The DSA Dependency Graph: A Logical Roadmap from Arrays to DP

Source: Dev.to

The Problem

We often treat Data Structures and Algorithms (DSA) like a grocery list—pick “Heaps” today and “Graphs” tomorrow. But computer‑science topics have dependencies. You cannot understand Heaps without first understanding Arrays (how they are stored) and Trees (how they are visualized).

I created a 7‑Phase Roadmap 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: Master sequential data and index manipulation before touching complex nodes.

• Time & Space Complexity (Big‑O): The measuring stick for all code.
• Arrays: Memory models (static vs. dynamic).
• Searching & Sorting Algorithms: Essential prerequisite for Two Pointers.
• Recursion (Pattern): Basics – base case vs. recursive case.
• Two Pointers (Pattern): Most common array optimisation.
• 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: Trade space for speed.

• Hash Table / Hash Map: The O(1) lookup king.
• Strings: Immutability and manipulation techniques.

Phase 3: Pointers & Recursion

Goal: Move from indexes to references.

• Linked List: Single and doubly linked.
• Recursion (Advanced): Multiple recursive calls (pre‑pares for memoisation).
• 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: Understand parent‑child relationships.

• Trees: Height, depth, diameter properties.
• Binary Trees: Standard interview structure.
• Tree Traversals: Preorder, Inorder, Postorder, Level‑order.
• Binary Search Tree (BST): Sorted hierarchical data.
• Heaps / Priority Queue: Organising by priority.
• Top K Elements (Pattern): Using heaps efficiently.
• Divide and Conquer (Pattern): Merge‑sort logic applied to trees.

Phase 5: Advanced Search & Backtracking

Goal: Explore all possibilities.

• Backtracking (Pattern): Solving puzzles (Sudoku, N‑Queens).
• Tries: Prefix trees for autocomplete.

Phase 6: Connectivity (Graphs)

Goal: Model many‑to‑many relationships.

• Graphs: Adjacency matrix vs. adjacency list.
• Matrix Traversal (Advanced): Treating grids as graphs.
• Graph Traversals: BFS (shortest path in unweighted graphs) & DFS.
• Union‑Find: Disjoint Set Union (DSU).
• Shortest Path: Dijkstra’s algorithm.

Phase 7: Optimisation (The Hardest Part)

Goal: Solve overlapping sub‑problems.

• Bit Manipulation: Binary logic.
• Dynamic Programming (DP):
  • The pipeline: Recursion → Memoisation → Tabulation → Space Optimisation.

Why This Order?

• Recursion Split: Basic recursion is needed for sorting; advanced recursion is required for trees and DP.
• Matrix Split: You must know how to loop through a matrix (Phase 1) before running BFS on it (Phase 6).
• Patterns First: “Two Pointers” follows Arrays because that’s how arrays are used in real‑world problems.

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