시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 256 MB95432539196625.730%

문제

이 문제는 삼각 그래프의 가장 위쪽 가운데 정점에서 가장 아래쪽 가운데 정점으로 가는 최단 경로를 찾는 문제이다.

삼각 그래프는 사이클이 없는 그래프로 N ≥ 2 개의 행과 3열로 이루어져 있다. 삼각 그래프는 보통 그래프와 다르게 간선이 아닌 정점에 비용이 있다. 어떤 경로의 비용은 그 경로에서 지나간 정점의 비용의 합이다.

오른쪽 그림은 N = 4인 삼각 그래프이고, 가장 위쪽 가운데 정점에서 가장 아래쪽 가운데 정점으로 경로 중 아래로만 가는 경로의 비용은 7+13+3+6 = 29가 된다. 삼각 그래프의 간선은 항상 오른쪽 그림과 같은 형태로 연결되어 있다.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스의 첫째 줄에는 그래프의 행의 개수 N이 주어진다. (2 ≤ N ≤ 100,000) 다음 N개 줄에는 그래프의 i번째 행에 있는 정점의 비용이 순서대로 주어진다. 비용은 정수이며, 비용의 제곱은 1,000,000보다 작다.

입력의 마지막 줄에는 0이 하나 주어진다.

출력

각 테스트 케이스에 대해서, 가장 위쪽 가운데 정점에서 가장 아래쪽 가운데 정점으로 가는 최소 비용을 테스트 케이스 번호와 아래와 같은 형식으로 출력한다.

k. n

k는 테스트 케이스 번호, n은 최소 비용이다.

예제 입력 1

4
13 7 5
7 13 6
14 3 12
15 6 16
0

예제 출력 1

1. 22
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

출처

ICPC > Regionals > Africa and Arab > Arab Collegiate Programming Contest > 2010 Arab Collegiate Programming Contest D번