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1. Kruskal algorithm design idea
The key to realize Kruskal's algorithm is to accurately determine whether the selected edge forms a loop with the existing edge in the spanning tree. This can be solved by judging the connected components of the two vertices of the edge. Kruskal's algorithm sets up an auxiliary array vset[0~n-1] for this purpose, which is used to determine whether two vertices are connected. The array element vset[i] represents the number of the connected vertex set to which the vertex with the numbered vertex i belongs. When the set numbers of the two vertices are different, adding the edge formed by the two vertices to the minimum spanning tree will not form a loop . Kruskal's algorithm uses the Node array to store all the edges in the graph, and uses the sorting method to sort all the edges from small to large in terms of weight.
The following code is for reference
only The following code is for reference only The
following code is for reference only
/**
*作者：魏宝航
*2020年11月23日,下午14:28
*/
import org.omg.CORBA.INTERNAL;
import java.io.IOException;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;
public class MatrixUDG {
private char[] mVexs;
private int[][] mMatrix;
private int num;
public MatrixUDG(char[] vexs, char[][] edges) {
num = vexs.length;
mVexs = new char[num];
for (int i = 0; i < mVexs.length; i++)
mVexs[i] = vexs[i];
mMatrix = new int[num][num];
for(int i=0;i<num;i++){
for(int j=0;j<num;j++){
if(edges[i][j]=='∞'){
mMatrix[i][j]=Integer.MAX_VALUE;
}else{
mMatrix[i][j]=Integer.parseInt(edges[i][j]+"");
}
}
}
}
public void InsertSort(Node arr[],int n){
int i=0,j=0;
Node temp;
for(i=1;i<n;i++){
temp=arr[i];
j=i-1;
while(j>=0&&temp.w<arr[j].w){
arr[j+1]=arr[j];
j--;
}
arr[j+1]=temp;
}
}
public void print() {
System.out.printf("Martix Graph:\n");
for (int i = 0; i < mVexs.length; i++) {
for (int j = 0; j < mVexs.length; j++){
if(mMatrix[i][j]<Integer.MAX_VALUE){
System.out.printf("%d ", mMatrix[i][j]);
}else{
System.out.print("∞ ");
}
}
System.out.printf("\n");
}
}
public void Kruskal(){
Node[] arr=new Node[1000];
int m1,m2,sn1,sn2,k;
int[] vset=new int[1000];
k=0;
for(int i=0;i<this.num;i++){
for(int j=i+1;j<this.num;j++){
if(this.mMatrix[i][j]!=0&&this.mMatrix[i][j]!=Integer.MAX_VALUE){
arr[k]=new Node(i,j,this.mMatrix[i][j]);
k++;
}
}
}
InsertSort(arr,k);
for(int i=0;i<this.num;i++){
vset[i]=i;
}
k=1;
int j=0;
for(;k<num;){
m1=arr[j].u;
m2=arr[j].v;
sn1=vset[m1];
sn2=vset[m2];
if(sn1!=sn2){
System.out.printf("边（%d，%d）：%d\n",m1,m2,arr[j].w);
k++;
for(int i=0;i<this.num;i++){
if(vset[i]==sn2){
vset[i]=sn1;
}
}
}
j++;
}
}
public static void main(String[] args) {
char[] vexs={
'0','1','2','3','4','5'};
char[][] edges=new char[][]{
{
'0','6','1','5','∞','∞'},
{
'6','0','5','∞','3','∞'},
{
'1','5','0','5','6','4'},
{
'5','∞','5','0','∞','2'},
{
'∞','3','6','∞','0','6'},
{
'∞','∞','4','2','6','0'},
};
MatrixUDG g=new MatrixUDG(vexs,edges);
g.print();
g.Kruskal();
}
}
class Node implements Comparable<Node>{
int u;
int v;
int w;
Node(int u,int v,int w){
this.u=u;
this.v=v;
this.w=w;
}
@Override
public int compareTo(Node o) {
return w-o.w;
}
}