The Problem
We often treat Data Structures and Algorithms (DSA) like a grocery list. We pick "Heaps" today and "Graphs" tomorrow. But computer science topics have dependencies. You cannot understand Heaps if you don't understand Arrays (how they are stored) and Trees (how they are visualized).
I created a 7-Phase Roadmap tailored to build a mental model step-by-step. This order ensures that every new topic uses tools you mastered in the previous phase.
🏗️ Phase 1: Basic Linear Structures & Their Patterns Goal: Mastering sequential data and index manipulation. Before touching complex nodes, master the line.
Time & Space Complexity (Big-O): The measuring stick for all code.Arrays: Memory models (Static vs Dynamic).
Searching and sorting Algorithms: Essential pre-requisite for Two Pointers.
Recursion (Pattern): Just the basics (Base case vs Recursive case).Two Pointers (Pattern): The most common array optimization.
Binary Search (Algorithm): $O(\log N)$ logic.
Sliding Window (Pattern): Subarrays and substrings.
Prefix Sum (Pattern): 1D and 2D range queries.Intervals (Pattern): Merging and inserting ranges.
Matrix Traversal (Pattern): Basics of iterating 2D grids.
🔍 Phase 2: The Power of Lookup (Hashing)Goal: Trading space for speed.
Hash Table / Hash Map: The $O(1)$ lookup king.
Strings: Immutability and manipulation techniques.
🔗 Phase 3: Pointers & Recursion Goal: Moving from Indexes to References.
Linked List: Single and Doubly linked.
Recursion (Advanced): Multiple recursive calls (Memoization prep).
Stack & Queue: LIFO and FIFO mechanics.
Monotonic Stack (Pattern): Finding the "next greater element.
"Fast & Slow Pointers (Pattern): Cycle detection.
🌳 Phase 4: Non-Linear Structures (Hierarchical)Goal: Parent-Child relationships.
Trees: Height, depth, diameter properties.
Binary Trees: The standard interview structure.
Tree Traversals: Preorder, Inorder, Postorder, Level-order.
Binary Search Tree (BST): Sorted hierarchical data.
Heaps / Priority Queue: Organizing by priority.
Top K Elements (Pattern): Using Heaps efficiently.
Divide and Conquer (Pattern): Merge Sort logic applied to trees.
🕵️ Phase 5: Advanced Search & BacktrackingGoal: Exploring all possibilities.
Backtracking (Pattern): Solving puzzles (Sudoku, N-Queens).
Tries: Prefix trees for autocomplete.
🌐 Phase 6: Connectivity (Graphs)Goal: Many-to-Many relationships.
Graphs: Adjacency Matrix vs. Adjacency List.
Matrix Traversal (Advanced): Treating Grids as Graphs.
Graph Traversals: BFS (Shortest path in unweighted) & DFS.
Union Find: Disjoint Set Union (DSU).
Shortest Path: Dijkstra's Algorithm.
🚀 Phase 7: Optimization (The Hardest Part)Goal: Solving overlapping sub-problems.
Bit Manipulation: Binary logic.
Dynamic Programming (DP):
The pipeline: Recursion → Memoization → Tabulation → Space Optimization.
Why this order?
Recursion is Split: You need basic recursion for sorting, but advanced recursion for Trees and DP.
Matrix is Split: You need to know how to loop through a matrix (Phase 1) before you can run BFS on it (Phase 6).
Patterns First: We learn "Two Pointers" immediately after Arrays because that is how you actually use arrays in the real world.
Save this roadmap and stop getting lost in the noise! 🚀
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