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下面用java实现了图，这个图使用邻接矩阵来实现。然后图的遍历使用了：深度遍历，广度遍历。最小生成树使用普利姆算法以及克鲁斯卡尔算法
package net.itaem.graph;
public class Edge implements Comparable<Edge>{
private int start; //起点
private int end; //终点
private int weight = Integer.MAX_VALUE / 2; //权值，默认为无穷大
public Edge(int start, int end, int weight){
this.start = start;
this.end = end;
this.weight = weight;
}
public int getStart() {
return start;
}
public void setStart(int start) {
this.start = start;
}
public int getEnd() {
return end;
}
public void setEnd(int end) {
this.end = end;
}
public int getWeight() {
return weight;
}
public void setWeight(int weight) {
this.weight = weight;
}
@Override
public String toString() {
return "Edge [start=" + start + ", end=" + end + ", weight=" + weight
+ "]";
}
//实现了Comparable<Edge>接口，用于排序的时候使用
@Override
public int compareTo(Edge that) {
if(that == this) return 0;
return this.getWeight() - that.getWeight();
}
}
package net.itaem.graph;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.LinkedList;
import java.util.List;
/**
* 使用邻接矩阵来实现图
* */
public class Graph {
private List<String> vexList;
private List<Edge> edgeList;
private int[][] edgeArray;
private boolean[] visited;
//创建一个图
public Graph(int size){
this.vexList = new ArrayList<String>();
this.edgeList = new ArrayList<Edge>();
this.edgeArray = new int[size][size];
for(int i=0; i<size; i++){
for(int j=0; j<size; j++){
edgeArray[i][j] = Integer.MAX_VALUE / 2;
}
}
createGraph();
}
public boolean isEdgeExists(int start, int end){
if(edgeArray[start][end] != Integer.MAX_VALUE/2){
return true;
}else{
return false;
}
}
private void createGraph(){
vexList.add("V0");
vexList.add("V1");
vexList.add("V2");
vexList.add("V3");
vexList.add("V4");
vexList.add("V5");
vexList.add("V6");
vexList.add("V7");
vexList.add("V8");
//初始化4条边，因为是无向边，所以都是成对出现
Edge edge1 = new Edge(0, 1, 10);
Edge edge2 = new Edge(0, 5, 11);
Edge edge3 = new Edge(1, 0, 10);
Edge edge4 = new Edge(5, 0, 11);
Edge edge5 = new Edge(1, 2, 18);
Edge edge6 = new Edge(1, 6, 16);
Edge edge7 = new Edge(1, 8, 12);
Edge edge8 = new Edge(2, 1, 18);
Edge edge9 = new Edge(6, 1, 16);
Edge edge10 = new Edge(8, 1, 12);
Edge edge11 = new Edge(2, 3, 22);
Edge edge12 = new Edge(2, 8, 8);
Edge edge13 = new Edge(3, 2, 22);
Edge edge14 = new Edge(8, 2, 8);
Edge edge15 = new Edge(3, 4, 20);
Edge edge16 = new Edge(3, 7, 16);
Edge edge17 = new Edge(3, 8, 21);
Edge edge18 = new Edge(4, 3, 20);
Edge edge19 = new Edge(7, 3, 16);
Edge edge20 = new Edge(8, 3, 21);
Edge edge21 = new Edge(4, 5, 26);
Edge edge22 = new Edge(4, 7, 7);
Edge edge23 = new Edge(5, 4, 26);
Edge edge24 = new Edge(7, 4, 7);
Edge edge25 = new Edge(5, 6, 17);
Edge edge26 = new Edge(6, 5, 17);
Edge edge27 = new Edge(6, 7, 19);
Edge edge28 = new Edge(7, 6, 19);
Edge edge29 = new Edge(1, 8, 12);
Edge edge30 = new Edge(8, 1, 12);
add(edge29);
add(edge30);
add(edge1);
add(edge2);
add(edge3);
add(edge4);
add(edge5);
add(edge6);
add(edge7);
add(edge8);
add(edge9);
add(edge10);
add(edge11);
add(edge12);
add(edge13);
add(edge14);
add(edge15);
add(edge16);
add(edge17);
add(edge18);
add(edge19);
add(edge20);
add(edge21);
add(edge22);
add(edge23);
add(edge24);
add(edge25);
add(edge26);
add(edge27);
add(edge28);
}
public void add(Edge edge){
for(int i=0; i<vexList.size(); i++){
for(int j=0; j<vexList.size(); j++){
//设置这个权值到数组中
if(i != j && i == edge.getStart() && j == edge.getEnd() && edgeArray[i][j] == Integer.MAX_VALUE/2){
edgeArray[i][j] = edge.getWeight();
}else if(i == j){
edgeArray[i][j] = 0;
}
}
}
edgeList.add(edge);
}
public String toString(){
StringBuilder sb = new StringBuilder();
for(int i=0; i<vexList.size(); i++){
for(int j=0; j<vexList.size(); j++){
if(edgeArray[i][j] != Integer.MAX_VALUE/2)
sb.append(edgeArray[i][j]+ " ");
else
sb.append("00" + " ");
}
sb.append("\n");
}
return sb.toString();
}
public static void main(String[] args) {
Graph graph = new Graph(9);
System.out.println(graph);
System.out.println("DFS======================================");
graph.DFS();
System.out.println("======================================DFS");
System.out.println();
System.out.println("BFS======================================");
graph.BFS();
System.out.println("end======================================BFS");
System.out.println("=======minSpanTreePrim==================");
graph.minSpanTreePrim();
System.out.println("=======minSpanTreePrim==================");
System.out.println("=======miniSpanTreeKruskal==================");
graph.miniSpanTreeKruskal();
System.out.println("=======miniSpanTreeKruskal==================");
}
//深度优先遍历这个图
public void DFS(){
visited = new boolean[vexList.size()]; //标识每个节点是否被访问，这里全部重置
for(int i=0; i<vexList.size(); i++){
if(!visited[i]){
DFS0(i);
}
}
}
public void DFS0(int index){
System.out.println("vex "+ index +" value is " + vexList.get(index)); //输出这个节点，也可以更换成其它操作
visited[index] = true; //设置该节点已经被访问过了
for(int j=0; j<vexList.size(); j++){
if(isEdgeExists(index, j) && !visited[j]){
DFS0(j);
}
}
}
//广度优先，遍历这个图
public void BFS(){
visited = new boolean[vexList.size()]; //标识每个节点是否被访问，这里全部重置
LinkedList<Integer> queue = new LinkedList<Integer>();
for(int i=0; i<vexList.size(); i++){
//如果这个节点没有被访问过，就访问
if(!visited[i]){
visited[i] = true;
System.out.println("vex " + i + " is " + vexList.get(i)); //输出这个节点，也可以更换成其它操作
queue.addLast(i); //将这个节点i加入队列
while(!queue.isEmpty()){
int index = queue.removeFirst(); //出队列，并且将这个下标记住
for(int j=0; j<vexList.size(); j++){
if(isEdgeExists(index, j) && !visited[j]){
visited[j] = true;
System.out.println("vex " + j + " is " + vexList.get(j)); //输出这个节点，也可以更换成其它操作
queue.addLast(j);
}
}
}
}else{
//System.out.println(i + " vex is visited");
}
}
}
/**
* 最小生成树,普利姆算法
* 出发点：从其中一个顶点出发
* 前提条件：无
*
* */
public void minSpanTreePrim(){
int min = 0, i = 0, j = 0, k = 0;
int[] adjvex = new int[vexList.size()]; //保存顶点相关下标
int[] lowcost = new int[vexList.size()]; //保存定点之间的权值
lowcost[0] = 0; //初始化第一个权值为0，也就是V0加入生成树
adjvex[0] = 0; //初始化顶一个定点下标为0
for(i=1; i<vexList.size(); i++){ //循环其它的定点
lowcost[i] = edgeArray[0][i]; //取出V0连的边的全部权值
adjvex[i] = 0; //初始化都为V0下标
}
for(i=1; i<vexList.size(); i++){
min = Integer.MAX_VALUE / 2; //初始化权值最小为无穷大
j = 1;
k = 0;
while(j < vexList.size()){
if(lowcost[j] != 0 && lowcost[j] < min){ //如果权值不为0并且小于MIN，也就是该节点相连的边中最小权值
min = lowcost[j];
k = j; //让最小的值的下标存入k
}
j++;
}
System.out.println("(" + adjvex[k] + "," + k + ")"); //输出边
lowcost[k] = 0; //将当前顶点的权值设置为0，表示此顶点已经完成任务
for(j = 1; j<vexList.size(); j++){
if(lowcost[j] != 0 && edgeArray[k][j] < lowcost[j]){
lowcost[j] = edgeArray[k][j];
adjvex[j] = k;
}
}
}
}
/**
* 库鲁斯卡尔算法
* 出发点：从边出发
*
* 前提：这些变都按照权值大小排序好
*
* 从图的每一条边出发，然后查看这条边是否形成环，如果没有，加入到最小生成树
*
* */
public void miniSpanTreeKruskal(){
int n = 0, m = 0, i = 0;
int[] parent = new int[vexList.size()]; //定义一个数组用来判断是否形成环路，初始化的值都为0
//获得排序好的所有边集合，也就是前提条件
Collections.sort(edgeList);
Edge[] edges = new Edge[edgeList.size()/2];
int index = 0;
for(int j=0; j < edgeList.size(); j++){
if(j % 2 == 0){
edges[index++] = edgeList.get(j);
}
}
//循环每一条边
for(i=0; i<edges.length; i++){
n = find(parent, edges[i].getStart()); //找到这条边的起点
m = find(parent, edges[i].getEnd()); //找到这条边的终点
//如果没有形成环，加入到最小生成树
if(n != m){ //如果不相等，说明没有构成环
parent[n] = m; //将此边的结尾顶点放入到下边起点的parent中，表示此顶点已经在生成树中
System.out.println("(" + edges[i].getStart() + "," + edges[i].getEnd() + ")" + " weight " + edges[i].getWeight());
}
}
}
private int find(int[] parent, int f){ //查找连线节点的尾部下标
while(parent[f] > 0)
f = parent[f];
return f;
}
}
下面是是输出结果
0 10 00 00 00 11 00 00 00 10 0 18 00 00 00 16 00 12 00 18 0 22 00 00 00 00 8 00 00 22 0 20 00 00 16 21 00 00 00 20 0 26 00 7 00 11 00 00 00 26 0 17 00 00 00 16 00 00 00 17 0 19 00 00 00 00 16 7 00 19 0 00 00 12 8 21 00 00 00 00 0 DFS====================================== vex 0 value is V0 vex 1 value is V1 vex 2 value is V2 vex 3 value is V3 vex 4 value is V4 vex 5 value is V5 vex 6 value is V6 vex 7 value is V7 vex 8 value is V8 ======================================DFS BFS====================================== vex 0 is V0 vex 1 is V1 vex 5 is V5 vex 2 is V2 vex 6 is V6 vex 8 is V8 vex 4 is V4 vex 3 is V3 vex 7 is V7 end======================================BFS =======minSpanTreePrim================== (0,1) (0,5) (1,8) (8,2) (1,6) (6,7) (7,4) (7,3) =======minSpanTreePrim================== =======miniSpanTreeKruskal================== (4,7) weight 7 (2,8) weight 8 (0,1) weight 10 (0,5) weight 11 (1,8) weight 12 (1,6) weight 16 (3,7) weight 16 (6,7) weight 19 =======miniSpanTreeKruskal==================
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