Java数据结构之图的两种搜索算法详解

/**
 * 图的深度优先搜索算法
 *
 * @author alvin
 * @date 2022/10/31
 * @since 1.0
 **/
public class DepthFirstSearch {
    //索引代表顶点，值表示当前顶点是否已经被搜索
    private boolean[] marked;
    //记录有多少个顶点与s顶点相通
    private int count;

    //构造深度优先搜索对象，使用深度优先搜索找出G图中s顶点的所有相邻顶点
    public DepthFirstSearch(Graph G, int s) {
        //创建一个和图的顶点数一样大小的布尔数组
        marked = new boolean[G.V()];
        dfs(G, s);
    }

    //使用深度优先搜索找出G图中v顶点的所有相邻顶点
    private void dfs(Graph G, int v) {
        //把当前顶点标记为已搜索
        marked[v] = true;
        //遍历v顶点的邻接表，得到每一个顶点w
        for (Integer w : G.adj(v)) {
            //遍历v顶点的邻接表，得到每一个顶点w
            if (!marked[w]) {
                //如果当前顶点w没有被搜索过，则递归搜索与w顶点相通的其他顶点
                dfs(G, w);
            }
        }

        //相通的顶点数量+1
        count++;
    }

    //判断w顶点与s顶点是否相通
    public boolean marked(int w) {
        return marked[w];
    }

    //获取与顶点s相通的所有顶点的总数
    public int count() {
        return count;
    }
}

public class DepthFirstSearchTest {

    @Test
    public void test() {
        //准备Graph对象
        Graph G = new Graph(13);
        G.addEdge(0,5);
        G.addEdge(0,1);
        G.addEdge(0,2);
        G.addEdge(0,6);
        G.addEdge(5,3);
        G.addEdge(5,4);
        G.addEdge(3,4);
        G.addEdge(4,6);
        G.addEdge(7,8);
        G.addEdge(9,11);
        G.addEdge(9,10);
        G.addEdge(9,12);
        G.addEdge(11,12);

        //准备深度优先搜索对象
        DepthFirstSearch search = new DepthFirstSearch(G, 0);
        //测试与某个顶点相通的顶点数量
        int count = search.count();
        System.out.println("与起点0相通的顶点的数量为:"+count);
        //测试某个顶点与起点是否相同
        boolean marked1 = search.marked(5);
        System.out.println("顶点5和顶点0是否相通："+marked1);
        boolean marked2 = search.marked(7);
        System.out.println("顶点7和顶点0是否相通："+marked2);
    }
}

/**
 * 图的广度优先搜索算法
 *
 * @author alvin
 * @date 2022/10/31
 * @since 1.0
 **/
public class BreadthFirstSearch {
    //索引代表顶点，值表示当前顶点是否已经被搜索
    private boolean[] marked;
    //记录有多少个顶点与s顶点相通
    private int count;
    //用来存储待搜索邻接表的点
    private Queue<Integer> waitSearch;

    //构造广度优先搜索对象，使用广度优先搜索找出G图中s顶点的所有相邻顶点
    public BreadthFirstSearch(Graph G, int s) {
        this.marked = new boolean[G.V()];
        this.count = 0;
        this.waitSearch = new ArrayDeque<>();

        bfs(G, s);
    }

    //使用广度优先搜索找出G图中v顶点的所有相邻顶点
    private void bfs(Graph G, int v) {
        //把当前顶点v标识为已搜索
        marked[v] = true;
        //让顶点v进入队列，待搜索
        waitSearch.add(v);
        //通过循环，如果队列不为空，则从队列中弹出一个待搜索的顶点进行搜索
        while (!waitSearch.isEmpty()) {
            //弹出一个待搜索的顶点
            Integer wait = waitSearch.poll();
            //遍历wait顶点的邻接表
            for (Integer w : G.adj(wait)) {
                if (!marked[w]) {
                    bfs(G, w);
                }
            }
        }
        //让相通的顶点+1；
        count++;

    }

    //判断w顶点与s顶点是否相通
    public boolean marked(int w) {
        return marked[w];
    }

    //获取与顶点s相通的所有顶点的总数
    public int count() {
        return count;
    }
}

public class BreadthFirstSearchTest {

    @Test
    public void test() {
        //准备Graph对象
        Graph G = new Graph(13);
        G.addEdge(0, 5);
        G.addEdge(0, 1);
        G.addEdge(0, 2);
        G.addEdge(0, 6);
        G.addEdge(5, 3);
        G.addEdge(5, 4);
        G.addEdge(3, 4);
        G.addEdge(4, 6);
        G.addEdge(7, 8);
        G.addEdge(9, 11);
        G.addEdge(9, 10);
        G.addEdge(9, 12);
        G.addEdge(11, 12);

        //准备广度优先搜索对象
        BreadthFirstSearch search = new BreadthFirstSearch(G, 0);
        //测试与某个顶点相通的顶点数量
        int count = search.count();
        System.out.println("与起点0相通的顶点的数量为:" + count);
        //测试某个顶点与起点是否相同
        boolean marked1 = search.marked(5);
        System.out.println("顶点5和顶点0是否相通：" + marked1);
        boolean marked2 = search.marked(7);
        System.out.println("顶点7和顶点0是否相通：" + marked2);
    }
}

public class TrafficProjectGraph {

    public static void main(String[] args) throws Exception{
        //城市数量
        int totalNumber =  20;
        Graph G = new Graph(totalNumber);
        //添加城市的交通路线
        G.addEdge(0,1);
        G.addEdge(6,9);
        G.addEdge(3,8);
        G.addEdge(5,11);
        G.addEdge(2,12);
        G.addEdge(6,10);
        G.addEdge(4,8);

        //构建一个深度优先搜索对象，起点设置为顶点9
        DepthFirstSearch search = new DepthFirstSearch(G, 9);

        //调用marked方法，判断8顶点和10顶点是否与起点9相通
        System.out.println("顶点8和顶点9是否相通："+search.marked(8));
        System.out.println("顶点10和顶点9是否相通："+search.marked(10));

    }
}