patterns catalog
Every coding-interview pattern on the site, one canonical deep-dive per pattern. Learn the template, then drill it against real problems.
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Arrays, strings & the core toolkit
Two pointersTwo Pointers Fundamentals Two pointers use two indices traversing an array or string to solve…Sliding windowThe Sliding Window Technique The sliding window technique optimizes brute-force O(n^2) or O(n^3) problems to…Binary searchWhy Binary Search Is Tested So Frequently Binary search appears in roughly 10-15% of FAANG…Hash-map patternsHash maps (dictionaries in Python, HashMaps in Java) provide O(1) average-case lookup, insertion, and deletion.…Prefix sumsBuild a prefix array where prefix[i] = arr[0] + arr[1] + ... + arr[i-1]. Then…String patternsStrings appear in roughly 25-30% of coding interviews. Unlike arrays or trees, string problems have…String matching (KMP / Z-algorithm)For each position i in text (0 to n-m): check if text[i:i+m] == pattern. O(n*m)…Rolling hash (Rabin-Karp)Given a text T of length n and a pattern P of length m, find…Sorting-algorithm patternsWhile most interviews don't ask you to implement sorting from scratch, understanding the algorithms helps…Matrix traversalMost matrix problems involve: (1) BFS from one or multiple source cells, (2) DFS to…
Stacks, queues, heaps & maps
Stack patternsA stack (LIFO) is the right tool when the most recently seen element determines the…Queue patternsMonotonic Deque Pattern - Sliding Window Maximum LeetCode 239. Given an array and window size…Monotonic stack & queueA monotonic stack maintains elements in strictly increasing or decreasing order. Elements that violate the…Heap / priority queueHeap Fundamentals A heap is a complete binary tree satisfying the heap property: in a…The two-heaps patternTwo heaps maintain the lower and upper halves of a data stream, allowing O(1) access…Ordered-map patternsAn ordered map maintains keys in sorted order with O(log n) insert, delete, and lookup,…Linked-list patternsLinked list problems trip up candidates because pointer manipulation is easy to mess up under…
Trees, tries & range structures
Binary-tree patternsBinary tree problems appear in nearly every technical interview. The foundation is traversal order, which…Tree traversalBinary tree traversals: Inorder (left, root, right) -- gives sorted order for a BST. Preorder…Advanced tree patternsA segment tree answers range queries (range sum, range minimum) in O(log n) and supports…Trie patternsTrie (prefix tree) problems appear frequently in coding interviews. This guide covers the core patterns…Segment tree & Fenwick treeRange query problems appear frequently in senior engineering interviews and competitive programming: "find the sum…Range-query patternsRange query problems appear frequently in competitive programming and technical interviews. Knowing which data structure…
Graphs
Graph patterns: the fundamentalsGraph problems appear in every serious technical interview. They cover a wide range of difficulty…BFS & DFSGraph traversal is one of the most tested interview topics. BFS (Breadth-First Search) and DFS…Topological sortA topological sort of a directed acyclic graph (DAG) produces a linear ordering of vertices…Union-Find (disjoint set)Union-Find (DSU) solves the dynamic connectivity problem: given a graph where edges are added one…Shortest paths (Dijkstra, Bellman-Ford)Shortest path problems are fundamental in graph interviews. Knowing when to apply BFS, Dijkstra, Bellman-Ford,…Minimum spanning treeA Minimum Spanning Tree (MST) of a weighted undirected graph is a spanning tree (connects…Advanced graph algorithmsFinds shortest paths from a source to all nodes, handling negative edge weights. Algorithm: initialize…
Dynamic programming
DP patterns: the overviewDynamic programming applies when a problem has two properties: (1) Optimal substructure: the optimal solution…1-D DP1D DP problems have a state space that reduces to a single index or value.…2-D and grid DP2D DP Pattern Overview 2D dynamic programming problems use a 2D table where dp[i][j] represents…Knapsack patternsThe 0/1 Knapsack problem is one of the most important DP patterns — its structure…DP on stringsString DP problems share a common structure: a 2D table where one dimension indexes into…Longest increasing subsequenceLIS: find the length of the longest strictly increasing subsequence of an array. Elements of…Stock-trading DPStock trading dynamic programming problems are a classic interview cluster. Every variant - one transaction,…Interval DPWhat is Interval DP? Interval DP is a dynamic programming pattern where you optimize over…State-machine DPState machine DP models problems as transitions between discrete states over a sequence. The key:…DP on treesTree DP solves optimization problems where the answer for each node depends on the answers…Advanced DP (digit, bitmask, tree)Tree DP, digit DP, and bitmask DP are three dynamic programming patterns, each matched to…
Recursion, greedy & everything else
Recursion patternsEvery recursive solution has: a base case (stops the recursion), a recursive case (reduces the…BacktrackingBacktracking is systematic trial and error — explore a decision tree, and when you reach…Divide & conquerDivide and conquer solves problems by: (1) Divide — split the problem into smaller subproblems…Greedy patternsGreedy algorithms make the locally optimal choice at each step. They are provably correct when…Interval algorithmsInterval problems appear constantly in coding interviews — at Google, Meta, Airbnb, and Uber. The…Bit manipulationBit manipulation problems appear at Google, Meta, and Amazon interviews. They test low-level reasoning and…Number theoryEuclidean algorithm: gcd(a,b) = gcd(b, a%b), base case gcd(a,0) = a. Time O(log min(a,b)). LCM:…Math patternsMath interview problems test number theory, combinatorics, and modular arithmetic. Common patterns: prime checking and…Concurrency patternsConcurrency problems appear at senior-level interviews (SDE-2 and above) at companies like Apple, Google, and…SQL question patternsThe recurring SQL patterns that show up across almost every database and data interview, each…LeetCode patterns by frequencyLeetCode has 3,000+ problems. You can't solve them all, and you don't need to. The…
