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DSA Advanced
DSA Advanced — Learning Roadmap
Advanced data structures and algorithms for competitive programming and interviews.
Topics
| # | Topic | Key Concepts |
|---|---|---|
| 01 | Dynamic Programming — Basics | Memoization, tabulation, overlapping subproblems, optimal substructure, 1D DP |
| 02 | DP — Patterns | Knapsack, LCS, LIS, coin change, matrix chain, partition DP, bitmask DP |
| 03 | DP — Advanced | DP on trees, DP on graphs, digit DP, interval DP, probability DP |
| 04 | Graph — BFS & DFS | Traversals, connected components, cycle detection, topological sort, bipartite check |
| 05 | Graph — Shortest Paths | Dijkstra, Bellman-Ford, Floyd-Warshall, A*, 0-1 BFS, negative cycles |
| 06 | Graph — Advanced | MST (Kruskal/Prim), bridges, articulation points, strongly connected components, Euler paths |
| 07 | Trees — Advanced | Segment tree, Fenwick tree (BIT), sparse table, range queries (min/max/sum) |
| 08 | Trie | Prefix trie, suffix trie, autocomplete, word search, XOR trie, compressed trie |
| 09 | Union-Find (DSU) | Union by rank/size, path compression, cycle detection, Kruskal's MST, dynamic connectivity |
| 10 | Backtracking | N-Queens, Sudoku, permutations, subsets, combination sum, constraint satisfaction |
| 11 | Greedy Algorithms | Activity selection, Huffman coding, fractional knapsack, interval scheduling, proof of correctness |
| 12 | Divide & Conquer | Merge sort analysis, quick select, closest pair, matrix multiplication, master theorem |
| 13 | String Algorithms | KMP, Rabin-Karp, Z-algorithm, suffix array, rolling hash, Aho-Corasick |
| 14 | Bit Manipulation | Bitwise operators, tricks, XOR properties, bit masking, subset enumeration, power set |
| 15 | Heap & Priority Queue | Min/max heap, k-th element, merge k sorted, median stream, custom comparators |
| 16 | Sliding Window & Two Pointers | Fixed/variable window, shrink/expand, two pointers patterns, subarray problems |
| 17 | Binary Search — Advanced | Search on answer, rotated arrays, first/last occurrence, binary search on floating point |
| 18 | Monotonic Stack & Queue | Next greater element, largest rectangle, sliding window max, stock span |
| 19 | Math & Number Theory | GCD, prime sieve, modular arithmetic, fast exponentiation, combinatorics, probability |
| 20 | Interview Patterns | Pattern recognition, time/space complexity analysis, problem-solving framework, common mistakes |
How to Use
- If new to DSA, complete DSA-Core first
- Start with Sliding Window, Two Pointers, Binary Search — most common in interviews
- Master DP Basics → Patterns → Advanced — the biggest interview topic
- Study Graph algorithms — BFS/DFS, shortest paths, advanced topics
- Learn Segment Tree, Trie, Union-Find for competitive programming
- Finish with Interview Patterns for problem-solving strategy