Doll Envelopes 2D LIS Patience Sort | Python Q769
Make Array Strictly Increasing DP Binary Search | Python Q770
Minimum Distance Two-Finger Keyboard DP | Python Q771
Minimum XOR Sum Two Arrays Bitmask DP | Python Q772
Painting Fence with K Colors DP | Python Q773
Restore IP Addresses Backtracking | Python Q774
Stickers to Spell Word Bitmask DP | Python Q775
Shortest Path Visiting All Nodes BFS Bitmask | Python Q776
Minimum Steps to Make Two Strings Anagram | Python Q777
Minimum Swaps to Group All 1s Sliding Window | Python Q778
Longest Subarray with Abs Diff Limit Monotonic Deque | Python Q779
Maximum Events Attended Greedy Heap | Python Q780
Paint Fence with K Colors | DP Python No Three Consecutive Same
Best Time to Buy Stock with Transaction Fee | DP Python
Minimum Path Sum Grid with Obstacles | DP Python
Word Break with Minimum Word Count | DP BFS Python
Palindrome Partitioning Minimum Cuts | DP Python
Longest Arithmetic Subsequence | DP Hash Map Python
Stone Game III: Two-Player Optimal Strategy | DP Python
Maximum Profit in Job Scheduling | Weighted Interval DP Python
Group Anagrams Together | Hash Map Python Solution
Two Sum Variants: Sorted Array, BST, Streaming | Python
Find All Duplicates in Array | O(1) Space Index Hash Python
Product of Array Except Self | No Division O(n) Python
Maximum Product Subarray | Track Max Min DP Python
Find Minimum in Rotated Sorted Array with Duplicates | Python
Count of Range Sum | Merge Sort Prefix Sum Python
Tower of Hanoi 3-Peg and 4-Peg Frame-Stewart | Python
Generate Balanced Parentheses with K Types | Backtracking Python
Sort Array by Parity: Evens First | Two-Pointer Python
Interval List Intersections | Two-Pointer Python
Word Ladder Minimum Transformation | BFS Python
Bellman-Ford Shortest Path | Negative Weights Python
Floyd-Warshall All-Pairs Shortest Paths | Python
Kruskal's MST Algorithm | Union-Find Python
Kosaraju's SCC Algorithm | Python
Bridges in Graph - Tarjan's Algorithm | Python
Bipartite Graph Check 2-Coloring | Python BFS
Burst Balloons Interval DP | Python
Traveling Salesman Bitmask DP (Held-Karp) | Python
Regular Expression Matching DP | Python
LFU Cache O(1) Implementation | Python
Token Bucket Rate Limiter Python | System Design Coding
Consistent Hashing Ring Python | System Design Coding
KMP String Search Algorithm | Python O(n+m)
Manacher's Algorithm Longest Palindrome | Python O(n)
Rabin-Karp Rolling Hash Pattern Matching | Python
Z-Algorithm Pattern Matching | Python O(n+m)
Trapping Rain Water II 3D Matrix | Python Heap BFS
Median of Two Sorted Arrays O(log n) | Python
Count Smaller Numbers After Self | Merge Sort Python
Minimum Window Substring Sliding Window | Python
Word Search II Trie Backtracking | Python
Largest Rectangle in Histogram Monotonic Stack | Python
Serialize Deserialize Binary Tree | Python
Stock Buy Sell with Cooldown DP State Machine | Python
Number of Islands II Dynamic Union-Find | Python
Thread-Safe Counter with Lock | Python Concurrency
Producer-Consumer Queue Python | threading.Queue
Semaphore Resource Pool Python | threading.Semaphore
asyncio gather Concurrent Fetch Python | Async Programming
asyncio Queue Producer Consumer Python | Async Queue
ThreadPoolExecutor map Python | Parallel Processing
ProcessPoolExecutor CPU Bound Python | Multiprocessing
Async Context Manager Python | __aenter__ __aexit__
threading.Event Condition Python | Thread Signaling
Deadlock Detection Resource Allocation Graph Python
Singleton Pattern Python | __new__ Thread-Safe
Observer Pattern Python | Publish Subscribe Event System
Strategy Pattern Python | Pluggable Algorithms OOP
Command Pattern Undo Redo Python | Design Patterns
Builder Pattern Fluent API Python | HTTP Request Builder
Decorator Pattern Python | Logging Timing Wrappers
Factory Method Pattern Python | Shape Factory OOP
Abstract Factory Pattern Python | Cross-Platform UI
Template Method Pattern Python | Data Pipeline
Flyweight Pattern Python | Glyph Object Pool
Chain of Responsibility Python | Middleware Pipeline
Iterator Protocol Python | Custom Range __iter__ __next__
Context Manager Protocol Python | DB Transaction
Descriptor Protocol Python | Validated Attribute
Metaclass Class Registry Python | Plugin Architecture
Implement lru_cache from Scratch Python | OrderedDict Cache
functools.reduce Python | Fold Scan Operations
itertools.groupby Python | Run Length Encoding
itertools combinations permutations Python | Combinatorics
collections.Counter Python | Top-K Anagram Grouping
collections.defaultdict Python | Nested Dict Builder
LRU Cache OrderedDict Python | collections.OrderedDict
heapq nlargest nsmallest Python | Streaming Top-K
bisect Module Python | Sorted List Binary Search
dataclasses __slots__ Python | Memory-Efficient Records
AVL Tree Insert Python | Self-Balancing BST Rotations
Red-Black Tree Insert Python | RB Tree Color Rotations
B-Tree Search Insert Python | Database Index Structure
Segment Tree Range Sum Python | Point Update O(log n)
Segment Tree Lazy Propagation Python | Range Update Query
Fenwick Tree BIT Python | Point Update Prefix Sum O(log n)
2D Fenwick Tree Python | Rectangle Sum Query
Trie Insert Search StartsWith Python | Prefix Tree
Trie Delete Python | Recursive Pruning
Trie Autocomplete Python | DFS Prefix Suggestions
Suffix Array Construction Python | O(n log^2 n)
Sparse Table RMQ Python | O(1) Range Minimum Query
Cartesian Tree Python | BST Heap Property O(n)
Splay Tree Python | Amortized O(log n) Self-Adjusting BST
Link-Cut Tree Python | Dynamic Tree Connectivity O(log n)
Egg Drop Problem Python | DP Binary Search O(k log n)
Palindrome Partitioning Min Cuts Python | DP O(n^2)
Wildcard Matching Python DP | ? and * Pattern Match
Edit Distance Levenshtein Python | DP Backtrack
Longest Common Substring Python | DP O(mn)
Longest Palindromic Subsequence Python | Interval DP
Distinct Subsequences Python | Count Ways DP
Stone Game DP Python | Game Theory Interval DP
Strange Printer Python | Interval DP Minimum Turns
Number of Music Playlists Python | Combinatorial DP
Cherry Pickup II Python | Two Robots Grid DP
Painting the Walls Python | Knapsack DP
Count Ways Build Good Strings Python | DP Modular
Minimum Cost Cut Stick Python | Interval DP
Maximum Profit Job Scheduling Python | Weighted Interval DP
Sieve of Eratosthenes Python | Prime Numbers O(n log log n)
Prime Factorization Python | Trial Division SPF Sieve
Extended Euclidean Algorithm Python | GCD Bezout Identity
Modular Exponentiation Python | Fast Power Binary Exp
Modular Inverse Python | Fermat Extended GCD
Chinese Remainder Theorem Python | System of Congruences
Catalan Numbers Python | DP Formula BST Count
nCr mod p Python | Lucas Theorem Factorial Precompute
Matrix Exponentiation Fibonacci Python | O(log n)
FFT Polynomial Multiplication Python | O(n log n)
Bloom Filter Python | Probabilistic Set Membership
Skip List Python | Probabilistic Ordered List O(log n)
Trie Autocomplete Service Python | Frequency Ranking Top-K
Write-Ahead Log WAL Python | Crash Recovery
Merkle Tree Python | Hash Tree Data Integrity
Inverted Index Python | Search Engine Build and Query
Count-Min Sketch Top-K Python | Heavy Hitters Stream
Sliding Window Rate Limiter Python | Deque O(1)
Snowflake ID Generator Python | Distributed Unique ID
Event Sourcing Store Python | Append Events Replay State
Convex Hull Graham Scan Python | O(n log n) Geometry
Line Segment Intersection Python | Cross Product Orientation
Closest Pair of Points Python | Divide and Conquer O(n log n)
Single Number III Python | Two Singles XOR Bit Manipulation
Reverse Bits Python | 32-bit Integer Bit Manipulation
Hamming Weight Python | Brian Kernighan Bit Count
Bit Manipulation Tricks Python | XOR Swap LSB Power of 2
XOR Linked List Python | Memory-Efficient Doubly Linked List
Gray Code Python | n-bit Gray Code Generation
Subsets Bitmask Python | Enumerate All 2^n Subsets
Eulerian Path Circuit Python | Hierholzer Algorithm
Hamiltonian Path Backtracking Python | NP-Complete
Max Flow Min Cut Python | Edmonds-Karp BFS Ford-Fulkerson
Hungarian Algorithm Python | Minimum Weight Bipartite Matching
Articulation Points Tarjan Python | Low-Link O(V+E)
