BFS의 목적?

임의의 정점에서 시작해서, 모든 정점을 한번씩 방문하는 것.

물론 DFS도 동일해서 BFS, DFS 아무거나 사용해도 상관 없다.

하지만 BFS는 모든 가중치가 1일때 최단거리 알고리즘이 될 수 있다.

가중치가 1이 아니면 최단거리를 구하는 알고리즘이 아니고 Dijkstra 알고리즘이 된다.

BFS가 최단거리 알고리즘이 되는 이유는 어떤 하나의 정점에서 연결되어 있으면서 아직 방문하지 않은 정점 모두를 방문하기 때문

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BFS의 조건

그래서 BFS를 이용해 해결할 수 있는 문제는 아래와 같은 조건을 만족해야함

1. 최소 비용 문제 → BFS가 최단거리 알고리즘이기 때문.
2. 간선의 가중치 1 → 최단거리 알고리즘이지만 무조건 가중치가 1이여야함
3. 정점과 간선의 개수가 적어야함 → BFS의 시간복잡도가 O(V+E)이기 때문에 (O(E)) 정점과 간선의 개수가 너무 많다면 BFS로 해결할 수 없다.

물론 이전에 문제의 상황을 보고 그래프로 그릴 수 있는지 봐야함

거리의 최소값을 구하는 문제라면 가중치는 거리를 의미해야하고, 시간의 최소값을 구하는 문제라면 가중치는 시간을 의미

만약 최단거리를 구하는데 가중치 (간선)이 시간이라면 그래프로 만들 수 없다.