强连通算法 Tarjan

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https://www.cnblogs.com/1pha/articles/7818320.html

只适用于有向图

#include<stdio.h>//求一个图存在多少个强连通分量
#include<string.h>
#include<vector>
#include<algorithm>
using namespace std;
#define maxn 1000000
vector<int>mp[maxn];
int ans[maxn];
int vis[maxn];
int dfn[maxn];
int low[maxn];
int n,m,cnt,sig,tt;

void Tarjian(int u)
{
    vis[u] = 1;
    low[u] = dfn[u] = cnt++;
    for(int i = 0;i< mp[u].size();i++)
    {
        int v = mp[u][i];
        if(vis[v] == 0) Tarjian(v);
        if(vis[v] == 1) low[u] = min(low[u],low[v]);
    }
    if(dfn[u] == low[u])
    {
        sig++;
    }
}
void init()
{
    memset(vis,0,sizeof(vis));
    memset(dfn,0,sizeof(dfn));
    memset(low,0,sizeof(low));
    for(int i = 1;i<=n;i++) mp[i].clear();
}
void solve()
{
    sig = 0,cnt = 1,tt = -1;
    for(int i=1;i<=n;i++)
    {
        if(vis[i] == 0)
        {
            Tarjian(i);
        }
    }
    printf("%d\n",sig);
}

int main()
{
    while(~scanf("%d",&n))
    {
        if(n==0)break;
        scanf("%d",&m);
        init();
        for(int i=0;i<m;i++)
        {
            int x,y;
            scanf("%d%d",&x,&y);
            mp[x].push_back(y);
        }
        solve();
    }
}

POJ2553

https://cn.vjudge.net/problem/POJ-2553

#include<stdio.h>//求一个图存在多少个强连通分量
#include<string.h>
#include<vector>
#include<algorithm>
using namespace std;
#define maxn 1000000
vector<int>mp[maxn];
int ans[maxn];
int degree[maxn]; //记录度
int clocr[maxn];//染色 判断两点是否强连通 
int Stack[maxn];
int vis[maxn];
int dfn[maxn];
int low[maxn];
int n,m,cnt,sig,tt;

void init()
{
    memset(vis,0,sizeof(vis));
    memset(dfn,0,sizeof(dfn));
    memset(low,0,sizeof(low));
    memset(degree,0,sizeof(degree));
    memset(clocr,0,sizeof(clocr));
    memset(Stack,0,sizeof(Stack));
    for(int i = 1;i<=n;i++) mp[i].clear();
}

void Tarjian(int u)
{
    vis[u] = 1;
    low[u] = dfn[u] = cnt++;
    Stack[++tt] =  u;
    for(int i = 0;i< mp[u].size();i++)
    {
        int v = mp[u][i];
        if(vis[v] == 0) Tarjian(v);
        if(vis[v] == 1) low[u] = min(low[u],low[v]);
    }
    if(dfn[u] == low[u])//找到强连通图 
    {
        sig++;
        do
        {
            clocr[Stack[tt]] = sig;
            vis[Stack[tt]] = -1;
        }
        while(Stack[tt--] != u); //染色
    }
}

void solve()
{
    sig = 0,cnt = 1,tt = -1;
    for(int i=1;i<=n;i++) 
    {
        if(vis[i] == 0)
        {
            Tarjian(i);
        }
    }
    for(int i = 1;i<=n;i++)
    {
        for(int j = 0;j<mp[i].size();j++)
        {
            int v = mp[i][j];
            if(clocr[i] != clocr[v]) //如果不是同一个强连通 算上边
            {
                degree[clocr[i]]++;
            }
        }
    }
    int tot = 0;
    for(int i = 1;i<=sig;i++)
    {
        if(degree[i] > 0) continue; //出度大于0 
        for(int j = 1;j<=n;j++) //等于0 查找强连通里的点
        {
            if(clocr[j] == i)
            {
                ans[tot++] = j;
            }
        }
    }
    sort(ans,ans+tot);
    for(int i = 0;i<tot;i++)
    {
        if(i == 0) printf("%d",ans[i]);
        else printf(" %d",ans[i]);
    }
    printf("\n");
}

int main()
{
    while(~scanf("%d",&n))
    {
        if(n==0)break;
        scanf("%d",&m);
        init();
        for(int i=0;i<m;i++)
        {
            int x,y;
            scanf("%d%d",&x,&y);
            mp[x].push_back(y);
        }
        solve();
    }
}