数据结构—prim最小生成树

原理：参考趣学数据结构

代码：

#include<stdio.h>
#include<stdlib.h>
#define N 100
#define elemType int
//const int MAX_INT = (1 << 31) - 1;
//const int MAX_INT = 0X7fffffff;
#define  INF    (((unsigned int)(-1)) >> 1)
bool visited[N];
typedef struct GraphMatrix {elemType vNode[N][N];int vNum, eNum;
}GraphMatrix;
void initGMaxtix(GraphMatrix &G) {//初始化邻接矩阵printf("输入顶点数和边数\n");scanf_s("%d%d", &G.vNum, &G.eNum);for (int i = 0; i < G.vNum; i++) {//初始化邻接矩阵for (int j = 0; j < G.vNum; j++) {G.vNode[i][j] = INF;}}printf("输入顶点v1到顶点v2和其边的权重\n");for (int i = 0; i < G.eNum; i++) {int v1, v2, weights;scanf_s("%d%d%d", &v1, &v2, &weights);G.vNode[v1][v2] = weights;}
}
void print15(GraphMatrix G) {printf("邻接矩阵如下:\n");for (int i = 0; i < G.vNum; i++) {for (int j = 0; j < G.vNum; j++) {printf("%d ", G.vNode[i][j]);}printf("\n");}
}
void prim(GraphMatrix G, int u0) {//最小生成树int lowcost[N], closeV[N];for (int i = 0; i < G.vNum; i++) {//初始化lowcost[i] = G.vNode[u0][i];closeV[i] = u0;if (u0 == i) {lowcost[u0] = 0;}}visited[u0] = true;printf("%d ", u0);for (int k = 0; k < G.vNum - 1; k++) {//最小生成树 顶点数-1条边int t = u0, Temp = INF;for (int i = 0; i < G.vNum; i++) {//寻找连接两个集合最短边（已经访问和未被访问）if (!visited[i] && Temp > lowcost[i]) {Temp = lowcost[i];t = i;}}if (t == u0) {break;}visited[t] = true;printf("%d ", t);for (int i = 0; i < G.vNum; i++) {//因为新结点的加入，可能会缩短两个顶点集合之间的距离,更新操作if (!visited[i]&&G.vNode[t][i] < lowcost[i]) {lowcost[i] = G.vNode[t][i];closeV[i] = t;}}}printf("\n哪些边有关系:\n");for (int i = 0; i < G.vNum; i++) {if (i != u0) {printf("%d---%d有边\n", i, closeV[i]);}}
}
int main() {GraphMatrix G;initGMaxtix(G);print15(G);printf("\n");for (int i = 0; i < G.vNum; i++) {visited[i] = false;}printf("prim最小生成树\n");prim(G, 0);printf("\n");system("pause");return 0;
}

测试截图：

时间复杂度O(n x n),空间复杂度O(n)

如果存在什么问题，欢迎批评指正！谢谢！