A comprehensive roadmap for mastering Data Structures and Algorithms, from foundational concepts to advanced problem-solving techniques.
Laying the foundation with the importance of DSA, complexity analysis, asymptotic notations, and recursion basics.
Covering essential mathematical concepts that form the backbone of many advanced algorithms.
Deepening the understanding of recursion and exploring backtracking as a powerful problem-solving technique.
Mastering array manipulations with techniques like prefix sum, sliding window, two pointers, and Kadane's algorithm.
Diving into advanced string algorithms like KMP, Rabin-Karp, Z-algorithm, Manacher's, tries, and hashing.
Revisiting classic searching and sorting algorithms with a focus on advanced applications and non-comparison sorts.
Covering all variations of linked lists, common operations, and classic problems like cycle detection and reversal.
Exploring stacks, queues, and their variations like deques, priority queues, and applications like the LRU Cache.
A deep dive into hash tables, collision resolution strategies, and advanced applications like Bloom filters.
Introducing the non-linear tree data structure, including binary trees, traversals, and key properties.
Mastering node-based binary trees with a focus on search, insertion, deletion, and balancing techniques like AVL and Red-Black Trees.
Delving into tree-based heaps, heapify operations, and their application as Priority Queues in scheduling and data compression.
Introducing graph theory, including representations (adjacency list/matrix), and fundamental traversal algorithms like BFS and DFS.
Tackling complex graph problems like topological sorting and finding shortest paths with Dijkstra's, Bellman-Ford, and other algorithms.
Learning to find the minimum weight subset of edges that connects all vertices in a graph, using Kruskal's and Prim's algorithms.
Exploring critical network points (articulation points, bridges), pathfinding challenges (Eulerian/Hamiltonian paths), and network flow problems.
Introducing the core concepts of Dynamic Programming: overlapping subproblems and optimal substructure, through classic problems.
Exploring complex DP techniques including DP on trees, graphs, digits, and bitmasking, along with common optimization strategies.
Mastering the greedy approach, where the optimal choice is made at each step, and analyzing when this strategy works.
Algorithms for solving problems with geometric inputs, such as finding convex hulls, line intersections, and the closest pair of points.
Exploring powerful data structures for specialized problems, particularly range queries, including Tries, Segment Trees, and Fenwick Trees.
Synthesizing all learned concepts to tackle interview-style problems, focusing on patterns, trade-offs, and optimization strategies.