• Network UVA


    #include <stdio.h>
    #include <algorithm>
    #include <iostream>
    #include <string.h>
    using namespace std;
    
    /*
    *  求 无向图的割点和桥
    *  可以找出割点和桥,求删掉每个点后增加的连通块。
    *  需要注意重边的处理,可以先用矩阵存,再转邻接表,或者进行判重
    */
    const int MAXN = 10010;
    const int MAXM = 100010;
    struct Edge
    {
        int to,next;
        bool cut;//是否为桥的标记
    }edge[MAXM];
    int head[MAXN],tot;
    int Low[MAXN],DFN[MAXN],Stack[MAXN];
    int Index,top;
    bool Instack[MAXN];
    bool cut[MAXN];
    int add_block[MAXN];//删除一个点后增加的连通块
    int bridge;
    
    void addedge(int u,int v)
    {
        edge[tot].to = v;edge[tot].next = head[u];edge[tot].cut = false;
        head[u] = tot++;
    }
    
    
    void Tarjan(int u,int pre)
    {
        int v;
        Low[u] = DFN[u] = ++Index;
        Stack[top++] = u;
        Instack[u] = true;
        int son = 0;
        for(int i = head[u];i != -1;i = edge[i].next)
        {
            v = edge[i].to;
            if(v == pre)continue;
            if( !DFN[v] )
            {
                son++;
                Tarjan(v,u);
                if(Low[u] > Low[v])Low[u] = Low[v];
                ////一条无向边(u,v)是桥,当且仅当(u,v)为树枝边,且满足DFS(u)<Low(v)。
                if(Low[v] > DFN[u])
                {
                    bridge++;
                    edge[i].cut = true;
                    edge[i^1].cut = true;
                }
                //割点
                //一个顶点u是割点,当且仅当满足(1)或(2) (1) u为树根,且u有多于一个子树。
                //(2) u不为树根,且满足存在(u,v)为树枝边(或称父子边,
                //即u为v在搜索树中的父亲),使得DFS(u)<=Low(v)
                if(u != pre && Low[v] >= DFN[u])//不是树根
                {
                    cut[u] = true;
                    add_block[u]++;
                }
            }
            else if( Low[u] > DFN[v])
                Low[u] = DFN[v];
        }
        //树根,分支数大于1
        if(u == pre && son > 1)cut[u] = true;
        if(u == pre)add_block[u] = son - 1;
        Instack[u] = false;
        top--;
    }
    
    void solve(int N)
    {
        memset(DFN,0,sizeof(DFN));
        memset(Instack,false,sizeof(Instack));
        memset(add_block,0,sizeof(add_block));
        memset(cut,false,sizeof(cut));
        Index = top = 0;
        bridge = 0;
        for(int i = 1;i <= N;i++)
            if(!DFN[i])
                Tarjan(i,i);
        int ans = 0;
        for(int i = 1;i <= N;i++)
            if(cut[i])
                ans++;
        printf("%d
    ",ans);
    }
    void init()
    {
        tot = 0;
        memset(head,-1,sizeof(head));
    }
    
    int main()
    {
        int n;
        while(scanf("%d",&n), n)
        {
    
            int a,b;
            char ch;
            init();
            while(scanf("%d",&a),a)
            {
                while(scanf("%d%c",&b,&ch))
                {
                    addedge(a,b);
                    addedge(b,a);
                    if(ch == '
    ')
                        break;
                }
            }
            solve(n);
        }
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/smallhester/p/11259383.html
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