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문제

월드산의 하부에는 동굴로 들어가는 입구가 있는데, 동굴은 터널을 통해 서로 연결되어 있는 여러 개의 작은 방들로 구성되어 있다. 동굴 입구는 탐험의 시작점이 되는 방 (이하 시작방)으로 곧장 연결되어 있다. 각 방을 연결하는 터널은 서로 교차하지 않으며, 두 개의 방을 연결하는 터널은 많아 봐야 하나이다.

"원쌤배 동굴 탐험 대회"가 개최될 예정이다. 대회의 목표는 시작방에서 출발하여 동굴 내부를 달려, 다시 시작방으로 되돌아 와 빠져 나오는 것인데, 그 경로는 참가자가 마음대로 정할 수 있지만 두 가지 조건을 지켜야 한다. 첫째 조건은, 시작방 이외의 방을 최소한 하나는 거쳐야 한다는 것이며, 둘째 조건은, 어떤 방과 터널도 최대 한 번밖에 방문할 수 없다는 것이다. (시작방은 물론 두 번 방문하게 되므로 예외이다.)

유명한 동굴 탐험가 김진영은 대회에 참가하기 위해 오랜 준비를 했고, 동굴을 여러 번 사전 답사하여 동굴 내부 구조를 알아내는 데 성공했다. 각각의 터널에 대해, 그는 그 터널을 가로지르는 데 필요한 시간을 계산했는데, 터널을 어느 방향으로 가로지르느냐에 따라 걸리는 시간이 서로 다른 경우도 있을 수 있다고 한다. 동굴 입구와 시작방 사이에서 소요되는 시간이나, 방 내부에서 이동하는데 필요한 시간은 무시할 수 있을 만했다. 이제 그는 경기의 규칙을 만족시키면서도, 가장 짧은 시간 내에 완주할 수 있는 경로를 찾아내려고 한다. 그를 돕기 위한 프로그램을 작성하라.

입력

첫째 줄에 n과 m이 주어진다. (3 ≤ n ≤ 5000, 3 ≤ m ≤ 10000) 이는 각각 동굴 내부의 방의 개수와, 터널의 개수를 나타낸다.

이어지는 m개의 줄에는 각각 터널의 정보를 제공하는 네 개의 숫자 a, b, c, d가 포함되어 있다. 이것은 a번 방에서 b번 방으로 갈 때는 c의 시간이 걸리고, 반대로 b번 방에서 a번 방으로 갈 때는 d의 시간이 걸린다는 의미이다. (1 ≤a, b ≤ n. a ≠ b. 1 ≤ c, d ≤ 10000)

방의 번호는 1번부터 n번까지 연속하여 붙어 있으며, 1번 방이 시작방이다. 언제나 조건을 만족하는 경로가 하나는 있다고 가정해도 좋다.

출력

동굴 탐험에 소요되는 최소시간을 출력한다.

예제 입력 1

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

예제 출력 1

6
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(\uc2dc\uc791\ubc29\uc740 \ubb3c\ub860 \ub450 \ubc88 \ubc29\ubb38\ud558\uac8c \ub418\ubbc0\ub85c \uc608\uc678\uc774\ub2e4.)<\/p>\r\n\r\n<p>\uc720\uba85\ud55c \ub3d9\uad74 \ud0d0\ud5d8\uac00 \uae40\uc9c4\uc601\uc740 \ub300\ud68c\uc5d0 \ucc38\uac00\ud558\uae30 \uc704\ud574 \uc624\ub79c \uc900\ube44\ub97c \ud588\uace0, \ub3d9\uad74\uc744 \uc5ec\ub7ec \ubc88 \uc0ac\uc804 \ub2f5\uc0ac\ud558\uc5ec \ub3d9\uad74 \ub0b4\ubd80 \uad6c\uc870\ub97c \uc54c\uc544\ub0b4\ub294 \ub370 \uc131\uacf5\ud588\ub2e4. \uac01\uac01\uc758 \ud130\ub110\uc5d0 \ub300\ud574, \uadf8\ub294 \uadf8 \ud130\ub110\uc744 \uac00\ub85c\uc9c0\ub974\ub294 \ub370 \ud544\uc694\ud55c \uc2dc\uac04\uc744 \uacc4\uc0b0\ud588\ub294\ub370, \ud130\ub110\uc744 \uc5b4\ub290 \ubc29\ud5a5\uc73c\ub85c \uac00\ub85c\uc9c0\ub974\ub290\ub0d0\uc5d0 \ub530\ub77c \uac78\ub9ac\ub294 \uc2dc\uac04\uc774 \uc11c\ub85c \ub2e4\ub978 \uacbd\uc6b0\ub3c4 \uc788\uc744 \uc218 \uc788\ub2e4\uace0 \ud55c\ub2e4. \ub3d9\uad74 \uc785\uad6c\uc640 \uc2dc\uc791\ubc29 \uc0ac\uc774\uc5d0\uc11c \uc18c\uc694\ub418\ub294 \uc2dc\uac04\uc774\ub098, \ubc29 \ub0b4\ubd80\uc5d0\uc11c \uc774\ub3d9\ud558\ub294\ub370 \ud544\uc694\ud55c \uc2dc\uac04\uc740 \ubb34\uc2dc\ud560 \uc218 \uc788\uc744 \ub9cc\ud588\ub2e4. \uc774\uc81c \uadf8\ub294 \uacbd\uae30\uc758 \uaddc\uce59\uc744 \ub9cc\uc871\uc2dc\ud0a4\uba74\uc11c\ub3c4, \uac00\uc7a5 \uc9e7\uc740 \uc2dc\uac04 \ub0b4\uc5d0 \uc644\uc8fc\ud560 \uc218 \uc788\ub294 \uacbd\ub85c\ub97c \ucc3e\uc544\ub0b4\ub824\uace0 \ud55c\ub2e4. \uadf8\ub97c \ub3d5\uae30 \uc704\ud55c \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\ub77c.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 n\uacfc m\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (3 &le; n &le; 5000, 3 &le; m &le; 10000) \uc774\ub294 \uac01\uac01 \ub3d9\uad74 \ub0b4\ubd80\uc758 \ubc29\uc758 \uac1c\uc218\uc640, \ud130\ub110\uc758 \uac1c\uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc5b4\uc9c0\ub294 m\uac1c\uc758 \uc904\uc5d0\ub294 \uac01\uac01 \ud130\ub110\uc758 \uc815\ubcf4\ub97c \uc81c\uacf5\ud558\ub294 \ub124 \uac1c\uc758 \uc22b\uc790 a, b, c, d\uac00 \ud3ec\ud568\ub418\uc5b4 \uc788\ub2e4. \uc774\uac83\uc740 a\ubc88 \ubc29\uc5d0\uc11c b\ubc88 \ubc29\uc73c\ub85c \uac08 \ub54c\ub294 c\uc758 \uc2dc\uac04\uc774 \uac78\ub9ac\uace0, \ubc18\ub300\ub85c b\ubc88 \ubc29\uc5d0\uc11c a\ubc88 \ubc29\uc73c\ub85c \uac08 \ub54c\ub294 d\uc758 \uc2dc\uac04\uc774 \uac78\ub9b0\ub2e4\ub294 \uc758\ubbf8\uc774\ub2e4. (1 &le;a, b &le; n. a &ne; b. 1 &le; c, d &le; 10000)<\/p>\r\n\r\n<p>\ubc29\uc758 \ubc88\ud638\ub294 1\ubc88\ubd80\ud130 n\ubc88\uae4c\uc9c0 \uc5f0\uc18d\ud558\uc5ec \ubd99\uc5b4 \uc788\uc73c\uba70, 1\ubc88 \ubc29\uc774 \uc2dc\uc791\ubc29\uc774\ub2e4. \uc5b8\uc81c\ub098 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \uacbd\ub85c\uac00 \ud558\ub098\ub294 \uc788\ub2e4\uace0 \uac00\uc815\ud574\ub3c4 \uc88b\ub2e4.<\/p>\r\n","output":"<p>\ub3d9\uad74 \ud0d0\ud5d8\uc5d0 \uc18c\uc694\ub418\ub294 \ucd5c\uc18c\uc2dc\uac04\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"1848","problem_lang":"1","title":"The Competition","description":"<p>At the foot of Mt. Byte there is an entrance to a cave. The cave consists of a complex system of chambers connected with tunnels. The cave entrance leads straight to a chamber called the front chamber. The tunnels do not intersect (they meet only in chambers). Two chambers can either be connected with a single tunnel, or not be connected at all (it may, however, be possible to reach one chamber from the other via remaining chambers). A tunnel always connects two distinct chambers.<\/p>\r\n\r\n<p>It has been decided that &#39;King&#39;s of Byteotia Cup&#39; competition is to be organized. The goal of each competitor is to traverse a freely chosen route in the cave and get out as quickly as possible. The route has to lead through at least one other chamber than the front one. Only two rules are in force: during the travel through the cave each chamber (with the exception of the front chamber) can be visited once at the most, similarly each corridor cannot be crossed more than once.<\/p>\r\n\r\n<p>A famous cave explorer Byteala is preparing himself for the competition. Byteala has been training in the cave for a long time and he has acquired a detailed knowledge of the corridor system. For each corridor he has calculated the amount of time needed to cross it in each direction. The time necessary to move within the chambers can be neglected. Now Byteala would like to calculate a route satisfying requirements of the competition, which can be traversed in the least time possible (the time necessary to traverse a route is the sum of the times needed to cross corridors which it consists of).<\/p>\r\n\r\n<p>Help Byteala! Write a programme which:<\/p>\r\n\r\n<ul>\r\n\t<li>reads from the standard input a description of the cave and times necessary to cross each corridor,<\/li>\r\n\t<li>calculates a route consistent with the requirements, for which the sum of times needed to cross the corridors it comprises is minimal,<\/li>\r\n\t<li>writes to the standard output the time required to traverse the calculated route.<\/li>\r\n<\/ul>\r\n","input":"<p>In the first line of the input there are two integers n and m (3 &le; n &le; 5 000, 3 &le; m &le; 10 000) separated by a single space and denoting the number of chambers in the cave and the number of interlinking corridors, respectively. The chambers are numbered from 1 to n. The front chamber is denoted by 1. The following m lines contain a description of the corridors. In each of these lines there are four integers separated by single spaces. A 4-tuple a,b,c,d means that chambers a and b are connected with a corridor, the crossing time from a to b is c and from b to a is d, 1 &le; a,b &le; n, a &ne; b, 1 &le; c,d &le; 10 000. You can assume that a route satisfying requirements of the competition always exists.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","output":"<p>Your programme should write in the first (and only) line of the output one integer - the minimal time required to traverse a route satisfying conditions of the competition.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

Olympiad > Polish Olympiad in Informatics > POI 2003/2004 > Stage 1 4번

  • 데이터를 추가한 사람: ntopia