有向图的强连通分量

在求有向图的强连通分量的时候，有一个特别重要的东西要记住：

有向图和无向图的low函数的意义是不同的。

有向图中，low所指，只能连回当前scc中的点，这也决定了这一行：

else if (!sccno[v])
        {
            lowu = min(lowu, dfn[v]);
        }

判断scc是否已经找到的因素是，low[u] == dfn[u]这也意味着u是当前scc的第一个发现的点。

sccno初始化为0.

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <stack>
 
using namespace std;

const int maxn = 105, maxm = maxn * maxn;

stack <int> s;

int n, m, tot, dfs_clock, scc_cnt;

int h[maxn], dfn[maxn], low[maxn], sccno[maxn]; 
 
struct edge
{
    int v, next;
}a[maxm];

void add(int x, int y)
{
    a[tot].v = y;
    a[tot].next = h[x];
    h[x] = tot++;
}

int dfs(int u, int fa)
{
    s.push(u);
    int lowu = dfn[u] = ++dfs_clock;
    for (int i = h[u]; ~i; i = a[i].next)
    {
        int v = a[i].v;
        if (!dfn[v])
        {
            int lowv = dfs(v, u);
            lowu = min(lowu, lowv);
        }else if (!sccno[v])
        {
            lowu = min(lowu, dfn[v]);
        }
    }
    if (lowu == dfn[u])
    {
        scc_cnt++;
        for(;;)
        {
            int x = s.top(); s.pop();
            sccno[x] = scc_cnt;
            if (x == u) break;
        }
    }
    low[u] = lowu;
    return lowu;
}

int main()
{
    freopen("有向图的强连通分量.in","r",stdin);
    scanf("%d%d", &n, &m);
    memset(h, -1, sizeof h); tot = dfs_clock = scc_cnt = 0;
    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])
        {
            dfs(i, 0);
        }
    for (int i = 1; i <= scc_cnt; i++)
    {
        for (int j = 1; j <= n; j++)
            if (sccno[j] == i)
                printf("%d ", j);
        printf("
");
    }
    return 0;
}