🧠 The Ultimate Guide to DSA Patterns (With Examples)

Whether you're preparing for coding interviews or just want to become a better problem solver, mastering patterns in Data Structures and Algorithms (DSA) can be a game-changer.

Instead of memorizing solutions to hundreds of problems, recognize the underlying patterns — these are the repeatable techniques behind most coding problems.

Here’s a comprehensive guide of 32 DSA patterns you must know, complete with recognition cues and classic examples.

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🔁 1. Sliding Window

Used for: Subarrays/substrings of fixed or variable size
Recognize When: Find sum, average, or max/min of subarrays of size K
Examples:

• Maximum Sum Subarray of Size K

• Longest Substring Without Repeating Characters

• Minimum Size Subarray Sum

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🔁 2. Two Pointers

Used for: Sorted arrays, merging, comparisons
Recognize When: Finding pairs, triplets, or merging sorted arrays
Examples:

• Two Sum (Sorted)

• 3Sum

• Merge Sorted Arrays

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🔁 3. Fast and Slow Pointers

Used for: Cycle detection, middle of linked list
Recognize When: Cycle, intersection, or middle node in linked list
Examples:

• Linked List Cycle

• Find Middle of Linked List

• Happy Number

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🔁 4. Prefix Sum / Difference Arrays

Used for: Range queries, frequency updates
Recognize When: Subarray/range queries or range modifications
Examples:

• Subarray Sum Equals K

• Difference Array Range Updates

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🧮 5. Binary Search

Used for: Searching in sorted or monotonic structures
Recognize When: Min/max/target value optimization in sorted array
Examples:

• Binary Search

• Find Minimum in Rotated Array

• Aggressive Cows

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🧱 6. Monotonic Stack / Queue

Used for: Next/Previous Greater/Lesser Element problems
Recognize When: NGE, PGE, histogram, stock span, rainfall trapping
Examples:

• Next Greater Element

• Largest Rectangle in Histogram

• Daily Temperatures

• Trapping Rain Water

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🌲 7. Tree & Recursion Patterns

Used for: Tree problems with recursion or traversal
Includes:

• DFS / BFS

• LCA

• Tree DP

• Segment Trees / BIT

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📏 8. Greedy

Used for: Optimization by local decisions
Recognize When: Maximize or minimize globally using local optimum
Examples:

• Activity Selection

• Fractional Knapsack

• Huffman Coding

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🔁 9. Backtracking

Used for: Permutations, combinations, constraint satisfaction
Examples:

• N-Queens

• Sudoku Solver

• Subsets / Permutations

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💾 10. Dynamic Programming (DP)

Used for: Optimal solutions using overlapping subproblems
Variants:

• 1D/2D DP

• Memoization / Tabulation

• Bitmask DP, Digit DP, Subset DP, Tree DP
  Examples:

• 0/1 Knapsack

• Longest Common Subsequence

• Matrix Chain Multiplication

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🔄 11. Recursion + Memoization

Top-down version of DP with caching results.

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🔌 12. Bit Manipulation

Used for: Subsets, toggling, counting, power of 2
Examples:

• Subsets

• Power of Two

• XOR Tricks

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🧮 13. Union Find (Disjoint Set)

Used for: Connected components, grouping, cycles
Examples:

• Number of Provinces

• Kruskal’s MST

• Detect Cycle in Undirected Graph

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🔍 14. Topological Sort / Dependency Graphs

Used for: Scheduling, course completion
Examples:

• Course Schedule

• Alien Dictionary

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🔁 15. Graph Traversals (BFS/DFS)

Used for: Exploring nodes and paths in graphs
Examples:

• Number of Islands

• Flood Fill

• Maze Solver

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🪜 16. Shortest Path Algorithms

• 0-1 BFS

• Dijkstra

• Bellman-Ford

• Floyd-Warshall

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🎯 17. Trie (Prefix Tree)

Used for: Prefix queries, word dictionaries
Examples:

• Replace Words

• Word Search II

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🧮 18. Counting / Hashing / Frequency Maps

Used for: Most frequent elements, anagrams
Examples:

• Group Anagrams

• Top K Frequent Words

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📉 19. Heap / Priority Queue

Used for: Kth largest, stream-based data
Examples:

• Kth Largest Element

• Median from Data Stream

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🏁 20. Two Heaps

Used for: Live median, partition balancing
Examples:

• Find Median from Data Stream

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🧮 21. Segment Tree / Fenwick Tree (BIT)

Used for: Range queries and updates
Examples:

• Range Minimum/Maximum Query

• Range Sum Query

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🧠 22. Matrix Patterns

Used for: Matrix traversal, spiral, diagonal
Examples:

• Spiral Order

• Rotate Matrix

• Word Search

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🔢 23. Mathematical Patterns

• GCD/LCM (Euclid’s Algorithm)

• Modular Arithmetic

• Sieve of Eratosthenes

• Combinatorics (nCr, Factorials)

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🗺️ 24. Coordinate Compression

Used for: Reducing large values to small indices for BITs or SegTrees.

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⌛ 25. Sweep Line / Event Sorting

Used for: Intervals, events, segment merging
Examples:

• Meeting Rooms

• Skyline Problem

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🧊 26. Meet in the Middle

Used for: Splitting large input spaces
Examples:

• Subset Sum

• Partition Problem

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🎲 27. Randomized Algorithms

Examples:

• Reservoir Sampling

• Quickselect

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🧮 28. Kadane’s Algorithm

Used for: Maximum Subarray Sum in O(n)

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🧮 29. Merge Sort Inversions

Used for: Counting inversions efficiently in O(n log n)

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🎛️ 30. Bitmasking / Subset Enumeration

Used for: Subset-based DP, state compression

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🧬 31. Palindrome Techniques

Used for: Substring palindromes
Examples:

• Expand Around Center

• Manacher’s Algorithm

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🧠 32. Game Theory / Sprague-Grundy

Used for: Winning strategy problems
Examples:

• NIM Game

• XOR-based tricks

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🚀 Final Thoughts

DSA is less about brute-forcing and more about recognizing the right approach for the right problem. These patterns will help you:

• Improve problem-solving speed

• Solve unseen problems with confidence

• Excel in coding interviews

💡 Save this blog, revisit often, and practice pattern-based problems on LeetCode, Codeforces, or wherever you grind.

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Happy coding! 🚀