英语题翻译22

该问题描述了一个图论中的经典问题,目标是最小化建立连接所有村庄的额外道路的成本。已知村庄间的部分道路,需要找出使得所有村庄都能通过这些道路相互连接的最小额外建设成本。输入包括村庄数量、现有道路的距离矩阵以及已建成的道路信息,输出是最小总成本。

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Constructing Roads | JXNUOJ

There are N villages, which are numbered from 1 to N, and you should build some roads such that every two villages can connect to each other. We say two village A and B are connected, if and only if there is a road between A and B, or there exists a village C such that there is a road between A and C, and C and B are connected.We know that there are already some roads between some villages and your job is the build some roads such that all the villages are connect and the length of all the roads built is minimum.

The first line is an integer N (3 <= N <= 100), which is the number of villages. Then come N lines, the i-th of which contains N integers, and the j-th of these N integers is the distance (the distance should be an integer within [1, 1000]) between village i and village j.Then there is an integer Q (0 <= Q <= N * (N + 1) / 2). Then come Q lines, each line contains two integers a and b (1 <= a < b <= N), which means the road between village a and village b has been built.

You should output a line contains an integer, which is the length of all the roads to be built such that all the villages are connected, and this value is minimum.

翻译:

有N个村庄,从1到N编号,你应该修一些道路,使每两个村庄可以相互连接。我们说两个村庄 A 和 B 是相连的,当且仅当 A 和 B 之间有一条道路,或者存在一个村庄 C 使得 A 和 C 之间有一条道路,并且 C 和 B 是相连的。我们知道一些村庄之间已经有一些道路,你的工作是建造一些道路,使所有村庄都连接起来,并且所有道路的长度最短。

第一行是一个整数 N (3 <= N <= 100),即村庄的数量。然后来N行,其中第i个包含N个整数,这N个整数中的第j个就是村庄i和村庄j之间的距离(距离应该是[1, 1000]内的整数)。那么有整数 Q (0 <= Q <= N * (N + 1) / 2)。然后是Q行,每行包含两个整数a和b(1 <= a < b <= N),表示a村和b村之间的路已经修好了。

你应该输出一行包含一个整数,它是连接所有村庄的所有道路的长度,这个值是最小值。

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