Q15Data Structures

Depth-First Search (DFS) is a fundamental, aggressive graph traversal algorithm. Its core methodology involves selecting an arbitrary starting vertex and immediately plunging as deeply as physically possible along each branching path before finally hitting a dead end and being forced to backtrack. This specific behavior is inherently Last-In-First-Out, meaning DFS requires a Stack data structure (either explicitly managed in memory, or implicitly utilizing the system call stack via mathematical recursion) to actively track the traversal path and facilitate backtracking. It also strictly requires an auxiliary boolean array to track previously visited vertices to prevent infinite cyclic loops.

Explicit Stack-Based Implementation Algorithm

This iterative algorithm guarantees that every reachable vertex in the connected component is systematically visited and processed exactly once, yielding an optimal $O(V+E)$ time complexity.