{模板}Tarjan缩环-人工栈

最新推荐文章于 2024-04-11 13:43:14 发布

FarmerJohnLYH

最新推荐文章于 2024-04-11 13:43:14 发布

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本文链接：https://blog.youkuaiyun.com/FarmerJohnOfZS/article/details/52549850

本文介绍了一种结合并查集与Tarjan算法的数据结构实现方法，通过使用点集、边集和并查集来解决图论问题。具体包括了如何通过递归查找根节点、合并集合以及进行Tarjan离线求割点与桥的过程。

点集+边集+并查集

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
const int N=500500;
int m,n,S,q;
long long ans,Dist[N];
int Fir[N],Edge[2*N][2],tot_edge,head[N];
int Father[N];
int dfn[N],low[N],List[N];
bool vis[N];
int Data[N],bz[N];
int Stack[N][2];
int read(int &n)
{
    char ch=' ';int q=0,w=1;
    for(;(ch!='-')&&((ch<'0')||(ch>'9'));ch=getchar());
    if(ch=='-')w=-1,ch=getchar();
    for(;ch>='0' && ch<='9';ch=getchar())q=q*10+ch-48;n=q*w;return n;
}
void link(int x,int y)
{
    if(!Fir[x]) head[x] = tot_edge + 1;
    Edge[++ tot_edge][0] = Fir[x];
    Fir[x] = tot_edge; 
    Edge[tot_edge][1] = y;
}
void tarjan(int x)
{
    int I = 1;
    bool P;
    Stack[I][0] = x;
    Stack[I][1] = 0;
    while (I)
    {
        P = 1;
        x = Stack[I][0];
        if(!Stack[I][1])
        {
            bz[x] = vis[x] = 1,
            List[ dfn[x] = low[x] = ++List[0] ]=x,
            Stack[I][1] = Fir[x];
        }
        else
        {
            low[x] = min(low[x],low[Edge[Stack[I][1]][1]]),
            Stack[I][1] = Edge[Stack[I][1]][0];
        } 
        for(int i = Stack[I][1];i;i = Edge[i][0])
            if(bz[Edge[i][1]]) 
            {
                low[x] = min(low[x],low[Edge[i][1]]);
            }
            else 
            if(!vis[Edge[i][1]])
            {
                Stack[I][1] = i;
                Stack[++I][0] = Edge[i][1];
                Stack[I][1] = 0;
                P=0;
                break;
            }
        if(P)
        {
            if(low[x] == dfn[x])
            {
                int t;
                while( (t = List[ List[0]-- ]) != x ) 
                {
                    bz[t] = 0;
                    Father[t] = x;
                }
                Father[x] = x;
                bz[x] = 0;
            }
            I --;
        }
    }
}
int Getfather(int x)
{
    return Father[x] = (Father[x]==x?x:Getfather(Father[x]));
}
int main()
{
    int x,y;
    read(n),read(m),read(q);
    for(int i = 1;i <= m;i ++)
    {
        read(x),read(y);
        link(x,y);
    }
    for(int i = 1;i <= n;i ++) 
        if(!vis[i]) 
            tarjan(i);
    for(int i = 1;i <= n;i ++)
    if( (x=Getfather(i)) != i )
    {
        Edge[head[i]][0] = Fir[x];
        Fir[x] = Fir[i];
        Fir[i] = 0;
    }

    for(int i = 1;i <= n;i ++)
        for(int j = Fir[i];j;j = Edge[j][0])
            Edge[j][1]=Father[Edge[j][1]];
}