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 = ; i < n; i++) {
         for (int j = ; j < n; j++)
             map[i][j] = INF;
     }
     for (int i = ; 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 = ;
     for(int i = ; i < n; i++){
         sum += lowcost[i];
     }
     cout<<sum;
     return ;
 }

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