시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 128 MB64927118038.793%

문제

코리아 통신회사에서는 3인통화 서비스를 제공한다. 이 서비스에서는 두 사람이 아니라 세 사람이 통화할 수 있도록 해준다. 전화망은 스위치들을 연결하여 구성되어 있으며, 각 통화자들은 스위치에 연결하여 전화망에 접속한다. 두 스위치들은 양방향으로 신호를 보낼 수 있는 링크에 의하여 연결되어 있다. 모든 스위치들은 전화망에 의하여 연결되어 있어서 스위치에 접속한 사람들은 다른 스위치에 연결한 사람과 항상 통화할 수 있다. 전화망에서 두 개의 스위치를 연결하는 링크를 사용하는 비용은 주어져 있다.

통신회사에서는 이들 세 사람을 전화망을 통하여 연결해주는데, 가장 비용이 적게 되도록 연결하고자한다. 세 사람이 연결한 스위치가 주어졌을 때, 이 스위치들을 비용이 가장 적게 되도록 연결하는 프로그램을 작성하시오.

입력

첫 번째 줄에는 두 개의 정수가 있다. 첫 번째 정수 n(1 ≤ n ≤ 1000) 는 전화망에 있는 스위치의 개수를 나타내며, 두 번째 정수 m은 스위치와 스위치를 연결하는 링크의 개수를 나타낸다. 단, 같은 스위치들을 연결하는 링크는 1 개 이상 존재하지 않는다. 각 스위치들은 1번부터 차례로 n 번 까지 번호가 부여된다. 다음 m개의 줄에는, 각 줄에 세 개의 정수가 주어진다. 처음의 두 개의 정수는 하나의 링크에 의하여 연결되는 두 스위치의 번호를 나타내며, 세 번째 정수는 그 링크를 사용하는 비용을 나타내는 양의 정수이다. 이 정수는 100 보다 작다. 입력의 마지막 줄에는 세 개의 정수가 주어 진다. 이 정수는 세 명의 통화자가 연결되어 있는 스위치 번호이며, 세 정수는 모두 다르다.

출력

첫 줄에는 3자 통화를 하는데 있어서 가장 적은 비용으로 통화할 때 드는 비용을 나타내는 정수와 세명의 통화자를 연결하는 네트워크 상에서의 링크의 수를 출력한다. 그 다음 줄부터 각 줄에는 하나의 링크에 연결되는 두 개의 스위치 번호를 출력한다. 비용이 최소가 되도록 연결하는 방법이 여러 가지인 경우에는 아무거나 출력한다.

예제 입력 1

8 12
1 2 20
2 3 8
2 4 3
2 5 3
2 6 6
3 5 2
3 6 9
4 7 5
5 6 1
5 7 7
6 8 4
7 8 6
1 4 6

예제 출력 1

27 4
1 2
2 4
2 5
5 6
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This service enables three customers to participate in a telephone conversation simultaneously. A customer accesses the interconnection network of the telephone system via a switch. The network consists of switches linked by bidirectional lines. Over the existing network, the three participants accessing the network via three different switches, must be connected with the minimum cost. Note that it is possible to connect any two switches. You will be given all the links between the switches of the network along with their associated costs. You are requested to find the connections which will minimize the total cost of interconnecting the three switches to which the participants in a conference call are connected.<\/p>\r\n","input":"<p>The input is a text file named conf.inp. The first line contains two numbers : The number of switches, designated by (N &lt;= 1000) and the number of switch-to-switch links in the network, designated by E, separated by a blank. Each of the following E input lines contains three integers, designated by i, j and c<sub>i,j<\/sub> where i and j are the numbers of two different switches and ci,jis the cost of using the link between i and j in a conference call (1 &lt;= c<sub>i,j<\/sub>&lt;= 100), each separated by one blank. The last line of input contains three integers, which designate the three switches that participate in the conference call, each separated by one blank. The switches are identified with integers 1 through N consecutively<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","output":"<p>The output must be a text file named conf.out. The first line must contain the total (minimal) cost of establishing a conference call among the given three switches and the number R of switch-to-switch connections needed to establish this conference call, separated by a blank. Each of the following R lines must contain two integers, which denote that the link between the switch numbered by the first integer and the switch numbered by the second integer is included in the solution -ordering of between the two switches is not important. The ordering among the last R lines of the output is also not important.<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/conf.gif\" style=\"height:272px; width:385px\" \/><\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

Olympiad > Balkan Olympiad in Informatics > BOI 1998 4번