Depth first traversal (DFS) and breadth first traversal (BFS)

Depth-first traversal

Depth first traversal starts from the initial vertex , The initial vertex may have an adjacent vertex , The strategy of depth first traversal is to visit the first adjacent vertex first , Then use the accessed adjacent vertex as the initial vertex to access its first adjacent vertex .

Depth first traversal steps

(1) Visit vertex v, And access points v Mark as accessed .
(2) Successively v Of the adjacent points that are not accessed , Depth first traversal of the graph ; Until the graph neutralizes v Vertices that have paths are all accessed .
(3) If there are still vertices in the graph that are not accessed , From a vertex that has not been visited , Do depth first traversal again , Until all the vertices in the graph have been visited .

↑↑↑（ Above this wx official account ）
Visual demonstration of data structure and Algorithm

Code

public class Graph {
    

    /* Store a collection of vertices */
    private ArrayList<String> vertexList;
    /* Store the adjacency matrix corresponding to the graph */
    private int[][] edges;
    /* The number of edges */
    private int numOfEdges;
    /* Record whether a vertex has been accessed */
    private boolean[] isVisited;

    public static void main(String[] args) {
    
        String[] vertexs = {
    "A","B","C","D","E"};
        /* Create a graph object */
        Graph graph = new Graph(vertexs.length);
        /* Add vertex */
        for (String vertex:vertexs) {
    
            graph.insertVertex(vertex);
        }
        /* Add edge */
        graph.insertEdges(0,1,1);
        graph.insertEdges(0,2,1);
        graph.insertEdges(1,2,1);
        graph.insertEdges(1,3,1);
        graph.insertEdges(1,4,1);
        System.out.println(" Depth-first traversal ");
        graph.dfs();
    }

    public Graph(int n){
    
        /* Initialize matrix and set */
        edges = new int[n][n];
        vertexList = new ArrayList<>(n);
        isVisited = new boolean[n];
        numOfEdges = 0;
    }

    /** *  Get the subscript of the first adjacent vertex  * @param index * @return  If it exists, return the corresponding subscript; otherwise, return -1 */
    public int getFirstNeighbor(int index){
    
        for (int i = 0; i < vertexList.size(); i++) {
    
            if (edges[index][i] > 0){
    
                return i;
            }
        }
        return -1;
    }

    /** *  Get the adjacent vertex subscript that has not been accessed  * @param v1  The current peak  * @param v2  Vertices that have been visited  * @return  The subscript of the next adjacent vertex  */
    public int getNextNeighbor(int v1,int v2){
    
        for (int j = v2+1; j < vertexList.size(); j++) {
    
            if (edges[v1][j] > 0){
    
                return j;
            }
        }
        return -1;
    }

    /** *  Depth-first traversal  * @param isVisited  Record whether the vertex has been visited  * @param i  Current vertex  */
    public void dfs(boolean[] isVisited,int i){
    
        System.out.print(getValueByIndex(i)+"->");
        isVisited[i] = true;
        int neighbor = getFirstNeighbor(i);
        while(neighbor != -1){
     // Indicates that there are adjacent vertices 
            if (!isVisited[neighbor]){
    
                /*neighbor Not interviewed */
                dfs(isVisited,neighbor);
            }
            /*neighbor The vertex has been accessed */
            neighbor = getNextNeighbor(i,neighbor);

        }

    }

	/* heavy load dfs*/
    public void dfs(){
    
        /* Traverse all the vertices */
        for (int i = 0; i < getNumOfVertex(); i++) {
    
            if (!isVisited[i]){
    
                dfs(isVisited,i);
            }
        }
    }

    /* Insert vertex */
    public void insertVertex(String vertex){
    
        vertexList.add(vertex);
    }

    /** *  Insert edge  * @param v1  Subscript of vertex in adjacency matrix  * @param v2  Subscript of vertex in adjacency matrix  * @param weight  A weight  */
    public void insertEdges(int v1,int v2,int weight){
    
        edges[v1][v2] = weight;
        edges[v2][v1] = weight;
        numOfEdges++;
    }
    /* Get the number of vertices */
    public int getNumOfVertex(){
    
        return vertexList.size();
    }
    /* According to the subscript index Get the corresponding data */
    public String getValueByIndex(int index){
    
        return vertexList.get(index);
    }
}

Running results

 Depth-first traversal 
A->B->C->D->E
Process finished with exit cod

Breadth first traversal

The breadth first traversal of a graph is similar to the sequence traversal of a tree , Breadth first traversal requires a queue to maintain the order of visited vertices , In order to access the adjacent vertices of these vertices in this order .

Breadth first traversal steps

(1) Access the initial vertex v And mark the vertices v Has been interviewed .
(2) Put the vertex v The team .
(3) When the queue is not empty, take out the head node of the queue u, If the queue is empty, the algorithm ends .
(4) Find the header node u The unreachable adjacent vertex of .
(5) Queue the adjacent vertices that are not accessed and mark them as accessed .
(6) Jump to step 3 Until all the vertices in the graph have been visited .

Code

/** *  Breadth first traversal  * @param isVisited  Whether the vertex has been accessed  * @param i  Current vertex  */
    public void bfs(boolean[] isVisited,int i){
    
        int u; // The queue header node corresponds to the subscript 
        int neighbor; // Adjacency vertex 
        /* queue , Record the order of accessing the top and bottom */
        LinkedList queue = new LinkedList();
        System.out.print(getValueByIndex(i)+"->");
        isVisited[i] = true;
        queue.addLast(i);
        while(!queue.isEmpty()){
    
            /* Take out the coordinates of the queue head node */
            u =(Integer) queue.removeFirst();
            neighbor = getFirstNeighbor(u);
            while(neighbor != -1){
     // Have adjacent vertices 
                /* Judge whether you have visited */
                if(!isVisited[neighbor]){
    
                    System.out.print(getValueByIndex(neighbor)+"->");
                    isVisited[neighbor] = true;
                    queue.addLast(neighbor);
                }
                /* Already visited */
                neighbor = getNextNeighbor(u,neighbor);
            }
        }
    }

    /** *  heavy load bfs *  Let all vertices be traversed by breadth first  */
    public void bfs(){
    
        for (int i = 0; i < getNumOfVertex(); i++) {
    
            if (!isVisited[i]){
    
                bfs(isVisited,i);
            }
        }
    }

 public static void main(String[] args) {
    
        String[] vertexs = {
    "A","B","C","D","E"};
        /* Create a graph object */
        Graph graph = new Graph(vertexs.length);
        /* Add vertex */
        for (String vertex:vertexs) {
    
            graph.insertVertex(vertex);
        }
        /* Add edge */
        graph.insertEdges(0,1,1);
        graph.insertEdges(0,2,1);
        graph.insertEdges(1,2,1);
        graph.insertEdges(1,3,1);
        graph.insertEdges(1,4,1);
      
        System.out.println(" Breadth first traversal ");
        graph.bfs();
    }

Running results

 Breadth first traversal 
A->B->C->D->E
Process finished with exit code 0