Logo
(追記) (追記ここまで)

30807번 - TSM 스페셜 저지다국어

시간 제한메모리 제한제출정답맞힌 사람정답 비율
8 초 1024 MB3731038930.690%

문제

가중치 있는 그래프가 주어졌을 때, 최소 스패닝 트리(MST)의 비용을 구하는 문제는 잘 알려져 있습니다. 최소 스패닝 트리의 비용이 주어졌을 때, 그래프의 간선에 가중치를 부여하는 문제를 해결하세요.

자세한 설명은 아래와 같습니다.

  • 최소 스패닝 트리란, 주어진 그래프의 모든 정점들을 연결하는 부분 그래프 중에서 비용이 최소인 트리를 뜻합니다. 스패닝 트리의 비용은 트리에 포함된 간선의 가중치 합으로 정의합니다.
  • 주어지는 그래프는 $N$개의 정점과 $M$개의 간선을 가진 무방향 연결 그래프입니다. 각 정점과 각 간선에는 1ドル$번부터 순서대로 번호가 붙어 있습니다. $i$번 간선은 $u_i$번 정점과 $v_i$번 정점을 이으며, $i$번 간선에는 $l_i$ 이상 $r_i$ 이하의 정수 가중치를 부여할 수 있습니다.
  • 각 간선에 적절한 가중치를 부여해서 최소 스패닝 트리의 비용이 $K$가 되도록 만드세요.

입력

첫 번째 줄에 그래프의 정점의 수 $N$과 간선의 수 $M,ドル 최소 스패닝 트리의 비용 $K$가 공백으로 구분되어 주어집니다. $(2 \le N \le 100,円 000;\ N-1 \le M \le 200,円 000;\ 0 \le K \le 10^{10})$

다음 $M$개의 줄의 $i$번째 줄에 정수 $u_i, v_i, l_i, r_i$가 공백으로 구분되어 주어집니다. $i$번 간선이 $u_i$번 정점과 $v_i$번 정점을 이으며, $i$번 간선에 $l_i$ 이상 $r_i$ 이하의 정수 가중치를 부여할 수 있음을 의미합니다. $(1 \le u_i, v_i \le N;\ u_i \ne v_i;\ 0 \le l_i \le r_i \le 100,円 000)$

주어지는 그래프는 연결 그래프이며, 서로 다른 간선은 같은 정점 쌍을 잇지 않습니다.

출력

스패닝 트리의 비용이 $K$가 되도록 가중치를 부여할 수 있다면 첫 줄에 YES, 불가능하다면 NO를 출력합니다.YES를 출력한 경우 추가로 $M$개의 줄을 출력합니다. 그중 $i$번째 줄에는 $i$번째 간선에 부여할 가중치를 출력합니다.

제한

예제 입력 1 

4 5 10
1 2 0 5
1 3 7 9
1 4 1 6
2 4 3 4
3 4 2 2

예제 출력 1 

YES
5
7
4
4
2

예제 입력 2 

4 5 12
1 2 0 5
1 3 7 9
1 4 1 6
2 4 3 4
3 4 2 2

예제 출력 2 

NO

힌트

[{"problem_id":"30807","problem_lang":"0","title":"TSM","description":"<p>\uac00\uc911\uce58 \uc788\ub294 \uadf8\ub798\ud504\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ucd5c\uc18c \uc2a4\ud328\ub2dd \ud2b8\ub9ac(MST)\uc758 \ube44\uc6a9\uc744 \uad6c\ud558\ub294 \ubb38\uc81c\ub294 \uc798 \uc54c\ub824\uc838 \uc788\uc2b5\ub2c8\ub2e4. \ucd5c\uc18c \uc2a4\ud328\ub2dd \ud2b8\ub9ac\uc758 \ube44\uc6a9\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uadf8\ub798\ud504\uc758 \uac04\uc120\uc5d0 \uac00\uc911\uce58\ub97c \ubd80\uc5ec\ud558\ub294 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uc138\uc694.<\/p>\r\n\r\n<p>\uc790\uc138\ud55c \uc124\uba85\uc740 \uc544\ub798\uc640 \uac19\uc2b5\ub2c8\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ucd5c\uc18c \uc2a4\ud328\ub2dd \ud2b8\ub9ac\ub780, \uc8fc\uc5b4\uc9c4 \uadf8\ub798\ud504\uc758 \ubaa8\ub4e0 \uc815\uc810\ub4e4\uc744 \uc5f0\uacb0\ud558\ub294 \ubd80\ubd84 \uadf8\ub798\ud504 \uc911\uc5d0\uc11c \ube44\uc6a9\uc774 \ucd5c\uc18c\uc778 \ud2b8\ub9ac\ub97c \ub73b\ud569\ub2c8\ub2e4. \uc2a4\ud328\ub2dd \ud2b8\ub9ac\uc758 \ube44\uc6a9\uc740 \ud2b8\ub9ac\uc5d0 \ud3ec\ud568\ub41c \uac04\uc120\uc758 \uac00\uc911\uce58 \ud569\uc73c\ub85c \uc815\uc758\ud569\ub2c8\ub2e4.<\/li>\r\n\t<li>\uc8fc\uc5b4\uc9c0\ub294 \uadf8\ub798\ud504\ub294 $N$\uac1c\uc758 \uc815\uc810\uacfc $M$\uac1c\uc758 \uac04\uc120\uc744 \uac00\uc9c4 \ubb34\ubc29\ud5a5 \uc5f0\uacb0 \uadf8\ub798\ud504\uc785\ub2c8\ub2e4. \uac01 \uc815\uc810\uacfc \uac01 \uac04\uc120\uc5d0\ub294 $1$\ubc88\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \ubc88\ud638\uac00 \ubd99\uc5b4 \uc788\uc2b5\ub2c8\ub2e4. $i$\ubc88 \uac04\uc120\uc740 $u_i$\ubc88 \uc815\uc810\uacfc $v_i$\ubc88 \uc815\uc810\uc744 \uc774\uc73c\uba70, $i$\ubc88 \uac04\uc120\uc5d0\ub294 $l_i$ \uc774\uc0c1 $r_i$ \uc774\ud558\uc758 \uc815\uc218 \uac00\uc911\uce58\ub97c \ubd80\uc5ec\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\r\n\t<li>\uac01 \uac04\uc120\uc5d0 \uc801\uc808\ud55c \uac00\uc911\uce58\ub97c \ubd80\uc5ec\ud574\uc11c \ucd5c\uc18c \uc2a4\ud328\ub2dd \ud2b8\ub9ac\uc758 \ube44\uc6a9\uc774 $K$\uac00 \ub418\ub3c4\ub85d \ub9cc\ub4dc\uc138\uc694.<\/li>\r\n<\/ul>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \uadf8\ub798\ud504\uc758 \uc815\uc810\uc758 \uc218 $N$\uacfc \uac04\uc120\uc758 \uc218 $M$, \ucd5c\uc18c \uc2a4\ud328\ub2dd \ud2b8\ub9ac\uc758 \ube44\uc6a9 $K$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. $(2 \\le N \\le 100\\, 000;\\ N-1 \\le M \\le 200\\, 000;\\ 0 \\le K \\le 10^{10})$<\/p>\r\n\r\n<p>\ub2e4\uc74c $M$\uac1c\uc758 \uc904\uc758 $i$\ubc88\uc9f8 \uc904\uc5d0 \uc815\uc218 $u_i, v_i, l_i, r_i$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. $i$\ubc88 \uac04\uc120\uc774 $u_i$\ubc88 \uc815\uc810\uacfc $v_i$\ubc88 \uc815\uc810\uc744 \uc774\uc73c\uba70, $i$\ubc88 \uac04\uc120\uc5d0 $l_i$ \uc774\uc0c1 $r_i$ \uc774\ud558\uc758 \uc815\uc218 \uac00\uc911\uce58\ub97c \ubd80\uc5ec\ud560 \uc218 \uc788\uc74c\uc744 \uc758\ubbf8\ud569\ub2c8\ub2e4. $(1 \\le u_i, v_i \\le N;\\ u_i \\ne v_i;\\ 0 \\le l_i \\le r_i \\le 100\\, 000)$<\/p>\r\n\r\n<p>\uc8fc\uc5b4\uc9c0\ub294 \uadf8\ub798\ud504\ub294 \uc5f0\uacb0 \uadf8\ub798\ud504\uc774\uba70, \uc11c\ub85c \ub2e4\ub978 \uac04\uc120\uc740 \uac19\uc740 \uc815\uc810 \uc30d\uc744 \uc787\uc9c0 \uc54a\uc2b5\ub2c8\ub2e4.<\/p>\r\n","output":"<p>\uc2a4\ud328\ub2dd \ud2b8\ub9ac\uc758 \ube44\uc6a9\uc774 $K$\uac00 \ub418\ub3c4\ub85d \uac00\uc911\uce58\ub97c \ubd80\uc5ec\ud560 \uc218 \uc788\ub2e4\uba74 \uccab \uc904\uc5d0 <span style=\"color:#e74c3c;\"><code>YES<\/code><\/span>, \ubd88\uac00\ub2a5\ud558\ub2e4\uba74 <span style=\"color:#e74c3c;\"><code>NO<\/code><\/span>\ub97c \ucd9c\ub825\ud569\ub2c8\ub2e4.<span style=\"color:#e74c3c;\"><code>YES<\/code><\/span>\ub97c \ucd9c\ub825\ud55c \uacbd\uc6b0 \ucd94\uac00\ub85c $M$\uac1c\uc758 \uc904\uc744 \ucd9c\ub825\ud569\ub2c8\ub2e4. \uadf8\uc911 $i$\ubc88\uc9f8 \uc904\uc5d0\ub294 $i$\ubc88\uc9f8 \uac04\uc120\uc5d0 \ubd80\uc5ec\ud560 \uac00\uc911\uce58\ub97c \ucd9c\ub825\ud569\ub2c8\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"30807","problem_lang":"1","title":"TSM","description":"<p>The problem of finding a Minimum Spanning Tree(MST) in a weighted graph is well-known. Solve the problem of assigning weights to the edges of a graph, given the cost of the Minimum Spanning Tree.<\/p>\r\n\r\n<p>The details of the problem are as follows:<\/p>\r\n\r\n<ul>\r\n\t<li>A Minimum Spanning Tree is a subgraph that connects all nodes of the given graph in the form of a tree with minimum cost. The cost of the tree is defined as the sum of the weights of the edges.<\/li>\r\n\t<li>The given graph is an undirected graph with $N$ nodes and $M$ edges. Each node and each edge is numbered in order starting from $1$. The $i$-th edge connects nodes $u_i$ and $v_i$, and a weight between $l_i$ and $r_i$ inclusive can be assigned to the $i$-th edge.<\/li>\r\n\t<li>By assigning suitable weights to the edges, set $K$ as the cost of the Minimum Spanning Tree.<\/li>\r\n<\/ul>\r\n","input":"<p>The first line of input contains three space-separated integers $N$, $M$, and $K$, denoting the number of nodes, the number of edges, and the cost of the Minimum Spanning Tree of the graph, respectively. $(2 \\le N \\le 100\\, 000;\\ N-1 \\le M \\le 200\\, 000;\\ 0 \\le K \\le 10^{10})$<\/p>\r\n\r\n<p>The $i$-th of the following $M$ lines of input contains four space-separated integers $u_i, v_i, l_i, r_i$, denoting that the $i$-th edge connects nodes $u_i$ and $v_i$, and a weight between $l_i$ and $r_i$ inclusive can be assigned to the $i$-th edge. $(1 \\le u_i, v_i \\le N;\\ u_i \\ne v_i;\\ 0 \\le l_i \\le r_i \\le 100\\, 000)$<\/p>\r\n\r\n<p>It is guaranteed that the given graph is connected and no two edges connect the same pair of nodes.<\/p>\r\n","output":"<p>If there exists an assignment of weights such that the cost of the Minimum Spanning Tree is $K$, print <span style=\"color:#e74c3c;\"><code>YES<\/code><\/span> in the first line. Otherwise, print <span style=\"color:#e74c3c;\"><code>NO<\/code><\/span>.<\/p>\r\n\r\n<p>If the answer is <span style=\"color:#e74c3c;\"><code>YES<\/code><\/span>, print an additional $M$ lines of output. The $i$-th of the $M$ lines should contain the weight to be assigned to the $i$-th edge.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]

출처

Contest > solved.ac > solved.ac Grand Arena #3 > Division 2 F번

Contest > solved.ac > solved.ac Grand Arena #3 > Division 1 B번

(追記) (追記ここまで)

출처

대학교 대회

  • 사업자 등록 번호: 541-88-00682
  • 대표자명: 최백준
  • 주소: 서울시 서초구 서초대로74길 29 서초파라곤 412호
  • 전화번호: 02-521-0487 (이메일로 연락 주세요)
  • 이메일: contacts@startlink.io
  • 통신판매신고번호: 제 2017-서울서초-2193 호

AltStyle によって変換されたページ (->オリジナル) /