Breadth-First Search

O(V + E)

Start

Speed

Pseudocode

bfs(graph, start): queue = [start], visited = {start} while queue: cur = queue.pop(0) for nb in graph[cur]: if nb not in visited: visited.add(nb), queue.push(nb)

Color Guide

Unvisited

Enqueued

Exploring

Visited

Queue

← Front Back →

Visit Order

Step Log

Complexity

Time	O(V + E)
Space	O(V)