最小生成树 Kruskal和Prim算法

农场铺网络问题

Sample Input

4
0 4 9 21
4 0 8 17
9 8 0 16
21 17 16 0

Sample Output

28

Kruskal算法解答：
#include <iostream>
#include <algorithm>
using namespace std;
 
typedef struct Edge{
    int x, y, dis;
};
Edge town[10002];    //存放边的两端和长度信息
bool flag[102];        //标记新的结点是否加入
int nodeSet[102];    //标记编号对应的结点所属的集合
bool compare(Edge a, Edge b)
{
    return (a.dis < b.dis);
}
int main()
{
    int n, nodeTag;
    while(cin>>n){
        nodeTag = 1;
        for(int i = 1; i <= n; i++){
            nodeSet[i] = i;    //结点所在的set即为其编号
            for(int j = 1; j <= n; j++){    
                scanf("%d", &town[nodeTag].dis);
                town[nodeTag].x = i;
                town[nodeTag].y = j;
                nodeTag++;
            }
        }
        sort(town+1, town+nodeTag, compare);
        nodeTag = n+1;    //去掉前面的n个0，从最小的边开始
        int sum = 0, edgeSet = 0;
        while(edgeSet < n-1){//n-1条边时完全所有结点的连接,访问过的结点都会加入到一个set中
            if((!flag[town[nodeTag].x]) && (flag[town[nodeTag].y])){
                sum += town[nodeTag].dis;
                edgeSet++;
                flag[town[nodeTag].x] = true;
                nodeSet[town[nodeTag].x] = nodeSet[town[nodeTag].y];
            }else if((flag[town[nodeTag].x]) && (!flag[town[nodeTag].y])){
                sum += town[nodeTag].dis;
                edgeSet++;
                flag[town[nodeTag].y] = true;
                nodeSet[town[nodeTag].y] = nodeSet[town[nodeTag].x];
            }else if((!flag[town[nodeTag].x]) && (!flag[town[nodeTag].y])){
                sum += town[nodeTag].dis;
                edgeSet++;
                flag[town[nodeTag].x] = true;
                flag[town[nodeTag].y] = true;
                nodeSet[town[nodeTag].x] = nodeSet[town[nodeTag].y];
            }else {    //两端顶点都加入了set，判断新加入的边是否使结点形成了环
                if(nodeSet[town[nodeTag].x] != nodeSet[town[nodeTag].y]){
                    sum += town[nodeTag].dis;
                    edgeSet++;
                    int tmp = nodeSet[town[nodeTag].y];
                    for(int i = 1; i <= n; i++)    //将两个set中的元素合到一个set中
                        if(nodeSet[i] == tmp)
                            nodeSet[i] = nodeSet[town[nodeTag].x];
                }
            }
            nodeTag ++;
        }
        cout<<sum<<endl;
        memset(flag, 0, sizeof(flag));
    }
    return 0;
}