• 点双连通分量


    在Tarjan算法的过程中维护一个栈,并按如下方法维护其中的元素
    1:当一个节点第一次被访问时,入栈。
    2:当割点判定法则中dfn[x]<=Low[y]成立时
    无论X是否为根,都要
    1:从栈顶不断顶出节点,直到节点Y被弹出
    2:刚才弹出的所有节点与节点X一起构成一个V-DCC
    注意节点X还在栈中

    #include<iostream>
    #include<cstdio>
    #include<cstring>
    #include<algorithm>
    #include<vector>
    #include<queue>
    using namespace std;
    const int N = 20010, M = 200010;
    int head[N], ver[M], Next[M];
    int dfn[N], low[N], stack[N], new_id[N], c[N], belong[M];
    int d[N], dist[N], f[N][16];
    int n, m, t, tot, num, root, top, cnt, tc;
    bool cut[N];
    vector<int> dcc[N];
    int hc[N], vc[M], nc[M];
    queue<int> q;
    
    void add(int x, int y) 
    {
    	ver[++tot] = y, Next[tot] = head[x], head[x] = tot;
    }
    
    void add_c(int x, int y) 
    {
    	vc[++tc] = y, nc[tc] = hc[x], hc[x] = tc;
    }
    
    void tarjan(int x) 
    {
    	dfn[x] = low[x] = ++num;
    	stack[++top] = x;
    	if (x == root && head[x] == 0) 
    	{ 
    		dcc[++cnt].push_back(x);
    		return;
    	}
    
    	int flag = 0;
    	for (int i = head[x]; i; i = Next[i]) 
    	{
    		int y = ver[i];
    		if (!dfn[y]) 
    		{
    			tarjan(y);
    			low[x] = min(low[x], low[y]);
    			if (low[y] >= dfn[x]) 
    			//x-->y,发现low[y]>=dfn[x],则X是一个割点 
    			{
    				flag++;
    				if (x != root || flag > 1) //如果X不为根,或者X为根,但有两个子树时 
    				      cut[x] = true;
    				cnt++;
    				int z;
    			
    				do 
    				//将栈中的元素不断弹出来,直到Y这个结点 
    				{
    					z = stack[top--];
    					dcc[cnt].push_back(z);
    				
    				} 
    				while (z != y);
    				dcc[cnt].push_back(x);//将X这个点也加入点双中,但X仍在栈中 
    			
    			}
    		}
    		else low[x] = min(low[x], dfn[y]);
    	}
    }
    
    
    int main() 
    {
    	    cin>>n>>m;
    		memset(head, 0, sizeof(head));
    		memset(hc, 0, sizeof(hc));
    		memset(dfn, 0, sizeof(dfn));
    		memset(d, 0, sizeof(d));
    		memset(cut, 0, sizeof(cut));
    		memset(c, 0, sizeof(c));
    		for (int i = 1; i <= n; i++) dcc[i].clear();
    		tot = 1; num = cnt = top = 0;
    		for (int i = 1; i <= m; i++) 
    		{
    			int x, y;
    			scanf("%d%d", &x, &y);
    			add(x, y), add(y, x);
    		}
    		for (int i = 1; i <= n; i++)
    			if (!dfn[i]) root = i, tarjan(i);
    		for (int i=1;i<=cnt;i++)
    		{
    			cout<<"e-dcc   "<<i<<endl;
    			for (int j=0;j<dcc[i].size();j++)
    			      cout<<dcc[i][j]<<"   ";
    			cout<<endl;
    		}
    		
    }
    
    
    /*
    4 4
    1 2 
    2 4
    2 3
    3 4
    */
    

      运行结果

    e-dcc 1
    4 3 2
    e-dcc 2
    2 1

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  • 原文地址:https://www.cnblogs.com/cutemush/p/12683083.html
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