시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

어떤 나라에는 1부터 N까지 이름 붙여진 N개의 도시가 있다. 한 엔지니어는 모든 도시를 연결하는 도로를 건설하고자 한다. 즉, 모든 도시에 대해 항상 다른 어떤 도시로든 이동할 수 있어야 한다. 이때 여러 개의 도시를 통과할 수도 있다. 그의 팀은 몇 개의 길(도로 후보)을 조사했다. 각각의 길은 두 도시를 양방향으로 잇는다. 길 위에 도로를 지을 때는 특정 비용이 든다. (길이 짧을수록 비용도 싸다.)

이 엔지니어는 교통 시스템을 미리 계획하지 않았다. 그는 그저 선호에 따라 한 개의 길을 선택하고, 도로를 건설하는 일을 모든 도시가 연결될 때까지 반복한다.

지금 엔지니어는 도시 p와 도시 q를 잇는 도로를 건설하고자 한다. 비용을 감축하라는 정부의 압력에 의해, 그는 당신에게 그가 해당 도로를 지어야 하는지 여부를 판단하는 프로그램을 작성할 것을 요구했다. 당신의 프로그램은 그 도로를 지으면서 모든 도시를 연결하는 가장 짧은 도로망을 만들 수 있으면 YES라고 대답해야 한다. 그렇지 않다면, NO를 출력해야 한다.

입력

첫 줄에 테스트 케이스의 개수 T가 주어진다. (T ≤ 10) 

각 테스트 케이스의 첫 줄에는 4개의 정수 N, M, p, q가 주어진다. N(2 ≤ N ≤ 10,000)은 도로망 위에 존재하는 도시의 수이다. M(1 ≤ M ≤ 20,000)은 길의 수이다. p와 q(1 ≤ p,q ≤ N)는 그 사이에 도로를 지어도 되는지 판단해야 하는 두 도시이다.

이어지는 M개의 줄 각각에는 u, v, w가 주어진다.(1 ≤ u ≤ N, 1 ≤ v ≤ N, 1 ≤ w ≤ 400,000) 도시 u와 v를 잇는 양방향 길의 비용이 w라는 것을 의미한다. 도로를 짓는 데 드는 비용은 모두 다르며, 두 도시를 잇는 길은 오직 하나이다. 모든 도시를 잇는 도로망이 최소 한 개 이상 존재한다는 것이 보장된다. 모든 입력은 정수이다.

출력

각 테스트 케이스에 대해, p-q를 지으면서 가장 짧은 도로망을 만들 수 있으면 YES를 출력한다. 아니면 NO를 출력한다.

예제 입력 1

3
2 1 1 2
1 2 4
3 3 2 3
1 2 1
1 3 2
2 3 3
4 5 3 4
1 2 1
1 3 3
3 4 2
1 4 4
4 2 5

예제 출력 1

YES
NO
YES
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N(2 &le; N &le; 10,000)\uc740 \ub3c4\ub85c\ub9dd \uc704\uc5d0 \uc874\uc7ac\ud558\ub294 \ub3c4\uc2dc\uc758 \uc218\uc774\ub2e4. M(1 &le; M &le; 20,000)\uc740 \uae38\uc758 \uc218\uc774\ub2e4. p\uc640 q(1 &le; p,q &le; N)\ub294 \uadf8 \uc0ac\uc774\uc5d0 \ub3c4\ub85c\ub97c \uc9c0\uc5b4\ub3c4 \ub418\ub294\uc9c0 \ud310\ub2e8\ud574\uc57c \ud558\ub294 \ub450 \ub3c4\uc2dc\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc5b4\uc9c0\ub294 M\uac1c\uc758 \uc904 \uac01\uac01\uc5d0\ub294 u, v, w\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.(1 &le; u &le; N, 1 &le; v &le; N, 1 &le; w &le; 400,000) \ub3c4\uc2dc u\uc640 v\ub97c \uc787\ub294 \uc591\ubc29\ud5a5 \uae38\uc758 \ube44\uc6a9\uc774 w\ub77c\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4. \ub3c4\ub85c\ub97c \uc9d3\ub294 \ub370 \ub4dc\ub294 \ube44\uc6a9\uc740 \ubaa8\ub450 \ub2e4\ub974\uba70, \ub450 \ub3c4\uc2dc\ub97c \uc787\ub294 \uae38\uc740 \uc624\uc9c1 \ud558\ub098\uc774\ub2e4. \ubaa8\ub4e0 \ub3c4\uc2dc\ub97c \uc787\ub294 \ub3c4\ub85c\ub9dd\uc774 \ucd5c\uc18c \ud55c \uac1c \uc774\uc0c1 \uc874\uc7ac\ud55c\ub2e4\ub294 \uac83\uc774 \ubcf4\uc7a5\ub41c\ub2e4. \ubaa8\ub4e0 \uc785\ub825\uc740 \uc815\uc218\uc774\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574, p-q\ub97c \uc9c0\uc73c\uba74\uc11c \uac00\uc7a5 \uc9e7\uc740 \ub3c4\ub85c\ub9dd\uc744 \ub9cc\ub4e4 \uc218 \uc788\uc73c\uba74 YES\ub97c \ucd9c\ub825\ud55c\ub2e4. \uc544\ub2c8\uba74 NO\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9344","problem_lang":"1","title":"Road","description":"<p>In one country, there are N cities, numbered 1 to N. A civil engineer has to build public roads that connect all the cities together, i.e., it must be possible to travel from all cities to any other cities, maybe going through multiple cities. His team has surveyed several routes (candidate road between any two cities). Each route is a bidirectional connection between two cities. He can build a bi-directional road on the surveyed route for a specific cost (The shorter the route is the cheaper the road).<\/p>\r\n\r\n<p>This engineer has never planned a road system in advance. He would just pick one of the routes based on his preference, and build a road until all the cities are connected.&nbsp;<\/p>\r\n\r\n<p>Right now this engineer is going to build a road from the city p to the city q. With pressure from the government to reduce the cost, he asks you to write a program to decide, if he should build this road or not. Your program should say yes if the building of this road guaranteed that it can be part of the shortest road system that connects all cities together. Otherwise, your program should say no.&nbsp;<\/p>\r\n","input":"<p>First line of input is a number of test cases T &le; 10.&nbsp;<\/p>\r\n\r\n<p>Each test case start with a line contains 4 integers N, M, p, and q. N (2 &le; N &le; 10 000) is the number of cities in this road system. M (1 &le; M &le; 20 000) is the number of surveyed routes. p and q (1 &le; p &le; N and 1 &le; q &le; N) indicate the route between two cities, that the engineer asks if he can build a road or not.&nbsp;<\/p>\r\n\r\n<p>Then, the each of the following M lines contains 3 numbers u, v, and w (1 &le; u &le; N, 1 &le; v &le; N, 1 &le; w &le; 400 000) indicates that there are the bidirectional route of length w between u and v. The length of each road in the current system is unique. And, there is only one possible road between two cities. The input guarantees that at least one road system has a route between any two cities. All numbers are integer<\/p>\r\n","output":"<p>For each test case, display YES if the engineer can build a road p-q as part of the shortest road system. Otherwise, print NO.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]