🎯 Depth-First Search (DFS): Deep Traversal Pattern for Frontend Interviews
Category: dsa
Difficulty: hard
Interview Importance: 🔴 Critical — This technique appears in 45% of frontend coding interviews for tree/graph traversal, backtracking problems, and component hierarchy analysis. Essential for React component trees, dependency resolution, and path finding. 1️⃣ What is Depth-First Search (DFS)? Depth-First Search (DFS) is a graph/tree traversal algorithm that explores as far as possible along each branch before backtracking. It uses a stack (either explicitly or via recursion call stack) to track the path, going deep into the structure before exploring siblings. Visual Representation: [code example] Real-World Analogy: Think of DFS like exploring a maze. You go down one path as far as you can, and only when you hit a dead end do you backtrack to try a different route. This is like how file explorers work - you open a folder, go into its first subfolder, then into that subfolder's first subfolder, and so on, until you reach the deepest level before coming back up. 2️⃣ Why Use DFS? / Why Does This Matter? Without DFS Benefit Iterate all possibilities Natural recursion Detect cycles in graph DFS with visited set Manual dependency ordering Optimal ordering Component tree traversal Recursive DFS Random exploration Systematic search Aspect BFS Data Structure Queue Traversal Order Breadth-first (level by level) Space Complexity O(w) width Shortest Path ✅ Yes (unweighted) Complete? ✅ Yes (finite branching) Optimal? ✅ Yes (unweighted) Best For Shortest path, level-order Frontend Use DOM traversal, friend suggestions Operation Space Complexity DFS tree traversal (recursive) O(h) O(n) Visit each node once; explicit stack depth = height DFS graph traversal O(V) O(V!) worst case Exponential paths possible; path length ≤ V Topological sort O(V) O(V + E) DFS with recursion stack LCA (Lowest Common Ancestor) O(h) Why DFS is O(V + E) for Graphs: [code example] Space Complexity - Why O(h) for Trees? [code example] Key Insight: Recursive DFS space depends on maximum recursion depth, wh...