시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

재현이는 N개의 정점으로 이루어진 트리를 가지고 있었다. 트리는 1~N까지의 번호가 정점에 매겨져 있었으며, 트리를 잇는 N-1개의 간선에는 두 정점을 잇는 거리가 저장되어 있었다. 재현이는 트리를 좋아하는 만큼 트리에게 많은 메모리를 주기 위해서, 모든 간선을 N*N 인접 행렬에 저장했다.

애석하게도, 재현이와 인접 행렬을 모두 싫어하는 수찬이가, 플로이드-와셜 알고리즘을 통해 인접 행렬을 채워버리고 말았다. 재현이에게 남은 건, 두 정점간의 최단거리를 저장해놓은 행렬 뿐이다.

재현이는 흉측하게 변해버린 트리를 본 후, 이제 더이상 트리를 좋아하지 않는다. 재현이는 트리에게 많은 메모리를 주고 싶지 않기에, 트리를 인접 리스트에 저장하려고 한다.

수찬이가 플로이드-와셜 알고리즘을 돌린 인접 행렬이 주어졌을 때, 인접 리스트 형태로 원래 트리를 표현해주자.

입력

첫번째 줄에 트리의 정점 수 N이 주어진다. (3 ≤ N ≤ 1024)

이후 N-1개의 줄에 트리의 각 노드간의 최단거리가 인접행렬 형태로 주어진다. 입력 속도를 빠르게 하기 위해서 대각선 위/오른쪽만 주어진다. 즉, 1번 줄에는 2 / 3 / 4와의 최단 거리. 2번 줄에는 3 / 4 / 5와의 최단 거리... 이런 식으로 입력이 주어진다.

모든 거리는 15000을 넘지 않는 양의 정수이다.

출력

N개의 줄에 인접 리스트 형태로 트리를 출력하라.

정확히 하자면, i번째 줄에는 해당 노드와 연결되어 있는 정점의 수를 출력하고, 이후 출력한 수만큼 연결된 정점의 번호를 출력하면 된다. 연결된 정점은 오름차순으로 출력되어야 한다.

예제 입력 1

5
5 14 3 7
13 2 6
11 7
4

예제 출력 1

1 4
1 4
1 5
3 1 2 5
2 3 4
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The agency of Peter designed a new cosmic station, composed of N modules, labeled from 1 to N. Some couples of different modules are linked by corridors in such way that it is possible to go from each module to each other module by unique path of corridors (see the Figure). The length of each of the corridors is positive integer. There is no more then one corridor that links two modules. The chiefs of Peter would like to keep in secret the project. That is why Peter encoded the topology of the station giving for each two modules the distance between them (i.e. the sum of the lengths of the corridors on the unique path between the modules).<\/p>\r\n\r\n<p>Now Stancho has a difficult task &ndash; he promised to his bosses to decrypt the coding of Peter and to reconstruct the topology of the station. Unfortunately, Stancho is not experienced enough. Help him. Write a program recon that solves the task.<\/p>\r\n","input":"<p>The first line of the standard input contains the number N of the modules (3 &le; N &le; 1024). Then N &ndash; 1 lines follow. On the first of these lines the distances from module 1 to modules 2, 3,&hellip;, N are given, separated by single spaces. On the second line re given, separated by single spaces also, the distances from module 2 to modules 3, 4,&hellip;, N, and so on. The last line contains only the distance from module N &ndash; 1 to module N. All distances are positive integers not grater than 1024.<\/p>\r\n","output":"<p>The program has to print N lines to the standard output. The first line has to contain the list of the neighbors of module 1, i.e. the modules that are linked with corridors to it. The list has to start with the number L of neighbors followed by their labels, sorted in increasing order. All numbers has to be separated by single spaces. On the second row of the output, formatted in&nbsp;the same way, the list of the neighbors of module 2 has to be printed, and so on. The output has to finish with the list of the neighbors of module N.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > International Tournament in Informatics > Shumen 2010 B1번

Olympiad > Junior Balkan Olympiad in Informatics > JBOI 2010 1번

  • 문제의 오타를 찾은 사람: kalmiaa
  • 문제를 번역한 사람: koosaga