DSA Mastery

Longest Common Subsequence (LCS)

2 Views Updated 5/6/2026

Longest Common Subsequence (LCS)

The LCS problem finds the longest sequence that appears in the same relative order in two strings. It is the core algorithm behind Git Diff, File Comparisons, and DNA Sequencing.

1. Substring vs Subsequence

  • Substring: Must be contiguous (e.g., "ABCD" in "ABCDEFG").
  • Subsequence: Does NOT have to be contiguous (e.g., "ACE" in "ABCDE").

2. The LCS Table

If characters match: dp[i][j] = 1 + dp[i-1][j-1]. If they don't: dp[i][j] = Max(dp[i-1][j], dp[i][j-1]). This builds a matrix from the bottom up, with the final answer sitting at the bottom-right cell.

4. Interview Mastery

Q: "How does Git use the LCS algorithm?"

Architect Answer: "Git calculates the LCS of two file versions. Any lines (characters) NOT in the LCS are considered 'Changes' (Additions or Deletions). By finding the longest common part, Git can minimize the 'Noise' in a diff and show the developer exactly what changed as efficiently as possible."

DSA Mastery
1. Algorithmic Foundations
Big O Notation: Analyzing Time and Space Complexity Memory Management: Stack vs Heap in C# Recursion: The foundation of modern algorithms
2. Linear Data Structures
Arrays Deep Dive: Static vs Dynamic (List<T> Internals) Linked Lists: Singly, Doubly, and Circular Stacks and Queues: Implementing Undo/Redo & Message Buffers Hash Tables: Handling Collisions like a Pro
3. Non-Linear Data Structures
Binary Trees & BST: Searching at Log(N) speed Balanced Trees: AVL and Red-Black Trees Internals Heaps: Implementing a Priority Queue Tries (Prefix Trees): Optimizing Auto-complete features Graphs (Part 1): Representation (Matrix vs List) Graphs (Part 2): BFS vs DFS Traversal
4. Searching & Sorting
Binary Search: The power of Divide & Conquer Elementary Sorts: Bubble, Selection, and Insertion Merge Sort: Stable sorting for massive datasets Quick Sort: In-place sorting and Pivot selection Heap Sort: Leveraging the Priority Queue
5. Algorithmic Patterns
Sliding Window Pattern: Optimizing array performance Two Pointers Pattern: Reversing and Finding cycles Fast & Slow Pointers (Hare & Tortoise) Backtracking: Solving Sudoku and N-Queens
6. Dynamic Programming (DP)
Memoization vs Tabulation: Top-down vs Bottom-up The Knapsack Problem: 0/1 DP optimization Longest Common Subsequence (LCS) Matrix Chain Multiplication
7. Advanced Graphs & Interview
Dijkstra's Algorithm: Shortest path in weighted graphs Prim's and Kruskal's: Minimum Spanning Trees Disjoint Set Union (DSU) / Union-Find DSA Interview: FAANG Style Coding Challenges