桥和割点，以及图的遍历树

目录

什么是桥

寻找桥的算法

代码实现

什么是割点

​寻找割点的算法

代码实现

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什么是桥

寻找桥的算法

代码实现

import java.util.ArrayList;

public class FindBridges {

    private Graph G;
    private boolean[] visited;

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

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

        for(int w: G.adj(v))
            if(!visited[w]){
                dfs(w, v);
                low[v] = Math.min(low[v], low[w]);
                if(low[w] > ord[v])
                    res.add(new Edge(v, w));
            }
            else if(w != parent)
                low[v] = Math.min(low[v], low[w]);
    }

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

    public static void main(String[] args){

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

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

什么是割点

寻找割点的算法

孩子的数量是根据树来说的，而不是看根节点有多少个邻边，遍历树不同孩子数量也不同。

代码实现

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 ++;

        int child = 0;

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

                if(v != parent && low[w] >= ord[v])
                    res.add(v);

                child ++;
                if(v == parent && child > 1)
                    res.add(v);
            }
            else if(w != parent)
                low[v] = Math.min(low[v], ord[w]);
    }

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

    public static void main(String[] args){

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

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

        Graph g3 = new Graph("g3.txt");
        FindCutPoints fc3 = new FindCutPoints(g3);
        System.out.println("Cut Points in g3 : " + fc3.result());

        Graph tree = new Graph("tree.txt");
        FindCutPoints fc4 = new FindCutPoints(tree);
        System.out.println("Cut Points in tree : " + fc4.result());

    }
}