문제
선인장 그래프란 모든 간선이 최대 하나의 단순 사이클에만 포함된 무향 그래프를 의미합니다. 흐즈로는 선인장 그래프를 하나 가지고 있으며, 각 간선에는 길이가 있습니다. 두 정점 $u,ドル $v$를 연결하며 길이가 $l$인 간선을 순서쌍 $(u,v,l)$로 표기합니다. 문득 흐즈로는 자신의 그래프를 보다가 이러한 생각을 하게 되었습니다.
- 어떤 선인장 그래프는 적당히 접어서 1차원으로 만들 수도 있지 않을까?
이 의문을 해결하기 전, 다음의 성질을 만족하는 그래프를 접어서 1차원으로 만들 수 있다고 정의합시다.
- 각 정점 $i$에 1차원 좌표 $x_i$를 배정하여, 각 간선 $(u,v,l)$에 대해 $|x_u-x_v|=l$이 성립하도록 할 수 있습니다.
이제 여러분이 해결해야 하는 문제는 다음과 같습니다. 입력으로 흐즈로가 가진 선인장 그래프가 주어집니다. 이 그래프를 접어서 1차원으로 만들 수 있는지 판단해 주세요.
출력
그래프를 접어서 1차원으로 만들 수 있다면, 한 줄에 YES를 출력하세요. 그렇지 않다면 NO를 출력하세요.
노트
본 문제에서 정의하는 선인장 그래프는 연결 그래프가 아닐 수 있음에 주의하세요.
[{"problem_id":"31223","problem_lang":"0","title":"\uc120\uc778\uc7a5 \uc811\uae30","description":"<p><strong>\uc120\uc778\uc7a5 \uadf8\ub798\ud504<\/strong>\ub780 \ubaa8\ub4e0 \uac04\uc120\uc774 \ucd5c\ub300 \ud558\ub098\uc758 \ub2e8\uc21c \uc0ac\uc774\ud074\uc5d0\ub9cc \ud3ec\ud568\ub41c \ubb34\ud5a5 \uadf8\ub798\ud504\ub97c \uc758\ubbf8\ud569\ub2c8\ub2e4. \ud750\uc988\ub85c\ub294 \uc120\uc778\uc7a5 \uadf8\ub798\ud504\ub97c \ud558\ub098 \uac00\uc9c0\uace0 \uc788\uc73c\uba70, \uac01 \uac04\uc120\uc5d0\ub294 \uae38\uc774\uac00 \uc788\uc2b5\ub2c8\ub2e4. \ub450 \uc815\uc810 $u$, $v$\ub97c \uc5f0\uacb0\ud558\uba70 \uae38\uc774\uac00 $l$\uc778 \uac04\uc120\uc744 \uc21c\uc11c\uc30d $(u,v,l)$\ub85c \ud45c\uae30\ud569\ub2c8\ub2e4. \ubb38\ub4dd \ud750\uc988\ub85c\ub294 \uc790\uc2e0\uc758 \uadf8\ub798\ud504\ub97c \ubcf4\ub2e4\uac00 \uc774\ub7ec\ud55c \uc0dd\uac01\uc744 \ud558\uac8c \ub418\uc5c8\uc2b5\ub2c8\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uc5b4\ub5a4 \uc120\uc778\uc7a5 \uadf8\ub798\ud504\ub294 \uc801\ub2f9\ud788 \uc811\uc5b4\uc11c 1\ucc28\uc6d0\uc73c\ub85c \ub9cc\ub4e4 \uc218\ub3c4 \uc788\uc9c0 \uc54a\uc744\uae4c?<\/li>\r\n<\/ul>\r\n\r\n<p>\uc774 \uc758\ubb38\uc744 \ud574\uacb0\ud558\uae30 \uc804, \ub2e4\uc74c\uc758 \uc131\uc9c8\uc744 \ub9cc\uc871\ud558\ub294 \uadf8\ub798\ud504\ub97c <strong>\uc811\uc5b4\uc11c 1\ucc28\uc6d0\uc73c\ub85c \ub9cc\ub4e4 \uc218 \uc788\ub2e4<\/strong>\uace0 \uc815\uc758\ud569\uc2dc\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uac01 \uc815\uc810 $i$\uc5d0 1\ucc28\uc6d0 \uc88c\ud45c $x_i$\ub97c \ubc30\uc815\ud558\uc5ec, \uac01 \uac04\uc120 $(u,v,l)$\uc5d0 \ub300\ud574 $|x_u-x_v|=l$\uc774 \uc131\ub9bd\ud558\ub3c4\ub85d \ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc774\uc81c \uc5ec\ub7ec\ubd84\uc774 \ud574\uacb0\ud574\uc57c \ud558\ub294 \ubb38\uc81c\ub294 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4. \uc785\ub825\uc73c\ub85c \ud750\uc988\ub85c\uac00 \uac00\uc9c4 <strong>\uc120\uc778\uc7a5 \uadf8\ub798\ud504<\/strong>\uac00 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. \uc774 \uadf8\ub798\ud504\ub97c <strong>\uc811\uc5b4\uc11c 1\ucc28\uc6d0\uc73c\ub85c \ub9cc\ub4e4 \uc218 \uc788<\/strong>\ub294\uc9c0 \ud310\ub2e8\ud574 \uc8fc\uc138\uc694.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \uadf8\ub798\ud504\uc758 \uc815\uc810\uc758 \uac1c\uc218 $n$\uacfc \uac04\uc120\uc758 \uac1c\uc218 $m$\uc774 \uacf5\ubc31\uc73c\ub85c \ubd84\ub9ac\ub418\uc5b4 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. ($1 \\le n \\le 10^5, 0 \\le m \\le \\min(\\lfloor 1.5(n-1) \\rfloor,10^5)$)<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 \ucd1d $m$\uac1c\uc758 \uc904\uc5d0 \uac04\uc120\uc758 \uc815\ubcf4\uac00 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. \uadf8 \uc911 $i$\ubc88\uc9f8 \uc904\uc5d0\ub294 $i$\ubc88\uc9f8 \uac04\uc120\uc774 \uc5f0\uacb0\ud558\ub294 \ub450 \uc815\uc810 $u_i$\uc640 $v_i$, \uadf8\ub9ac\uace0 \uac04\uc120\uc758 \uae38\uc774 $l_i$\uc774 \uacf5\ubc31\uc73c\ub85c \ubd84\ub9ac\ub418\uc5b4 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. ($1 \\le u_i,v_i \\le n$, $u \\neq v$, $0 \\le l_i \\le 50$)<\/p>\r\n\r\n<p>\uc8fc\uc5b4\uc9c4 \uadf8\ub798\ud504\ub294 \uc911\ubcf5 \uac04\uc120\uc774\ub098 \uc790\uae30 \uc790\uc2e0\uc744 \ud5a5\ud558\ub294 \uac04\uc120\uc744 \ud3ec\ud568\ud558\uc9c0 \uc54a\uc73c\uba70, \uc120\uc778\uc7a5 \uadf8\ub798\ud504\uc784\uc774 \ubcf4\uc7a5\ub429\ub2c8\ub2e4.<\/p>\r\n","output":"<p>\uadf8\ub798\ud504\ub97c <strong>\uc811\uc5b4\uc11c 1\ucc28\uc6d0\uc73c\ub85c \ub9cc\ub4e4 \uc218 \uc788<\/strong>\ub2e4\uba74, \ud55c \uc904\uc5d0 <span style=\"color:#e74c3c;\"><code><strong>YES<\/strong><\/code><\/span>\ub97c \ucd9c\ub825\ud558\uc138\uc694. \uadf8\ub807\uc9c0 \uc54a\ub2e4\uba74 <span style=\"color:#e74c3c;\"><code><strong>NO<\/strong><\/code><\/span>\ub97c \ucd9c\ub825\ud558\uc138\uc694.<\/p>\r\n","hint":"<p>\ubcf8 \ubb38\uc81c\uc5d0\uc11c \uc815\uc758\ud558\ub294 <strong>\uc120\uc778\uc7a5 \uadf8\ub798\ud504<\/strong>\ub294 \uc5f0\uacb0 \uadf8\ub798\ud504\uac00 \uc544\ub2d0 \uc218 \uc788\uc74c\uc5d0 \uc8fc\uc758\ud558\uc138\uc694.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"31223","problem_lang":"1","title":"Cactus Folding","description":"<p>A <strong>cactus graph<\/strong> is an undirected graph where each edge is included in at most one simple cycle. Chromate has a cactus graph, where each edge has a certain length. The edge connecting $u$ and $v$ with length $l$, is denoted as a tuple $(u,v,l)$. Looking at his graph, Chromate came up with this idea.<\/p>\r\n\r\n<ul>\r\n\t<li>Would it be possible to fold some cactus graphs into one dimension?<\/li>\r\n<\/ul>\r\n\r\n<p>Before dealing with this question, let us call a graph <strong>foldable into one dimension<\/strong> if it satisfies the following condition.<\/p>\r\n\r\n<ul>\r\n\t<li>It is possible to make $|x_u-x_v|=l$ hold for every edge $(u,v,l)$, by assigning an one-dimensional coordinate $x_i$ to each vertex $i$.<\/li>\r\n<\/ul>\r\n\r\n<p>Now the task is as follows. Chromate&#39;s <strong>cactus graph<\/strong> is given as input. Please determine if the graph is <strong>foldable into one dimension<\/strong>.<\/p>\r\n","input":"<p>On the first line, two integers $n$ and $m$ &mdash; the number of vertices and edges &mdash; are given. ($1 \\le n \\le 10^5, 0 \\le m \\le \\min(\\lfloor 1.5(n-1) \\rfloor,10^5)$)<\/p>\r\n\r\n<p>The following $m$ lines contain information of the edges. The $i$-th line out of them contains the two vertices $u_i$ and $v_i$ connected by the $i$-th edge, and $l_i$, the length of the edge. ($1 \\le u_i,v_i \\le n$, $u \\neq v$, $0 \\le l_i \\le 50$)<\/p>\r\n\r\n<p>The graph does not have duplicate edges or self loops, and is guaranteed to be a cactus graph.<\/p>\r\n","output":"<p>If the graph is <strong>foldable into one dimension<\/strong>, output <span style=\"color:#e74c3c;\"><tt><strong>YES<\/strong><\/tt><\/span> on one line. Otherwise, output <span style=\"color:#e74c3c;\"><tt><strong>NO<\/strong><\/tt><\/span>.<\/p>\r\n","hint":"<p>Do note that the <strong>cactus graph<\/strong> defined in this task is not necessarily&nbsp;a connected graph.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"English"}]