Java--算法--图

1. 图的基本介绍：

2. 图的代码实现：

   2. package com.model.graph;
      
      import java.util.ArrayList;
      import java.util.Arrays;
      import java.util.List;
      
      /**
       * @Description:测试类
       * @Author: 张紫韩
       * @Crete 2021/7/17 15:16
       * 演示图的实现，图的快速入门
       */
      public class GraphDemo01 {
          public static void main(String[] args) {
              Graph graph = new Graph(5);
              graph.insertVertex("A");
              graph.insertVertex("B");
              graph.insertVertex("C");
              graph.insertVertex("D");
              graph.insertVertex("E");
              graph.addEdges(0, 1, 1);
              graph.addEdges(0, 2, 1);
              graph.addEdges(1, 2, 1);
              graph.addEdges(1, 3, 1);
              graph.addEdges(1, 4, 1);
              graph.showGraph();
      
          }
      }
      class Graph{
          private List<String> vertexList=null;//保存节点的list
          private int[][] edges=null;//保存边的矩阵
          private int numEdges=0;//边的数目
      
          public Graph(int n) {
              vertexList=new ArrayList<>(n);
              edges=new int[n][n];
              numEdges=0;
          }
      
          //    保存节点的值，第一个节点的名字
          public void insertVertex(String vertex){
              vertexList.add(vertex);
          }
      //    添加边
          public void addEdges(int v1,int v2,int weight){
              edges[v1][v2]=weight;
              edges[v2][v1]=weight;
              numEdges++;
          }
          public int getNumOfVertex(){
              return vertexList.size();
          }
          public int getNumEdges(){
              return numEdges;
          }
      //    返回节点的值，名字
          public String getVertex(int index){
              return vertexList.get(index);
          }
          public int getWeight(int v1,int v2){
              return edges[v1][v2];
          }
          public void showGraph(){
             for (int[] arr:edges){
                 System.out.println(Arrays.toString(arr));
             }
          }
      
      }

3. 图的遍历-深度优先（DFS）：

   3. public void dfs(){
              for (int i = 0; i < getNumEdges(); i++) {
                  if (!isVisited[i]){
                      dfs(isVisited, i);
                  }
              }
      
          }
          //    深度优先算法
          private void dfs(boolean[] isVisited, int index) {
              isVisited[index] = true;
              System.out.print(vertexList.get(index)+"->");
              int neighbor = getFirstNeighbor(index);
              while (neighbor != -1) {
                  if (!isVisited[neighbor]) {
                      dfs(isVisited, neighbor);
                  }
                  neighbor = getNextNeighbor(index, neighbor);
              }
      
      
          }

4. 图的遍历-广度优先算法（BFS）:

   3. //    广度优先遍历算法
          public void bfs(){
              isVisited = new boolean[getNumOfVertex()];
              for (int i = 0; i < isVisited.length; i++) {
                  if (!isVisited[i]){
                      bfs(isVisited,i);
                  }
              }
      
          }
          //    广度优先遍历算法
          public void bfs(boolean[] isVisited, int index){
              int u; //队列的头节点的小标
              int w;//邻接节点
              LinkedList queue=new LinkedList();//记录节点的访问顺序
              System.out.print(getVertex(index)+"->");
              isVisited[index]=true;
              queue.addLast(index);
              while(!queue.isEmpty()){
                  u= (int) queue.removeFirst();
                  w=getFirstNeighbor(u);
                  while (w!=-1){
                      if (!isVisited[w]){
                          System.out.print(getVertex(w)+"->");
                          isVisited[w]=true;
                          queue.addLast(w);
                      }else {
                          w=getNextNeighbor(u, w);
                      }
                  }
              }
      
          }

5. 深度优先算法和广度优先算法的比较;
   2.         Graph graph1 = new Graph(8);
              graph1.insertVertex("1");
              graph1.insertVertex("2");
              graph1.insertVertex("3");
              graph1.insertVertex("4");
              graph1.insertVertex("5");
              graph1.insertVertex("6");
              graph1.insertVertex("7");
              graph1.insertVertex("8");
              graph1.addEdges(0, 1, 1);
              graph1.addEdges(0, 2, 1);
              graph1.addEdges(1, 3, 1);
              graph1.addEdges(1, 4, 1);
              graph1.addEdges(3, 7, 1);
              graph1.addEdges(4, 7, 1);
              graph1.addEdges(2, 5, 1);
              graph1.addEdges(2, 6, 1);
              graph1.addEdges(5, 6, 1);
              graph1.showGraph();
              System.out.println("深度优先算法");
              graph1.dfs();
              System.out.println();
              System.out.println("广度优先算法");
              graph1.bfs();