图的广度遍历和深度遍历

地图是否存在一个路径使的可以从起始点（图的左上角）走出去（到达另一个点，一般为图的右下角）

import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;

//图
public class Graph {
     private ArrayList<String> vertextList;//存储顶点集合
     private int[][] edges; //存储图对应的邻结矩阵
     private int numOfEdges;//表示边的数目
     private boolean[] isVisited;

     public static void main(String[] args) {

        int n = 5;//结点个数
         String vertexs[] = {"A", "B", "C", "D", "E"};
         Graph graph = new Graph(n);
         //添加结点
         for (int i = 0; i < vertexs.length; i++) {
             graph.insertVertex(vertexs[i]);
         }
         //添加边
         //A-B  A-C  B-C  B-D  B-E
         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);

        graph.showGraph();
         System.out.println("\n深度遍历");
         graph.dfs();

         System.out.println("\n广度遍历");
         graph.bfs();

     }

    public Graph(int n) {
         this.edges = new int[n][n];
         this.vertextList = new ArrayList<String>(n);
         this.numOfEdges = 0;

    }

    //遍历所有结点，进行广度优先遍历
     private void bfs() {
         isVisited = new boolean[5];
         for (int i = 0; i < getNumOfVertex(); i++) {
             if (!isVisited[i]) {
                 bfs(isVisited, i);
             }
         }

    }

    //对一个结点进行广度优先遍历
     private void bfs(boolean[] isVisited, int i) {
         int u;//表示队列的头结点
         int w;//邻接结点
         //队列
         LinkedList<Integer> queue = new LinkedList<>();
         System.out.print(getValueByIndex(i) + "->");
         isVisited[i] = true;
         //将结点加入队列
         queue.add(i);
         while (!queue.isEmpty()) {
             //拿到队列头结点
             u = queue.removeFirst();
             //得到邻接结点
             w = getFirstNeighbor(u);
             while (w != -1) {
                 if (!isVisited[w]) {
                     System.out.print(getValueByIndex(w) + "->");
                     isVisited[w] = true;
                     //入队
                     queue.addLast(w);
                 }
                 //w已经访问过了,找下一个邻接结点
                 w = getNextNeighbor(u, w);
             }
         }

    }

     //重载dfs,遍历所有结点
     public void dfs() {
         isVisited = new boolean[5];
         for (int i = 0; i < getNumOfVertex(); i++) {
             if (!isVisited[i]) {
                 dfs(isVisited, i);
             }
         }
     }

     //深度优先遍历算法
     private void dfs(boolean[] isVisited, int i) {
         //访问
         System.out.print(getValueByIndex(i) + "->");
         //将结点设置为已经访问
         isVisited[i] = true;
         //找到i的领接结点
         int w = getFirstNeighbor(i);
         while (w != -1) {
             if (!isVisited[w]) {
                 dfs(isVisited, w);
             }
             //如果w已经被访问过
             w = getNextNeighbor(i, w);
         }

    }

     /**
      * 得到第一个邻接结点的下标
      *
      * @param index 给定节点
      * @return 返回相邻结点下标
      */
     public int getFirstNeighbor(int index) {
         for (int i = 0; i < vertextList.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 < vertextList.size(); i++) {
             if (edges[v1][i] > 0) {
                 return i;
             }
         }
         return -1;
     }

     //插入结点
     public void insertVertex(String vertex) {
         vertextList.add(vertex);
     }

     /**
      * 插入边
      *
      * @param v1     表示第一个点的下标
      * @param v2     表示第二个点的下标
      * @param weight 权值
      */
     public void insertEdge(int v1, int v2, int weight) {
         edges[v1][v2] = weight;
         edges[v2][v1] = weight;
         numOfEdges++;
     }

    public int getNumOfVertex() {
         return vertextList.size();
     }

    public int getNumOfEdges() {
         return numOfEdges;
     }

    //返回结点的值
     public String getValueByIndex(int i) {
         return vertextList.get(i);
     }

    //返回权值
     public int getWeight(int v1, int v2) {
         return edges[v1][v2];
     }

    //显示图矩阵
     public void showGraph() {
         for (int[] edge : edges) {
             System.out.println(Arrays.toString(edge));
         }
     }

}