一、引入

二、基本概念

三、图的表示

package com.gyh.grapg;import java.util.ArrayList;
import java.util.Arrays;/*** @author Gao YongHao* @version 1.0*/
public class Graph {private ArrayList<String> vertexList; // 存储顶点的集合private int[][] edges; // 领接矩阵private int numOfEdges = 0;// 表示边的数目public static void main(String[] args) {int n = 5;String[] VertexValue = {"A", "B", "C", "D", "E"};// 创建图对象Graph graph = new Graph(5);for (String s : VertexValue) {graph.insertVertex(s);}// 添加边graph.insertEdge(0,1,1);graph.insertEdge(0,2,1);graph.insertEdge(1,2,1);graph.insertEdge(1,3,1);graph.insertEdge(1,4,1);// 显示邻接矩阵graph.showGraph();}public Graph(int n) {this.edges = new int[n][n];vertexList = new ArrayList<>();}// 图中常用的能方法// 返回结点的个数public int getNumOfVertex() {return vertexList.size();}// 返回边的个数public int getNumOfEdges() {return numOfEdges;}// 显示图对应的矩阵public void showGraph() {for (int[] edge : edges) {System.out.println(Arrays.toString(edge));}}public int getWeight(int v1, int v2) {return edges[v1][v2];}// 添加结点public void insertVertex(String vertex) {vertexList.add(vertex);}// 添加边public void insertEdge(int v1, int v2, int weight) {if (v1 >= edges.length || v2 >= edges.length) {throw new RuntimeException("该结点标号越界");}// 考虑无向图edges[v1][v2] = weight;edges[v2][v1] = weight;numOfEdges++;}}

四、图的遍历

4.1 图的深度优先遍历（DFS）

4.2 图的广度优先遍历（BFS）

package com.gyh.grapg;import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;/*** @author Gao YongHao* @version 1.0*/
public class Graph {private ArrayList<String> vertexList; // 存储顶点的集合private int[][] edges; // 领接矩阵private int numOfEdges = 0;// 表示边的数目// 定义数组boolean[]，记录某个结点是否被访问过private boolean[] isVisited;public static void main(String[] args) {int n = 5;String[] VertexValue = {"A", "B", "C", "D", "E"};// 创建图对象Graph graph = new Graph(n);for (String s : VertexValue) {graph.insertVertex(s);}// 添加边graph.insertEdge(0, 1, 1);graph.insertEdge(0, 2, 1);graph.insertEdge(1, 2, 1);graph.insertEdge(1, 3, 1);graph.insertEdge(1, 4, 1);// 显示邻接矩阵graph.showGraph();// 深度优先搜索
//        graph.dfs(0);// 广度优先搜索graph.bfs(2, new LinkedList<>());}/*** 广度优先遍历(借助队列实现)** @param v 起始位置*/public void bfs(int v, Queue<Integer> queue) {// 打印当前结点queue.add(v);isVisited[v] = true;while (queue.size() > 0) {v = queue.poll();System.out.println(vertexList.get(v));// 将同一层中各未遍历过的结点下标加入至队列for (int i = 0; i < edges.length; i++) {if (edges[v][i] != 0 && !isVisited[i]) {queue.add(i);isVisited[i] = true; // 加入队列时即设置已访问，不设置可能重复加入队列}}}}/*** 深度优先遍历** @param v 起始位置*/public void dfs(int v) {if (v < 0 || v >= edges.length) {return;}// 打印当前信息(遍历后则设置已经遍历)System.out.println(vertexList.get(v));isVisited[v] = true;// 对其所有的邻接结点进行轮询的递归遍历for (int i = 0; i < edges.length; i++) {if (edges[v][i] != 0 && !isVisited[i]) {dfs(i);}}}public Graph(int n) {this.edges = new int[n][n];vertexList = new ArrayList<>();isVisited = new boolean[n];}// 图中常用的能方法// 返回结点的个数public int getNumOfVertex() {return vertexList.size();}// 返回边的个数public int getNumOfEdges() {return numOfEdges;}// 显示图对应的矩阵public void showGraph() {for (int[] edge : edges) {System.out.println(Arrays.toString(edge));}}public int getWeight(int v1, int v2) {return edges[v1][v2];}// 添加结点public void insertVertex(String vertex) {vertexList.add(vertex);}// 添加边public void insertEdge(int v1, int v2, int weight) {if (v1 >= edges.length || v2 >= edges.length) {throw new RuntimeException("该结点标号越界");}// 考虑无向图edges[v1][v2] = weight;edges[v2][v1] = weight;numOfEdges++;}}

4.3 图的深度优先 VS 广度优先