Tarjan算法求有向图强连通分量并缩点

Posted 2022-07-09 dwvictor

 

// Tarjan算法求有向图强连通分量并缩点
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<vector>
#include<queue>
using namespace std;
const int N = 100010, M = 1000010;
//
int ver[M], Next[M], head[N], dfn[N], low[N];
int stack[N], ins[N], c[N];

int vc[M], nc[M], hc[N], tc;
//强连通分量
vector<int> scc[N];

int n, m, tot, num, top, cnt;

void add(int x, int y) 
    ver[++tot] = y, Next[tot] = head[x], head[x] = tot;

//缩点后建图
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, ins[x] = 1;//标记x点
    for (int i = head[x]; i; i = Next[i])
        //未走过
        if (!dfn[ver[i]]) 
            tarjan(ver[i]);
            //递归更新
            low[x] = min(low[x], low[ver[i]]);
        
        else if (ins[ver[i]])
            //直接更新
            low[x] = min(low[x], dfn[ver[i]]);
    if (dfn[x] == low[x]) 
        //一个强连通
        cnt++; int y;
        do 
            y = stack[top--], ins[y] = 0;
            //属于哪一个强连通
            c[y] = cnt, scc[cnt].push_back(y);
         while (x != y);
    


int main() 
    cin >> n >> m;
    for (int i = 1; i <= m; i++) 
        int x, y;
        scanf("%d%d", &x, &y);
        add(x, y);
    
    for (int i = 1; i <= n; i++)
        if (!dfn[i]) tarjan(i);
    for (int x = 1; x <= n; x++)
        for (int i = head[x]; i; i = Next[i]) 
            int y = ver[i];
            if (c[x] == c[y]) continue;
            add_c(c[x], c[y]);