public class PrimAlgorithm {
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},
{7,10000,10000,10000,8,10000,10000},
{10000,9,10000,10000,10000,4,10000},
{10000,10000,8,10000,10000,5,4},
{10000,10000,10000,4,5,10000,6},
{2,3,10000,10000,4,6,10000},};
MGraph graph = new MGraph(verxs);
MinTree minTree = new MinTree();
minTree.createGraph(graph, verxs, data, weight);
minTree.showGraph(graph);
minTree.prim(graph, 1);
}
}
class MinTree {
// verxs 图对应的顶点个数
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];
}
}
}
public void showGraph(MGraph graph) {
for(int[] link: graph.weight) {
System.out.println(Arrays.toString(link));
}
}
// @param v 表示从图的第几个顶点开始生成‘A‘->0 ‘B‘->1..
public void prim(MGraph graph, int v) {
int visited[] = new int[graph.verxs];
visited[v] = 1;
int h1 = -1; //h1 和 h2 记录两个顶点的下标
int h2 = -1;
int minWeight = 10000;
for(int k = 1; k < graph.verxs; k++) { // 边
//这个是确定每一次生成的子图 ，和哪个结点的距离最近
for(int i = 0; i < graph.verxs; i++) { // i结点表示被访问过的结点
for(int j = 0; j< graph.verxs;j++) { // j结点表示还没有访问过的结点
if(visited[i] == 1 && visited[j] == 0 && graph.weight[i][j] < minWeight) {
minWeight = graph.weight[i][j];
h1 = i;
h2 = j;
}
}
}
System.out.println("边<" + graph.data[h1] + "," + graph.data[h2] + "> 权值:" + minWeight);
//将当前这个结点标记为已经访问
visited[h2] = 1;
//minWeight 重新设置为最大值 10000
minWeight = 10000;
}
}
}
class MGraph {
int verxs; //表示图的节点个数
char[] data; //存放结点数据
int[][] weight; //存放边，就是我们的邻接矩阵
public MGraph(int verxs) {
this.verxs = verxs;
data = new char[verxs];
weight = new int[verxs][verxs];
}
}
public class KruskalCase {
private int edgeNum; //边的个数
private char[] vertexs; //顶点数组
private int[][] matrix; //邻接矩阵
private static final int INF = Integer.MAX_VALUE;
public static void main(String[] args) {
char[] vertexs = {‘A‘, ‘B‘, ‘C‘, ‘D‘, ‘E‘, ‘F‘, ‘G‘};
int matrix[][] = {
/*A*//*B*//*C*//*D*//*E*//*F*//*G*/
/*A*/ { 0, 12, INF, INF, INF, 16, 14},
/*B*/ { 12, 0, 10, INF, INF, 7, INF},
/*C*/ { INF, 10, 0, 3, 5, 6, INF},
/*D*/ { INF, INF, 3, 0, 4, INF, INF},
/*E*/ { INF, INF, 5, 4, 0, 2, 8},
/*F*/ { 16, 7, 6, INF, 2, 0, 9},
/*G*/ { 14, INF, INF, INF, 8, 9, 0}};
KruskalCase kruskalCase = new KruskalCase(vertexs, matrix);
kruskalCase.print();
kruskalCase.kruskal();
}
public KruskalCase(char[] vertexs, int[][] matrix) {
int vlen = vertexs.length; //初始化顶点数和边的个数
this.vertexs = new char[vlen];
for(int i = 0; i < vertexs.length; i++) {
this.vertexs[i] = vertexs[i];
}
this.matrix = new int[vlen][vlen];
for(int i = 0; i < vlen; i++) {
for(int j= 0; j < vlen; j++) {
this.matrix[i][j] = matrix[i][j];
}
}
//统计边的条数
for(int i =0; i < vlen; i++) {
for(int j = i+1; j < vlen; j++) {
if(this.matrix[i][j] != INF) {
edgeNum++;
}
}
}
}
public void kruskal() {
int index = 0; // 表示最后结果数组的索引
int[] ends = new int[edgeNum]; // 用于保存"已有最小生成树" 中的每个顶点在最小生成树中的终点
EData[] rets = new EData[edgeNum]; // 创建结果数组, 保存最后的最小生成树
EData[] edges = getEdges();
System.out.println("图的边的集合=" + Arrays.toString(edges) + " 共"+ edges.length); //12
sortEdges(edges);
for(int i=0; i < edgeNum; i++) {
int p1 = getPosition(edges[i].start); //p1=4
int p2 = getPosition(edges[i].end); //p2 = 5
int m = getEnd(ends, p1); //m = 4 //获取p1这个顶点在已有最小生成树中的终点
int n = getEnd(ends, p2); // n = 5 //获取p2这个顶点在已有最小生成树中的终点
//是否构成回路
if(m != n) { //没有构成回路
ends[m] = n; // 设置m 在"已有最小生成树"中的终点 <E,F> [0,0,0,0,5,0,0,0,0,0,0,0]
rets[index++] = edges[i]; //有一条边加入到rets数组
}
}
System.out.println("最小生成树为");
for(int i = 0; i < index; i++) {
System.out.println(rets[i]);
}
}
public void print() {
System.out.println("邻接矩阵为: \n");
for(int i = 0; i < vertexs.length; i++) {
for(int j=0; j < vertexs.length; j++) {
System.out.printf("%12d", matrix[i][j]);
}
System.out.println();//换行
}
}
private void sortEdges(EData[] edges) {
for(int i = 0; i < edges.length - 1; i++) {
for(int j = 0; j < edges.length - 1 - i; j++) {
if(edges[j].weight > edges[j+1].weight) {//交换
EData tmp = edges[j];
edges[j] = edges[j+1];
edges[j+1] = tmp;
}
}
}
}
// 找顶点对应的下标
private int getPosition(char ch) {
for(int i = 0; i < vertexs.length; i++) {
if(vertexs[i] == ch) {//找到
return i;
}
}
return -1;
}
// 获取图中边，放到EData[] 数组中，后面我们需要遍历该数组
private EData[] getEdges() {
int index = 0;
EData[] edges = new EData[edgeNum];
for(int i = 0; i < vertexs.length; i++) {
for(int j=i+1; j <vertexs.length; j++) {
if(matrix[i][j] != INF) {
edges[index++] = new EData(vertexs[i], vertexs[j], matrix[i][j]);
}
}
}
return edges;
}
/**
* 功能: 获取下标为i的顶点的终点(), 用于后面判断两个顶点的终点是否相同
* @param ends ： 数组就是记录了各个顶点对应的终点是哪个,ends 数组是在遍历过程中，逐步形成
* @param i : 表示传入的顶点对应的下标
* @return 返回的就是 下标为i的这个顶点对应的终点的下标, 一会回头还有来理解
*/
private int getEnd(int[] ends, int i) { // i = 4 [0,0,0,0,5,0,0,0,0,0,0,0]
while(ends[i] != 0) {
i = ends[i];
}
return i;
}
}
//创建一个类EData ，它的对象实例就表示一条边
class EData {
char start; // 边的一个点
char end; // 边的另外一个点
int weight; // 边的权值
public EData(char start, char end, int weight) {
this.start = start;
this.end = end;
this.weight = weight;
}
@Override
public String toString() {
return "EData [<" + start + ", " + end + ">= " + weight + "]";
}
}
原文：https://www.cnblogs.com/ming-michelle/p/14705145.html