JS实现最小生成树之克鲁斯卡尔（Kruskal）算法

  1 //定义邻接矩阵
  2 let Arr2 = [
  3     [0, 10, 65535, 65535, 65535, 11, 65535, 65535, 65535],
  4     [10, 0, 18, 65535, 65535, 65535, 16, 65535, 12],
  5     [65535, 18, 0, 22, 65535, 65535, 65535, 65535, 8],
  6     [65535, 65535, 22, 0, 20, 65535, 65535, 16, 21],
  7     [65535, 65535, 65535, 20, 0, 26, 65535, 7, 65535],
  8     [11, 65535, 65535, 65535, 26, 0, 17, 65535, 65535],
  9     [65535, 16, 65535, 65535, 65535, 17, 0, 19, 65535],
 10     [65535, 65535, 65535, 16, 7, 65535, 19, 0, 65535],
 11     [65535, 12, 8, 21, 65535, 65535, 65535, 65535, 0],
 12 ]
 13 
 14 let numVertexes = 9, //定义顶点数
 15     numEdges = 15; //定义边数
 16 
 17 // 定义图结构  
 18 function MGraph() {
 19     this.vexs = []; //顶点表
 20     this.arc = []; // 邻接矩阵，可看作边表
 21     this.numVertexes = null; //图中当前的顶点数
 22     this.numEdges = null; //图中当前的边数
 23 }
 24 let G = new MGraph(); //创建图使用
 25 
 26 //创建图
 27 function createMGraph() {
 28     G.numVertexes = numVertexes; //设置顶点数
 29     G.numEdges = numEdges; //设置边数
 30 
 31     //录入顶点信息
 32     for (let i = 0; i < G.numVertexes; i++) {
 33         G.vexs[i] = ‘V‘ + i; //scanf(‘%s‘); //ascii码转字符 //String.fromCharCode(i + 65);
 34     }
 35     console.log(G.vexs) //打印顶点
 36 
 37     //邻接矩阵初始化
 38     for (let i = 0; i < G.numVertexes; i++) {
 39         G.arc[i] = [];
 40         for (j = 0; j < G.numVertexes; j++) {
 41             G.arc[i][j] = Arr2[i][j]; //INFINITY; 
 42         }
 43     }
 44     console.log(G.arc); //打印邻接矩阵
 45 }
 46 
 47 function Edge() {
 48     this.begin = 0;
 49     this.end = 0;
 50     this.weight = 0;
 51 }
 52 
 53 function Kruskal() {
 54     let n, m;
 55     let parent = []; //定义一数组用来判断边与边是否形成环路
 56     let edges = []; //定义边集数组
 57 
 58     for (let i = 0; i < G.numVertexes; i++) {
 59         for (let j = i; j < G.numVertexes; j++) { //因为是无向图所以相同的边录入一次即可，若是有向图改为0
 60             if (G.arc[i][j] != 0 && G.arc[i][j] != 65535) {
 61                 let edge = new Edge();
 62                 edge.begin = i;
 63                 edge.end = j;
 64                 edge.weight = G.arc[i][j];
 65                 edges.push(edge);
 66             }
 67         }
 68     }
 69 
 70     edges.sort((v1, v2) => {
 71         return v1.weight - v2.weight
 72     });
 73 
 74     console.log(‘**********打印所有边*********‘);
 75     console.log(edges);
 76 
 77     for (let i = 0; i < G.numVertexes; i++) {
 78         parent[i] = 0;
 79     }
 80 
 81     for (let i = 0; i < edges.length; i++) {
 82         n = Find(parent, edges[i].begin)
 83         m = Find(parent, edges[i].end)
 84         if (n != m) { //假如n与m不等，说明此边没有与现有生成树形成环路
 85             parent[n] = m;
 86             console.log("(%s,%s) %d", G.vexs[edges[i].begin], G.vexs[edges[i].end], edges[i].weight);
 87         }
 88     }
 89 }
 90 
 91 
 92 function Find(parent, f) { //查找连线顶点的尾部下标
 93     while (parent[f] > 0) {
 94         f = parent[f]
 95     }
 96     return f;
 97 }
 98 
 99 createMGraph();
100 console.log(‘*********打印最小生成树**********‘)
101 Kruskal();