图的遍历 : 即是对结点的访问。
图的深度优先搜索(Depth First Search) 。
深度优先遍历算法步骤
图的广度优先搜索(Broad First Search) 。
广度优先遍历算法步骤
代码实现
package com.ssm.graph;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
/**
* @author shaoshao
* @version 1.0
* @date 2021/10/13 18:18
*/
public class Graph {
private ArrayList<String> vertexList; //存储顶点的集合
private int[][] edges;//存储图对应的邻接矩阵
private int numOfEdge; // 表示边的数目
private boolean[] isVisited; //
public static void main(String[] args) {
int n = 8;
//String[] vertexs = {"A", "B", "C", "D", "E"};
String[] vertexs = {"1", "2", "3", "4", "5", "6", "7", "8"};
Graph graph = new Graph(n);
//添加顶点
for (String vertex : vertexs
) {
graph.insertVertex(vertex);
}
//添加边
/*graph.insertEdge(0, 1, 1); // A-B
graph.insertEdge(0, 2, 1); // A-C
graph.insertEdge(1, 2, 1);
graph.insertEdge(1, 3, 1);
graph.insertEdge(1, 4, 1);*/
graph.insertEdge(0, 1, 1);
graph.insertEdge(0, 2, 1);
graph.insertEdge(1, 3, 1);
graph.insertEdge(1, 4, 1);
graph.insertEdge(3, 7, 1);
graph.insertEdge(4, 7, 1);
graph.insertEdge(2, 5, 1);
graph.insertEdge(2, 6, 1);
graph.insertEdge(5, 6, 1);
graph.showGarph();
System.out.println("深度优先遍历");
graph.dfs();
System.out.println();
System.out.println("广度优先遍历");
graph.bfs();
}
public Graph(int n) {
edges = new int[n][n];
vertexList = new ArrayList<String>(n);
numOfEdge = 0;
}
//得到第一个邻接点的下标
public int getFirstNeighbor(int index) {
for (int i = 0; i < vertexList.size(); i++) {
if (edges[index][i] > 0) {
return i;
}
}
return -1;
}
//根据前一个邻接结点的下标来获取下一个邻接结点
public int getNextNeighbor(int v1, int v2) {
for (int i = v2 + 1; i < vertexList.size(); i++) {
if (edges[v1][i] > 0) {
return i;
}
}
return -1;
}
//深度优先遍历 i 第一次是0
private void dfs(boolean[] isVisited, int i) {
System.out.print(getValByIndex(i) + "->");
isVisited[i] = true;
int w = getFirstNeighbor(i);
while (w != -1) {
if (!isVisited[w]) { //说明有
dfs(isVisited, w);
}
//如果w结点已经被访问过
w = getNextNeighbor(i, w);
}
}
//对dfs重载 遍历所有的结点
public void dfs() {
isVisited = new boolean[vertexList.size()];
for (int i = 0; i < getNumOfVertex(); i++) {
if (!isVisited[i]) {
dfs(isVisited, i);
}
}
}
//广度优先遍历
private void bfs(boolean[] isVisited, int i) {
int u; //队列头结点对应的下标
int w; //邻接点w
//记录结点访问顺序
LinkedList linkedList = new LinkedList();
System.out.print(getValByIndex(i) + "->");
isVisited[i] = true;
linkedList.addLast(i);
while (!linkedList.isEmpty()) {
//取出队列头结点的下标
u = (Integer) linkedList.removeFirst();
// 得到第一个邻接结点的下标
w = getFirstNeighbor(u);
while (w != -1) {
if (!isVisited[w]) {
System.out.print(getValByIndex(w) + "->");
isVisited[w] = true;
linkedList.addLast(w);
}
//以u为前驱结点,找w后面的下一个邻接结点
w = getNextNeighbor(u, w); //体现出广度优先
}
}
}
//bfs重载 遍历所有的结点
public void bfs() {
isVisited = new boolean[vertexList.size()];
for (int i = 0; i < getNumOfVertex(); i++) {
if (!isVisited[i]) {
bfs(isVisited, i);
}
}
}
//返回节点的个数
public int getNumOfVertex() {
return vertexList.size();
}
//返回边的个数
public int getNumOfEdge() {
return numOfEdge;
}
//返回结点i(下标)对应的数据
public String getValByIndex(int i) {
return vertexList.get(i);
}
//返回v1 v2的权值
public int getWeight(int v1, int v2) {
return edges[v1][v2];
}
//插入节点
public void insertVertex(String vertex) {
vertexList.add(vertex);
}
//添加边
/**
* @param v1 表示点的下标即是第几个顶点
* @param v2 第二个顶点对应的下标
* @param weight
*/
public void insertEdge(int v1, int v2, int weight) {
edges[v1][v2] = weight;
edges[v2][v1] = weight;
numOfEdge++;
}
//显示图对应的矩阵
public void showGarph() {
for (int[] link : edges
) {
System.out.println(Arrays.toString(link));
}
}
}
运行结果
[0, 1, 1, 0, 0, 0, 0, 0]
[1, 0, 0, 1, 1, 0, 0, 0]
[1, 0, 0, 0, 0, 1, 1, 0]
[0, 1, 0, 0, 0, 0, 0, 1]
[0, 1, 0, 0, 0, 0, 0, 1]
[0, 0, 1, 0, 0, 0, 1, 0]
[0, 0, 1, 0, 0, 1, 0, 0]
[0, 0, 0, 1, 1, 0, 0, 0]
深度优先遍历
1->2->4->8->5->3->6->7->
广度优先遍历
1->2->3->4->5->6->7->8->