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我们在图的定义中说过，带有权值的图就是网结构。一个连通图的生成树是一个极小的连通子图，它含有图中全部的顶点，但只有足以构成一棵树的n-1条边。所谓的最小成本，就是n个顶点，用n-1条边把一个连通图连接起来，并且使得权值的和最小。综合以上两个概念，我们可以得出：构造连通网的最小代价生成树，即最小生成树(Minimum Cost Spanning Tree)。找连通图的最小生成树，经典的有两种算法，普里姆算法和克鲁斯卡尔算法。
prim实现：
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;
public class Prim {
public static void main(String[] args) {
// TODO Auto-generated method stub
Scanner sc = new Scanner(System.in);
while (sc.hasNext()) {
int n = sc.nextInt();
int m = sc.nextInt();
if (n == 0 && m == 0) {
break;
}
int[][] map = new int[n][n];
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
map[i][j] = Integer.MAX_VALUE;
}
}
for (int i = 0; i < m; i++) {
int u = sc.nextInt();
int v = sc.nextInt();
int w = sc.nextInt();
map[u][v] = w;
map[v][u] = w;
}
Edge[] e = new Edge[n];
prim(map, e, n);
for (int i = 0; i < n - 1; i++) {
System.out.println(e[i].from + " " + e[i].end + " "
+ e[i].weight);
}
}
}
static void prim(int[][] map, Edge[] e, int n) {
Set<Integer> set1 = new HashSet<>();
Set<Integer> set2 = new HashSet<>();
set1.add(0);
for (int i = 1; i < n; i++)
set2.add(i);
int min = Integer.MAX_VALUE;
int k=0;
while (!set2.isEmpty()) {
min = Integer.MAX_VALUE;
int flag1 = 0;
int flag2 = 0;
for (int i : set1) {
for (int j : set2) {
if (map[i][j] < min) {
min = map[i][j];
flag1 = i;
flag2 = j;
}
}
}
set1.add(flag2);
set2.remove(flag2);
e[k]=new Edge();
e[k].from=flag1;
e[k].end=flag2;
e[k].weight=min;
k++;
}
}
private static class Edge {
int from;
int end;
int weight;
}
}
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原文地址：http://www.cnblogs.com/mlz-2019/p/4840925.html
