poj 1258 Agri-Net 【最小生成树-Kruskal】

Agri-Net

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 56076 Accepted: 23245

Description

Farmer John has been elected mayor of his town! One of his campaign promises was to bring internet connectivity to all farms in the area. He needs your help, of course.
Farmer John ordered a high speed connection for his farm and is going to share his connectivity with the other farmers. To minimize cost, he wants to lay the minimum amount of optical fiber to connect his farm to all the other farms.
Given a list of how much fiber it takes to connect each pair of farms, you must find the minimum amount of fiber needed to connect them all together. Each farm must connect to some other farm such that a packet can flow from any one farm to any other farm.
The distance between any two farms will not exceed 100,000.

Input

The input includes several cases. For each case, the first line contains the number of farms, N (3 <= N <= 100). The following lines contain the N x N conectivity matrix, where each element shows the distance from on farm to another. Logically, they are N lines of N space-separated integers. Physically, they are limited in length to 80 characters, so some lines continue onto others. Of course, the diagonal will be 0, since the distance from farm i to itself is not interesting for this problem.

Output

For each case, output a single integer length that is the sum of the minimum length of fiber required to connect the entire set of farms.

Sample Input

40 4 9 214 0 8 179 8 0 1621 17 16 0

Sample Output

28

Source

USACO 102

题意：一位被竞选为市场的农民John,想把本市的所有农场实现网络化，为了节省开支，需要找到最小的且能把所有农场连接起来的方案。

AC代码：

# include <stdio.h># include <string.h># include <math.h># include <algorithm># define M 105using namespace std;struct EDGE{int u;int v;int w;} es[10005];int father[M];/*把每个点初始化,即把每个点分为各自的一组中去*/void Init(int n)  {for (int i = 1; i <= n; i++){father[i] = i;}}/*查找根节点*/int Find(int e){if (e == father[e]){return e;}return father[e] = Find(father[e]);}bool cmp(EDGE a, EDGE b){return a.w < b.w;}void Kruskal(int e){sort(es, es + e, cmp);int sum = 0;for (int i = 0; i < e; i++){EDGE m = es[i];int vf1 = Find(m.u);int vf2 = Find(m.v);if (vf1 != vf2){father[vf1] = vf2; //把两个点设置为一组sum += m.w;}}printf("%d\n", sum);}int main(void){int n;while (~scanf("%d", &n)){int i, j, cost;int k = 0;for (i = 1; i <= n; i++){for (j = 1; j <= n; j++){scanf("%d", &cost);es[k].u = i;es[k].v = j;es[k].w = cost;k++;}}Init(n);Kruskal(k);}return 0;}