시간 제한메모리 제한제출정답맞힌 사람정답 비율
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문제

요즘 많은 자동차에서는 GPS 네비게이션 장비가 설치되어 있다. 네비게이션은 사용자가 입력한 출발점과 도착점 사이의 최단 경로를 검색해 준다. 하지만, 교통 상황을 고려하지 않고 최단 경로를 검색하는 경우에는 극심한 교통 정체를 경험할 수 있다.

상근이는 오직 자기 자신만 사용 가능한 네비게이션을 만들고 있다. 이 네비게이션은 절대로 최단 경로를 찾아주지 않는다. 항상 거의 최단 경로를 찾아준다.

거의 최단 경로란 최단 경로에 포함되지 않는 도로로만 이루어진 경로 중 가장 짧은 것을 말한다. 

예를 들어, 도로 지도가 아래와 같을 때를 생각해보자. 원은 장소를 의미하고, 선은 단방향 도로를 나타낸다. 시작점은 S, 도착점은 D로 표시되어 있다. 굵은 선은 최단 경로를 나타낸다. (아래 그림에 최단 경로는 두 개가 있다)거의 최단 경로는 점선으로 표시된 경로이다. 이 경로는 최단 경로에 포함되지 않은 도로로 이루어진 경로 중 가장 짧은 경로이다. 거의 최단 경로는 여러 개 존재할 수도 있다. 예를 들어, 아래 그림의 길이가 3인 도로의 길이가 1이라면, 거의 최단 경로는 두 개가 된다. 또, 거의 최단 경로가 없는 경우도 있다.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스의 첫째 줄에는 장소의 수 N (2 ≤ N ≤ 500)과 도로의 수 M (1 ≤ M ≤ 104)가 주어진다. 장소는 0부터 N-1번까지 번호가 매겨져 있다. 둘째 줄에는 시작점 S와 도착점 D가 주어진다. (S ≠ D; 0 ≤ S, D < N) 다음 M개 줄에는 도로의 정보 U, V, P가 주어진다. (U ≠ V ; 0 ≤ U, V < N; 1 ≤ P ≤ 103) 이 뜻은 U에서 V로 가는 도로의 길이가 P라는 뜻이다. U에서 V로 가는 도로는 최대 한 개이다. 또, U에서 V로 가는 도로와 V에서 U로 가는 도로는 다른 도로이다. 

입력의 마지막 줄에는 0이 두 개 주어진다.

출력

각 테스트 케이스에 대해서, 거의 최단 경로의 길이를 출력한다. 만약, 거의 최단 경로가 없는 경우에는 -1을 출력한다.

예제 입력 1

7 9
0 6
0 1 1
0 2 1
0 3 2
0 4 3
1 5 2
2 6 4
3 6 2
4 6 4
5 6 1
4 6
0 2
0 1 1
1 2 1
1 3 1
3 2 1
2 0 3
3 0 2
6 8
0 1
0 1 1
0 2 2
0 3 3
2 5 3
3 4 2
4 1 1
5 1 1
3 0 1
0 0

예제 출력 1

5
-1
6
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(\uc544\ub798 \uadf8\ub9bc\uc5d0 \ucd5c\ub2e8 \uacbd\ub85c\ub294 \ub450 \uac1c\uac00 \uc788\ub2e4)\uac70\uc758 \ucd5c\ub2e8 \uacbd\ub85c\ub294 \uc810\uc120\uc73c\ub85c \ud45c\uc2dc\ub41c \uacbd\ub85c\uc774\ub2e4. \uc774 \uacbd\ub85c\ub294 \ucd5c\ub2e8 \uacbd\ub85c\uc5d0 \ud3ec\ud568\ub418\uc9c0 \uc54a\uc740 \ub3c4\ub85c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uacbd\ub85c \uc911 \uac00\uc7a5 \uc9e7\uc740 \uacbd\ub85c\uc774\ub2e4. \uac70\uc758 \ucd5c\ub2e8 \uacbd\ub85c\ub294 \uc5ec\ub7ec \uac1c \uc874\uc7ac\ud560 \uc218\ub3c4 \uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc544\ub798 \uadf8\ub9bc\uc758 \uae38\uc774\uac00 3\uc778 \ub3c4\ub85c\uc758 \uae38\uc774\uac00 1\uc774\ub77c\uba74, \uac70\uc758 \ucd5c\ub2e8 \uacbd\ub85c\ub294 \ub450 \uac1c\uac00 \ub41c\ub2e4. \ub610, \uac70\uc758 \ucd5c\ub2e8 \uacbd\ub85c\uac00 \uc5c6\ub294 \uacbd\uc6b0\ub3c4 \uc788\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/almost.png\" style=\"height:174px; width:265px\" \/><\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \uc7a5\uc18c\uc758 \uc218 N (2 &le; N &le; 500)\uacfc \ub3c4\ub85c\uc758 \uc218 M (1 &le; M &le; 10<sup>4<\/sup>)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc7a5\uc18c\ub294 0\ubd80\ud130 N-1\ubc88\uae4c\uc9c0 \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 \uc2dc\uc791\uc810 S\uc640 \ub3c4\ucc29\uc810 D\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (S &ne; D; 0 &le; S, D &lt; N) \ub2e4\uc74c M\uac1c \uc904\uc5d0\ub294 \ub3c4\ub85c\uc758 \uc815\ubcf4 U, V, P\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (U &ne; V ; 0 &le; U, V &lt; N; 1 &le; P &le; 10<sup>3<\/sup>) \uc774 \ub73b\uc740 U\uc5d0\uc11c V\ub85c \uac00\ub294 \ub3c4\ub85c\uc758 \uae38\uc774\uac00 P\ub77c\ub294 \ub73b\uc774\ub2e4. U\uc5d0\uc11c V\ub85c \uac00\ub294 \ub3c4\ub85c\ub294 \ucd5c\ub300 \ud55c \uac1c\uc774\ub2e4. \ub610, U\uc5d0\uc11c V\ub85c \uac00\ub294 \ub3c4\ub85c\uc640 V\uc5d0\uc11c U\ub85c \uac00\ub294 \ub3c4\ub85c\ub294 \ub2e4\ub978 \ub3c4\ub85c\uc774\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ub450 \uac1c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \uac70\uc758 \ucd5c\ub2e8 \uacbd\ub85c\uc758 \uae38\uc774\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub9cc\uc57d, \uac70\uc758 \ucd5c\ub2e8 \uacbd\ub85c\uac00 \uc5c6\ub294 \uacbd\uc6b0\uc5d0\ub294 -1\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"5719","problem_lang":"1","title":"Almost Shortest Path","description":"<p>Finding the shortest path that goes from a starting point to a destination point given a set of points and route lengths connecting them is an already well known problem, and it&rsquo;s even part of our daily lives, as shortest path programs are widely available nowadays.<\/p>\r\n\r\n<p>Most people usually like very much these applications as they make their lives easier. Well, maybe not that much easier.<\/p>\r\n\r\n<p>Now that almost everyone can have access to GPS navigation devices able to calculate shortest paths, most routes that form the shortest path are getting slower because of heavy tra\ufb03c. As most people try to follow the same path, it&rsquo;s not worth it anymore to follow these directions.<\/p>\r\n\r\n<p>With this in his mind, your boss asks you to develop a new application that only he will have access to, thus saving him time whenever he has a meeting or any urgent event. He asks you that the program must answer not the shortest path, but the almost shortest path. He de\ufb01nes the almost shortest path as the shortest path that goes from a starting point to a destination point such that no route between two consecutive points belongs to any shortest path from the starting point to the destination.<\/p>\r\n\r\n<p>For example, suppose the \ufb01gure below represents the map given, with circles representing location points, and lines representing direct, one-way routes with lengths indicated. The starting point is marked as S and the destination point is marked as D. The bold lines belong to a shortest path (in this case there are two shortest paths, each with total length 4). Thus, the almost shortest path would be the one indicated by dashed lines (total length 5), as no route between two consecutive points belongs to any shortest path. Notice that there could exist more than one possible answer, for instance if the route with length 3 had length 1. There could exist no possible answer as well.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/almost.png\" style=\"height:174px; width:265px\" \/><\/p>\r\n","input":"<p>The input contains several test cases. The \ufb01rst line of a test case contains two integers N (2 &le; N &le; 500) and M (1 &le; M &le; 10<sup>4<\/sup>), separated by a single space, indicating respectively the number of points in the map and the number of existing one-way routes connecting two points directly. Each point is identi\ufb01ed by an integer between 0 and N &minus; 1. The second line contains two integers S and D, separated by a single space, indicating respectively the starting and the destination points (S &ne; D; 0 &le; S, D &lt; N). Each one of the following M lines contains three integers U, V and P (U &ne; V ; 0 &le; U, V &lt; N; 1 &le; P &le; 10<sup>3<\/sup>), separated by single spaces, indicating the existence of a one-way route from U to V with distance P. There is at most one route from a given point U to a given point V , but notice that the existence of a route from U to V does not imply there is a route from V to U, and, if such road exists, it can have a di\ufb00erent length. The end of input is indicated by a line containing only two zeros separated by a single space.<\/p>\r\n","output":"<p>For each test case in the input, your program must print a single line, containing -1 if it is not possible to match the requirements, or an integer representing the length of the almost shortest path found.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Latin America > South America Regional Contests 2008 A번