说明

闵老师的文章链接：日撸 Java 三百行（总述）_minfanphd的博客-CSDN博客
自己也把手敲的代码放在了github上维护：https://github.com/fulisha-ok/sampledata

day33 图的广度优先遍历

1.思路

结合下图，广度优先遍历假设从a节点出发，a访问后，访问领接点b/c,b访问了再访问c,又接着访问b的领接点，c的领接点，这样一层一层的访问，这就好比树的层次遍历一样。在访问图时要借助一个队列来实现.如图广度优先遍历的一种顺序是：a->b->c->d->e
在这里插入图片描述
根据上图，所结点所存储的矩阵值：
$\begin{array}{c} % 总表格 \begin{array}{c|cccc} % 第二行 Delta 值数组 \Delta & a & b & c & d & e \\ \hline a & 0 & 1 & 1 & 0 & 0 \\ b & 1 & 0 & 0 & 1 & 0 \\ c & 0 & 0 & 0 & 1 & 1 \\ d & 0 & 0 & 0 & 0 & 1 \\ e & 0 & 0 & 0 & 0 & 0 \\ \end{array} % 第二行表格结束 \end{array} % 总表格结束$
通过上图的实现可以知道，当我们出队一个结点，如a，就需要把a结点相应邻结点入队（这里我们采用的数据结构是矩阵，可以通过矩阵的行列值是否为1来判断是否与出结点是否相邻）则发现a行b列和a行c列是连接的，则说明b,c是a的领结点，则将b，c入队列。其他一样。

//代码中判断相邻结点
if (connectivityMatrix.getData()[tempIndex][i] == 0) {
       //Not directly connected.
       continue;
}

2.多个连通分量

在今天的文章中，这个遍历只能遍历只有一个连通分量的图(有向图)，若有多个连通分量，则会漏一些节点数据（需要加一个循环来验证节点是否访问完）。在代码中有一个布尔类型数组：boolean[] tempVisitedArray = new boolean[tempNumNodes];若我们在一次广度遍历完遍历这个tempVisitedArray数组，再循环遍历是否有false，若有则说明图有多个连通分量，这是我们还需要把未遍历的节点再遍历完。

    /**
     * Judge connectivity
     * @param tempVisitedArray
     * @return
     */
        public boolean isConnectivity(int paraStartIndex){
        int tempNumNodes = connectivityMatrix.getRows();
        breadthFirstTraversal(paraStartIndex);

        for (int i = 0; i < tempNumNodes; i++){
            if (!tempVisitedArray[i]){
                breadthFirstTraversal(i);
                return false;
            }
        }
        return true;
    }

2 代码实现

我在原来的基础上做了一些小的改动，来遍历所有的结点。加了一个方法isConnectivity，来遍历所有的结点，将tempVisitedArray， resultString作为成员变量。

package graph;

import datastructure.queue.CircleObjectQueue;
import matrix.IntMatrix;

/**
 * @author： fulisha
 * @date： 2023/4/18 15:43
 * @description：
 */
public class Graph {

    IntMatrix connectivityMatrix;

    /**
     * The first constructor.
     * @param paraNumNodes The number of nodes in the graph.
     */
    public Graph(int paraNumNodes){
        connectivityMatrix = new IntMatrix(paraNumNodes, paraNumNodes);
    }

    /**
     * The second constructor.
     * @param paraMatrix The data matrix.
     */
    public Graph(int[][] paraMatrix){
        connectivityMatrix = new IntMatrix(paraMatrix);
    }

    @Override
    public String toString(){
        return "This is the connectivity matrix of the graph.\r\n" + connectivityMatrix;
    }

    /**
     * Get the connectivity of the graph.
     * @return
     */
    public boolean getConnectivity() throws Exception {
        // Step 1. Initialize accumulated matrix.
        IntMatrix tempConnectivityMatrix = IntMatrix.getIdentityMatrix(connectivityMatrix.getData().length);

        //Step 2. Initialize
        IntMatrix tempMultipliedMatrix = new IntMatrix(connectivityMatrix);

        //Step 3. Determine the actual connectivity.
        for (int i = 0; i < connectivityMatrix.getData().length - 1; i++){
            // M_a = M_a + M^k
            tempConnectivityMatrix.add(tempMultipliedMatrix);
            // M^k
            tempMultipliedMatrix = IntMatrix.multiply(tempMultipliedMatrix, connectivityMatrix);
        }

        // Step 4. Check the connectivity.
        System.out.println("The connectivity matrix is: " + tempConnectivityMatrix);
        int[][] tempData = tempConnectivityMatrix.getData();
        for (int i = 0; i < tempData.length; i++) {
            for (int j = 0; j < tempData.length; j++){
                if (tempData[i][j] == 0){
                    System.out.println("Node " + i + " cannot reach " + j);
                    return false;
                }
            }
        }
        return true;
    }

    /**
     * Unit test for getConnectivity.
     */
    public static void getConnectivityTest(){
        int[][] tempMatrix = { { 0, 1, 0 }, { 1, 0, 1 }, { 0, 1, 0 } };
        Graph tempGraph2 = new Graph(tempMatrix);
        System.out.println(tempGraph2);

        boolean tempConnected = false;
        try {
            tempConnected = tempGraph2.getConnectivity();
        } catch (Exception ee) {
            System.out.println(ee.getMessage());
        }
        System.out.println("Is the graph connected? " + tempConnected);

        //Test a directed graph. Remove one arc to form a directed graph.
        tempGraph2.connectivityMatrix.setValue(1, 0, 0);
        tempConnected = false;
        try {
            tempConnected = tempGraph2.getConnectivity();
        } catch (Exception ee) {
            System.out.println(ee);
        }

        System.out.println("Is the graph connected? " + tempConnected);

    }

    /**
     * Breadth first Traversal
     * @param paraStartIndex The start index.
     * @return The sequence of the visit.
     */
    boolean[] tempVisitedArray;
    String resultString = "";
    public String breadthFirstTraversal(int paraStartIndex) {
        CircleObjectQueue tempQueue = new CircleObjectQueue();
        int tempNumNodes = connectivityMatrix.getRows();
        tempVisitedArray = new boolean[tempNumNodes];

        // Initialize the queue
        tempVisitedArray[paraStartIndex] = true;
        resultString += paraStartIndex;
        tempQueue.enqueue(paraStartIndex);

        //Now visit the rest of the graph.
        int tempIndex;
        Integer tempInteger = (Integer) tempQueue.dequeue();
        while (tempInteger != null){
            tempIndex = tempInteger.intValue();

            //Enqueue all its unvisited neighbors.
            for (int i = 0; i < tempNumNodes; i++){
                if (tempVisitedArray[i]){
                    // Already visited.
                    continue;
                }
                if (connectivityMatrix.getData()[tempIndex][i] == 0) {
                    //Not directly connected.
                    continue;
                }
                tempVisitedArray[i] = true;
                resultString += i;
                tempQueue.enqueue(i);
            }

            //Take out one from the head.
            tempInteger = (Integer)tempQueue.dequeue();
        }
        return resultString;
    }

    /**
     * Judge connectivity
     * @param
     * @return
     */
    public boolean isConnectivity(int paraStartIndex){
        int tempNumNodes = connectivityMatrix.getRows();
        breadthFirstTraversal(paraStartIndex);

        for (int i = 0; i < tempNumNodes; i++){
            if (!tempVisitedArray[i]){
                breadthFirstTraversal(i);
                return false;
            }
        }
        return true;
    }

    public static void breadthFirstTraversalTest() {
        // Test an undirected graph.
        //int[][] tempMatrix = { { 0, 1, 1, 0 }, { 1, 0, 0, 1 }, { 1, 0, 0, 1}, { 0, 1, 1, 0} };
        //int[][] tempMatrix = { { 0, 1, 1, 0 , 0}, { 1, 0, 0, 1, 0 }, { 1, 0, 0, 1, 0}, { 0, 1, 1, 0, 0}, { 0, 0, 0, 0, 0} };
          int[][] tempMatrix = { { 0, 1, 1, 0 , 0, 0, 0}, { 1, 0, 0, 1, 0, 0, 0 }, { 1, 0, 0, 1, 0, 0, 0}, { 0, 1, 1, 0, 0, 0, 0}, { 0, 0, 0, 0, 0, 1, 1}, { 0, 0, 0, 0, 1, 0, 0}, { 0, 0, 0, 0, 0, 0, 0} };
        Graph tempGraph = new Graph(tempMatrix);
        System.out.println(tempGraph);

        String tempSequence = "";
        try {
            tempGraph.isConnectivity(2);
            //tempSequence = tempGraph.breadthFirstTraversal(2);
        } catch (Exception ee) {
            System.out.println(ee.getMessage());
            return;
        }

        System.out.println("The breadth first order of visit: " + tempGraph.resultString);
    }

    public static void main(String[] args) {
        System.out.println("Hello!");
        Graph tempGraph = new Graph(3);
        System.out.println(tempGraph);

        // Unit test.
        getConnectivityTest();

        breadthFirstTraversalTest();

    }


}