B - Networking

最新推荐文章于 2020-08-01 00:54:42 发布

龍木

最新推荐文章于 2020-08-01 00:54:42 发布

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分类专栏： ACM 最小生成树 kuangbin带我飞

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博客围绕设计网络连接问题展开，需使各点互连且电缆总长最小。输入包含点和路线信息，输出为设计网络的电缆总长度。这是最小生成树问题，可采用kruskal算法，运用并查集思想，对边排序后遍历合并，最终输出结果。

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https://vjudge.net/contest/66965#problem/B

You are assigned to design network connections between certain points in a wide area. You are given a set of points in the area, and a set of possible routes for the cables that may connect pairs of points. For each possible route between two points, you are given the length of the cable that is needed to connect the points over that route. Note that there may exist many possible routes between two given points. It is assumed that the given possible routes connect (directly or indirectly) each two points in the area.
Your task is to design the network for the area, so that there is a connection (direct or indirect) between every two points (i.e., all the points are interconnected, but not necessarily by a direct cable), and that the total length of the used cable is minimal.

Input

The input file consists of a number of data sets. Each data set defines one required network. The first line of the set contains two integers: the first defines the number P of the given points, and the second the number R of given routes between the points. The following R lines define the given routes between the points, each giving three integer numbers: the first two numbers identify the points, and the third gives the length of the route. The numbers are separated with white spaces. A data set giving only one number P=0 denotes the end of the input. The data sets are separated with an empty line.
The maximal number of points is 50. The maximal length of a given route is 100. The number of possible routes is unlimited. The nodes are identified with integers between 1 and P (inclusive). The routes between two points i and j may be given as i j or as j i.

Output

For each data set, print one number on a separate line that gives the total length of the cable used for the entire designed network.

Sample Input

1 0

2 3

1 2 37

2 1 17

1 2 68

3 7

1 2 19

2 3 11

3 1 7

1 3 5

2 3 89

3 1 91

1 2 32

5 7

1 2 5

2 3 7

2 4 8

4 5 11

3 5 10

1 5 6

4 2 12

Sample Output

思路：

这还是一道最小生成树的问题，我们可以用kruskal算法来写，即运用并查集的思想解决，我们先将所有的边存入结构体数组中，要存入起始点终点和权重，然后我们将结构体按权重从小到大排序，遍历所有边，如果这条边的两点的父节点不同，则合并成一个点，并把权重加入和中，否则则已合并成一个点，跳过。遍历完所有的边后，输出和即可。

代码