贪心算法之Prim

Prim与Dijistra算法有异曲同工之妙，只不过Dijistra是求最短路径，每次添加到集合中的是到固定起始点的最短距离，而Prim是求最小生成树，是整个图所有权重的最小和，每次添加到集合中的是到整个集合最短距离的点。

Prim算法具体如下所示：

#include <iostream>

using namespace std;

#define INF 1e7
#define MAXNODE 100

bool flag[MAXNODE];
int closest[MAXNODE];
int lowcost[MAXNODE];

void prim(int n, int u0, int map[MAXNODE][MAXNODE]);

int main() {
    int n, m, u, v, w;
    cout << "请输入节点数n和边数m:";
    cin >> n >> m;
    cout << "请输入节点边的权值：";
    int map[MAXNODE][MAXNODE];
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++)
            map[i][j] = INF;
    }
    for (int i = 0; i < m; i++) {
        cin >> u >> v >> w;
        map[u][v] = map[v][u] = min(w, map[u][v]);
    }
    cout << "请输入开始点：";
    int u0;
    cin >> u0;
    prim(n, u0, map);
    int sum = 0;
    for(int i = 0; i < n; i++){
        sum += lowcost[i];
    }
    cout<<sum;
    return 0;
}

void prim(int n, int u0, int map[MAXNODE][MAXNODE]) {
    //初始化
    flag[u0] = true;
    for (int i = 0; i < n; i++) {
        if (i != u0) {
            lowcost[i] = map[u0][i];
            closest[i] = u0;
        } else {
            lowcost[i] = 0;
        }
    }
    //开始找最近点
    for (int i = 0; i < n-1; i++) {
        int m = INF;
        int temp = u0;
        for(int j = 0; j < n; j++) {
            if (flag[j] == false && lowcost[j] < m){
                m = lowcost[j];
                temp = j;
            }
        }
        if(temp == u0){
            break;
        }
        flag[temp] = true;
        for(int j = 0; j < n; j++){
            if(flag[j] == false && lowcost[j] > map[j][temp]){
                lowcost[j] = map[j][temp];
                closest[j] = temp;
            }
        }
    }
}