图论09-桥和割点-CSDN博客

1 寻找桥的算法

2 桥的代码实现

package Chapt06_Bridge;

import java.util.ArrayList;

public class FindBridges {

    private Graph G;
    private boolean[] visited;

    //ord数组记录访问的顺序
    private int ord[];

    //low数组记录该顶点可以访问到的ord[值]最小的[顶点]
    private int low[];

    //cnt用来记录步数给order赋值
    private int cnt;

    // Edge类型的动态数组
    private ArrayList<Edge> res;

    public FindBridges(Graph G){
        this.G = G;
        visited = new boolean[G.V()];
        res = new ArrayList<>();
        ord = new int[G.V()];
        low = new int[G.V()];
        cnt = 0;

        for(int v = 0; v < G.V(); v ++)
            if(!visited[v])
                dfs(v, v);
    }

    private void dfs(int v, int parent){

        visited[v] = true;
        ord[v] = cnt;

        // 初始的时候low的值就是访问的顺序值在递归return的时候才进行更新
        low[v] = ord[v];

        cnt ++;

        // 通过邻接表挨个查找相邻的节点
        for(int w: G.adj(v))
            //如果有相邻的节点还没有被访问过就dfs
            if(!visited[w]){
                dfs(w, v);

                // 对上一个节点的low值进行更新
                low[v] = Math.min(low[v], low[w]);

                // 如果子节点的low值比父节点的ord大说明两点之间是一座桥。
                // 因为如果都在同一个环内low值一定是父节点之前的节点数字会更小那么就不是桥桥是不可回头的。
                if(low[w] > ord[v])
                    res.add(new Edge(v, w));
            }
            else if(w != parent) //如果该点访问过不继续dfs只更新low值
                low[v] = Math.min(low[v], low[w]);
    }

    public ArrayList<Edge> result(){
        return res;
    }

    public static void main(String[] args){

        Graph g = new Graph("g2.txt");
        FindBridges fb = new FindBridges(g);
        System.out.println("Bridges in g2 : " + fb.result());

        Graph g2 = new Graph("g8.txt");
        FindBridges fb2 = new FindBridges(g2);
        System.out.println("Bridges in g8 : " + fb2.result());

        Graph g3 = new Graph("g3.txt");
        FindBridges fb3 = new FindBridges(g3);
        System.out.println("Bridges in g3 : " + fb3.result());

        Graph tree = new Graph("tree.txt");
        FindBridges fb_tree = new FindBridges(tree);
        System.out.println("Bridges in tree : " + fb_tree.result());
    }
}

3 寻找割点的算法

4 割点的代码实现

package Chapt06_Bridge_And_CutPoints;

import java.util.HashSet;

public class FindCutPoints {

    private Graph G;
    private boolean[] visited;

    private int[] ord;
    private int[] low;
    private int cnt;

    private HashSet<Integer> res;

    public FindCutPoints(Graph G){

        this.G = G;
        visited = new boolean[G.V()];

        res = new HashSet<>();
        ord = new int[G.V()];
        low = new int[G.V()];
        cnt = 0;

        for(int v = 0; v < G.V(); v ++)
            if(!visited[v])
                dfs(v, v);
    }

    private void dfs(int v, int parent){

        visited[v] = true;
        ord[v] = cnt;
        low[v] = ord[v];
        cnt ++;

        // 记录子节点的数量
        int child = 0;

        for(int w: G.adj(v))
            if(!visited[w]){
                dfs(w, v);
                low[v] = Math.min(low[v], low[w]);

                //割点的判断
                if(v != parent && low[w] >= ord[v])
                    res.add(v);

                child ++;
                if(v == parent && child > 1)
                    res.add(v);

               // if(v == parent && child = 1) -- 单环肯定不是割点
            }
            else if(w != parent)
                low[v] = Math.min(low[v], low[w]);
    }

    public HashSet<Integer> result(){
        return res;
    }

    public static void main(String[] args){

        Graph g = new Graph("g8.txt");
        FindCutPoints fc = new FindCutPoints(g);
        System.out.println("Cut Points in g8 : " + fc.result());

        Graph g2 = new Graph("g2.txt");
        FindCutPoints fc2 = new FindCutPoints(g2);
        System.out.println("Cut Points in g2 : " + fc2.result());

        Graph tree = new Graph("tree.txt");
        FindCutPoints fc3 = new FindCutPoints(tree);
        System.out.println("Cut Points in tree : " + fc3.result());
    }
}