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🧩 Problem Solving

[BOJ] 백준 2146번: 다리만들기

date
Sep 21, 2022
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boj-2146
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Public
category
🧩 Problem Solving
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BOJ
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Post
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백준 문제.png

문제링크

2146번: 다리 만들기
2146번: 다리 만들기
https://www.acmicpc.net/problem/2146
2146번: 다리 만들기
 

문제분석 및 설계

N ≤ 100
각 섬 그룹화 및 구분 → DFS / BFS
섬 사이의 최단 거리 → BFS
항상 2개 이상의 섬이 있으므로 다리를 건설하지 못하는 경우는 없음

풀이

  • map 정보 받아오기
    • BFS 시행해야 하므로 Node 객체 선언하여
    • Node[][] map; 의 형태로 값 저장
  • 각 칸에서 DFS 시행(BFS도 가능)하여 섬 번호 부여
    • main 에서 DFS 호출할 때마다 섬 번호++
    • DFS 내에서 인접 칸 재귀호출하며 해당 섬 번호로 갱신
  • 각 칸에서 BFS 시행하며 다른 섬까지의 최단 거리 갱신
    • BFS( ): 해당 칸에서 다른 섬까지 갈 수 있는 최단 거리 구하기
      • 하좌우 인접노드에 대하여
        • 인접 노드가 바다면 BFS 진행
        • 인접노드가 바다가 아니고 나와 다른 섬이면 BFS 중단 및 길이 리턴
    • 현재 저장된 가장 짧은 다리 길이와 비교하여 최솟값 갱신
  • 최단거리 출력
    • 항상 2개 이상의 섬이 있으므로 다리를 건설하지 못하는 경우는 없음
    • 따라서 초기값이 아닌 무조건 최솟값으로 갱신되어 있을 것임

BFS 가지치기

  1. 탐색 시 올라갈 필요 없음(상하좌우 인접노드 中 ‘상’ 노드 탐색 필요X)
      • 위로 올라가는 경로는 어차피 위에 있는 칸에서 이미 탐색했음
  1. bfs의 레벨이 현재 가장 작은 경로보다 멀리 가면 탐색 중단
      • 어차피 현재 저장된 가장 짧은 다리보다 길기 때문에 탐색할 필요가 없음
 

테스트케이스 및 반례

5
1 0 0 0 1
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 1 0 0 1
2
5
1 0 0 0 0
1 0 0 0 1
1 1 1 0 1
0 0 0 0 0
0 0 0 1 0
1
100 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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