시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

Innovative Consumer Products Company (ICPC)는 비밀 프로젝트를 시작하려하고 있다. 이 프로젝트는 s개의 하위 프로젝트로 구성된다. 이 프로젝트에 관련된 b(≥s)개의 ICPC의 지사들이 있고, ICPC는 각 지사에 하위 프로젝트들 중 하나를 맡기고자 한다. 다시 말하자면, 지사들은 s개의 분리된 그룹으로 나누어지고, 각 그룹이 한 하위 프로젝트를 맡게 된다.

각 달의 마지막에, 각 지사는 그 그룹에 있는 다른 모든 지사에게 메시지를 보낼 것이다(서로 다른 지사에는 다른 메시지를 보낸다). ICPC는 통신을 위한 특별한 프로토콜을 가지고 있다. 각 지사 i는 그 지사와 본부에만 공개된 비밀키 kI를 가지고 있다. 지사 i가 지사 j에 메시지를 보내고 싶어한다고 하자. 지사 i는 비밀키 kI로 메시지를 암호화한다. 신뢰할 수 있는 운반원이 이 메시지를 지사로부터 본부까지 전달한다. 본부는 키 kI로 메시지를 복호화하고, 키 kj로 다시 암호화시킨다. 운반원은 새롭게 암호화된 메시지를 (키 kj를 가지고 있는) 지사 j로 전달한다. 보안적인 문제 때문에, 운반원은 동시에 오직 하나의 메시지만 전달할 수 있다.

도로망과 지사와 본부의 위치가 주어졌을 때, 당신은 각 지사에 하위 프로젝트를 배정하는 모든 경우에 대해서, 월말에 운반원이 메시지를 전달하기 위해 이동해야하는 최소 거리를 알아내야 한다.

입력

입력의 첫줄은 4개의 정수 n, b, s, 그리고 r로 이루어진다. n (2 ≤ n ≤ 5 000)은 교차로의 개수, b (1 ≤ b ≤ n − 1)는 지사의 수, s (1 ≤ s ≤ b)는 하위 프로젝트의 수, r (1 ≤ r ≤ 50 000)은 도로의 수를 나타낸다. 교차로들은 1부터 n까지 숫자가 주어지고, 지사들은 교차로 1부터 교차로 b에 위치하고, 본부는 교차로 b+1에 위치한다. 다음 r개의 줄은 각각 3개의 정수 u, v, l로 이루어진다. 이것은 교차로 u에서 교차로 v로 가는 길이 있고(1 ≤ u, v ≤ n), 이 길이가 l(0 ≤ ℓ ≤ 10 000)임을 뜻한다. u에서 v로 가는 길은 두번 이상 주어지지 않고, 어느 교차로에서든 다른 모든 교차로로 갈 수 있음이 보장된다.

출력

운반원이 이동해야 할 최소 거리를 출력한다.

예제 입력 1

5 4 2 10
5 2 1
2 5 1
3 5 5
4 5 0
1 5 1
2 3 1
3 2 5
2 4 5
2 1 1
3 4 2

예제 출력 1

13

예제 입력 2

5 4 2 10
5 2 1
2 5 1
3 5 5
4 5 10
1 5 1
2 3 1
3 2 5
2 4 5
2 1 1
3 4 2

예제 출력 2

24
[{"problem_id":"12766","problem_lang":"0","title":"\uc9c0\uc0ac \ubc30\uc815","description":"<p>Innovative Consumer Products Company (ICPC)\ub294 \ube44\ubc00 \ud504\ub85c\uc81d\ud2b8\ub97c \uc2dc\uc791\ud558\ub824\ud558\uace0 \uc788\ub2e4. \uc774 \ud504\ub85c\uc81d\ud2b8\ub294 s\uac1c\uc758 \ud558\uc704 \ud504\ub85c\uc81d\ud2b8\ub85c \uad6c\uc131\ub41c\ub2e4. \uc774 \ud504\ub85c\uc81d\ud2b8\uc5d0 \uad00\ub828\ub41c&nbsp;b(&ge;s)\uac1c\uc758 ICPC\uc758 \uc9c0\uc0ac\ub4e4\uc774 \uc788\uace0, ICPC\ub294 \uac01 \uc9c0\uc0ac\uc5d0 \ud558\uc704 \ud504\ub85c\uc81d\ud2b8\ub4e4 \uc911 \ud558\ub098\ub97c \ub9e1\uae30\uace0\uc790 \ud55c\ub2e4. \ub2e4\uc2dc \ub9d0\ud558\uc790\uba74, \uc9c0\uc0ac\ub4e4\uc740 s\uac1c\uc758 \ubd84\ub9ac\ub41c \uadf8\ub8f9\uc73c\ub85c \ub098\ub204\uc5b4\uc9c0\uace0, \uac01 \uadf8\ub8f9\uc774 \ud55c \ud558\uc704 \ud504\ub85c\uc81d\ud2b8\ub97c \ub9e1\uac8c \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ub2ec\uc758 \ub9c8\uc9c0\ub9c9\uc5d0, \uac01 \uc9c0\uc0ac\ub294 \uadf8 \uadf8\ub8f9\uc5d0 \uc788\ub294 \ub2e4\ub978 \ubaa8\ub4e0 \uc9c0\uc0ac\uc5d0\uac8c \uba54\uc2dc\uc9c0\ub97c \ubcf4\ub0bc \uac83\uc774\ub2e4(\uc11c\ub85c \ub2e4\ub978 \uc9c0\uc0ac\uc5d0\ub294 \ub2e4\ub978 \uba54\uc2dc\uc9c0\ub97c \ubcf4\ub0b8\ub2e4). ICPC\ub294 \ud1b5\uc2e0\uc744 \uc704\ud55c \ud2b9\ubcc4\ud55c \ud504\ub85c\ud1a0\ucf5c\uc744 \uac00\uc9c0\uace0 \uc788\ub2e4. \uac01 \uc9c0\uc0ac i\ub294&nbsp;\uadf8 \uc9c0\uc0ac\uc640 \ubcf8\ubd80\uc5d0\ub9cc \uacf5\uac1c\ub41c&nbsp;\ube44\ubc00\ud0a4 k<sub>I<\/sub>\ub97c \uac00\uc9c0\uace0 \uc788\ub2e4. \uc9c0\uc0ac i\uac00 \uc9c0\uc0ac j\uc5d0 \uba54\uc2dc\uc9c0\ub97c \ubcf4\ub0b4\uace0 \uc2f6\uc5b4\ud55c\ub2e4\uace0 \ud558\uc790. \uc9c0\uc0ac i\ub294 \ube44\ubc00\ud0a4 k<sub>I<\/sub>\ub85c \uba54\uc2dc\uc9c0\ub97c \uc554\ud638\ud654\ud55c\ub2e4. \uc2e0\ub8b0\ud560 \uc218 \uc788\ub294 \uc6b4\ubc18\uc6d0\uc774 \uc774 \uba54\uc2dc\uc9c0\ub97c \uc9c0\uc0ac\ub85c\ubd80\ud130 \ubcf8\ubd80\uae4c\uc9c0 \uc804\ub2ec\ud55c\ub2e4. \ubcf8\ubd80\ub294 \ud0a4 k<sub>I<\/sub>\ub85c \uba54\uc2dc\uc9c0\ub97c \ubcf5\ud638\ud654\ud558\uace0, \ud0a4 k<sub>j<\/sub>\ub85c \ub2e4\uc2dc \uc554\ud638\ud654\uc2dc\ud0a8\ub2e4. \uc6b4\ubc18\uc6d0\uc740 \uc0c8\ub86d\uac8c \uc554\ud638\ud654\ub41c \uba54\uc2dc\uc9c0\ub97c (\ud0a4 k<sub>j<\/sub>\ub97c \uac00\uc9c0\uace0 \uc788\ub294) \uc9c0\uc0ac j\ub85c \uc804\ub2ec\ud55c\ub2e4. \ubcf4\uc548\uc801\uc778 \ubb38\uc81c \ub54c\ubb38\uc5d0, \uc6b4\ubc18\uc6d0\uc740 \ub3d9\uc2dc\uc5d0 \uc624\uc9c1 \ud558\ub098\uc758 \uba54\uc2dc\uc9c0\ub9cc \uc804\ub2ec\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub3c4\ub85c\ub9dd\uacfc \uc9c0\uc0ac\uc640 \ubcf8\ubd80\uc758 \uc704\uce58\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ub2f9\uc2e0\uc740 \uac01 \uc9c0\uc0ac\uc5d0 \ud558\uc704 \ud504\ub85c\uc81d\ud2b8\ub97c \ubc30\uc815\ud558\ub294 \ubaa8\ub4e0 \uacbd\uc6b0\uc5d0 \ub300\ud574\uc11c,&nbsp;\uc6d4\ub9d0\uc5d0 \uc6b4\ubc18\uc6d0\uc774 \uba54\uc2dc\uc9c0\ub97c \uc804\ub2ec\ud558\uae30 \uc704\ud574 \uc774\ub3d9\ud574\uc57c\ud558\ub294 \ucd5c\uc18c \uac70\ub9ac\ub97c \uc54c\uc544\ub0b4\uc57c \ud55c\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc758 \uccab\uc904\uc740 4\uac1c\uc758 \uc815\uc218 n, b, s, \uadf8\ub9ac\uace0 r\ub85c \uc774\ub8e8\uc5b4\uc9c4\ub2e4. n (2 &le; n &le; 5 000)\uc740 \uad50\ucc28\ub85c\uc758 \uac1c\uc218, b (1 &le; b &le; n &minus; 1)\ub294 \uc9c0\uc0ac\uc758 \uc218, s (1 &le; s &le; b)\ub294 \ud558\uc704 \ud504\ub85c\uc81d\ud2b8\uc758 \uc218, r (1 &le; r &le; 50 000)\uc740 \ub3c4\ub85c\uc758 \uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4. \uad50\ucc28\ub85c\ub4e4\uc740 1\ubd80\ud130 n\uae4c\uc9c0 \uc22b\uc790\uac00 \uc8fc\uc5b4\uc9c0\uace0, \uc9c0\uc0ac\ub4e4\uc740 \uad50\ucc28\ub85c 1\ubd80\ud130 \uad50\ucc28\ub85c b\uc5d0 \uc704\uce58\ud558\uace0, \ubcf8\ubd80\ub294 \uad50\ucc28\ub85c b+1\uc5d0 \uc704\uce58\ud55c\ub2e4. \ub2e4\uc74c r\uac1c\uc758 \uc904\uc740 \uac01\uac01 3\uac1c\uc758 \uc815\uc218 u, v, l\ub85c \uc774\ub8e8\uc5b4\uc9c4\ub2e4.&nbsp;\uc774\uac83\uc740 \uad50\ucc28\ub85c u\uc5d0\uc11c \uad50\ucc28\ub85c v\ub85c \uac00\ub294 \uae38\uc774 \uc788\uace0(1 &le; u, v &le; n), \uc774 \uae38\uc774\uac00 l(0 &le; \u2113 &le; 10 000)\uc784\uc744 \ub73b\ud55c\ub2e4. u\uc5d0\uc11c v\ub85c \uac00\ub294 \uae38\uc740 \ub450\ubc88 \uc774\uc0c1 \uc8fc\uc5b4\uc9c0\uc9c0 \uc54a\uace0, \uc5b4\ub290 \uad50\ucc28\ub85c\uc5d0\uc11c\ub4e0 \ub2e4\ub978 \ubaa8\ub4e0 \uad50\ucc28\ub85c\ub85c \uac08 \uc218 \uc788\uc74c\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/p>\r\n","output":"<p>\uc6b4\ubc18\uc6d0\uc774 \uc774\ub3d9\ud574\uc57c \ud560 \ucd5c\uc18c \uac70\ub9ac\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"12766","problem_lang":"1","title":"Branch Assignment","description":"<p>The Innovative Consumer Products Company (ICPC) is planning to start a top-secret project. This project consists of s subprojects. There will be b &ge; s branches of ICPC involved in this project and ICPC wants to assign each branch to one of the subprojects. In other words, the branches will form s disjoint groups, with each group in charge of a subproject.<\/p>\r\n\r\n<p>At the end of each month, each branch will send a message to every other branch in its group (a different message to each branch). ICPC has a particular protocol for its communications. Each branch i has a secret key k<sub>i<\/sub> known only to the branch and the ICPC headquarters. Assume branch i wants to send a message to branch j. Branch i encrypts its message with its key k<sub>i<\/sub>. A trusted courier picks up this message from this branch and delivers it to the ICPC headquarters. Headquarters decrypts the message with key k<sub>i<\/sub> and re-encrypts it with key k<sub>j<\/sub>. The courier then delivers this newly encrypted message to branch j, which decrypts it with its own key k<sub>j<\/sub>. For security reasons, a courier can carry only one message at a time.<\/p>\r\n\r\n<p>Given a road network and the locations of branches and the headquarters in this network, your task is to determine the minimum total distance that the couriers will need to travel to deliver all the end-of-month messages, over all possible assignments of branches to subprojects.<\/p>\r\n","input":"<p>The first line of input contains four integers n, b, s, and r, where n (2 &le; n &le; 5 000) is the number of intersections, b (1 &le; b &le; n &minus; 1) is the number of branches, s (1 &le; s &le; b) is the number of subprojects, and r (1 &le; r &le; 50 000) is the number of roads. The intersections are numbered from 1 through n. The branches are at intersections 1 through b, and the headquarters is at intersection b + 1. Each of the next r lines contains three integers u, v, and \u2113, indicating a one-way road from intersection u to a different intersection v (1 &le; u, v &le; n) of length \u2113 (0 &le; \u2113 &le; 10 000). No ordered pair (u, v) appears more than once, and from any intersection it is possible to reach every other intersection.<\/p>\r\n","output":"<p>Display the minimum total distance that the couriers will need to travel.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > World Finals > 2016 World Finals B번