从A开始，A作为定点，找到与A相连并且未被处理(不在顶点集合中)的进行处理，找到权值最小的并加入集合，A-C[7]、A-G[2]、A-B[5]，最小的是A-G[2],所以把G加入集合，这里是有A-G的连接的。

然后把A、G作为顶点，找到与A、G相连未被处理的进行处理，A-C[7]、A-B[5]、G-E[4]、G-B[3]、G-F[6],最小的是G-B[3]，把B加入集合，

直到全部遍历完成！

在这里插入图片描述

代码

package Algorithm.prim;import java.util.Arrays;public class PrimAlgorihm {public static void main(String[] args) {char data [] = new char[]{'A','B','C','D','E','F','G'};int verxs = data.length;int weight [][] = new int[][]{{10000,5,7,10000,10000,10000,2},{5,10000,10000,9,10000,10000,3},{7,10000,10000,10000,8,10000,1},{10000,9,10000,10000,10000,4,1},{10000,10000,8,10000,10000,5,4},{10000,10000,10000,4,5,10000,6},{2,3,10000,10000,4,6,10000},};MGraph mGraph = new MGraph(verxs);MinTree minTree = new MinTree();minTree.createGraph(mGraph,verxs,data,weight);minTree.showGraph(mGraph);//测试普里姆算法minTree.prim(mGraph,6);}
}//创建最小生成树 ->
class MinTree{//创建图的邻接矩阵/**** @param graph 图对象* @param verxs 顶点个数* @param data  各个顶点的值* @param weight 图的邻接矩阵*/public void createGraph(MGraph graph, int verxs, char [] data, int weight [][]){int i,j;for (i = 0; i < verxs; i++) {graph.data[i] = data[i];for (j = 0; j < verxs; j++){graph.weight[i][j] = weight[i][j];}}}//显示图的邻接矩阵public void  showGraph(MGraph graph){for (int [] link : graph.weight){System.out.println(Arrays.toString(link));}}//编写prim算法,得到最小生成树/**** @param graph 图* @param v 从图的哪个顶点开始生产*/public void prim(MGraph graph, int v){//visited[] 标记顶点是否被访问过，默认都为0int visited [] = new int[graph.verxs];//把当前节点标记为以访问visited[v] = 1;//用h1和h2记录两个顶点的下标int h1 = -1;int h2 = -1;int minWeight = 10000;//将minWeight先初始化为一个大数，后面遍历过程中会被替换for (int k = 0; k < graph.verxs -1; k++) {//因为有graph.verxs顶点，普里姆算法结束后，有graph.verxs-1边//这个是确定每一次生成的子图，和哪个节点的距离最近//就是把所有的节点都给遍历了，所有的线都遍历一遍，找到与当前顶点相连的未被访问过的for (int i = 0; i < graph.verxs; i++) {//i节点表示被访问过的节点for (int j = 0; j < graph.verxs; j++) {//j节点表示未被访问过的节点if (visited[i] == 1 && visited[j] == 0 && graph.weight[i][j] < minWeight){//替换minWeight(寻找已经访问过的节点和未访问过的节点之间的权值最小的)minWeight = graph.weight[i][j];h1 = i;h2 = j;}}}//找到一条边是最小的System.out.println("边 <" + graph.data[h1]+","+graph.data[h2]+"> 权值：" + minWeight);//把当前节点标记为已经访问过visited[h2] = 1;//重置minWeightminWeight = 10000;}}
}
class MGraph{int verxs; //图的节点个数char[] data;//保存节点数据int[][] weight;//存放边,邻接矩阵public MGraph(int verxs) {this.verxs = verxs;data = new char[verxs];weight = new int[verxs][verxs];}}