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tarjan找强连通分量

admin 11月 13, 2020 0

今天说一说找强连通分量的tarjan算法

这篇真的很好，我就是靠这个真正明白的。

例题：

代码：

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#include<cstdio>
#include<cstring>
using namespace std;
int n,m;
const int N = 100005;
struct 
{
    int v,next;
}e[N*2],e1[N*2];
int front[N],cnt = 0,val[N],co[N],stk[N],dfn[N],low[N],f[N],vl[N];
bool instk[N];
int cnt1 = 0, front1[N],tot = 0;
int tp = 0, t = 0;
void AddEdge(int u,int v)
{
    e[++cnt].v = v;
    e[cnt].next = front[u];
    front[u] = cnt;
}
void AddEdge1(int u,int v)
{
    e1[++cnt1].v = v;
    e1[cnt1].next = front1[u];
    front1[u] = cnt1;
}
void tarjan(int now)
{
    dfn[now] = low[now] = ++t;
    instk[now] = true;
    stk[++tp] = now;
    for (int i = front[now]; i; i = e[i].next)
    {
        int xx = e[i].v;
        if(!dfn[xx])
        {
            tarjan(xx);
            low[now] = min(low[now],low[xx]);
        }
        else if (instk[xx])
        {
            low[now] = min(low[now],dfn[xx]);
        }
    }
    if(dfn[now] == low[now])
    {
        tot++;
        vl[tot] = 0;
        while(stk[tp+1] != now)
        {
            int xx = stk[tp];
            vl[tot] += val[xx];
            tp--;
            instk[xx] = false;
            co[xx] = tot;
        }
    }
}
void search(int x)
{
    if(f[x]) return;
    f[x] = vl[x];
    int maxs = 0;
    for (int i = front1[x]; i; i = e1[i].next)
    {
        int xx = e1[i].v;
        if(!f[xx]) search(xx);
        maxs = max(maxs, f[xx]);
    }
    f[x] += maxs;
}
int main()
{
    scanf("%d%d",&n,&m);
    for (int i = 1; i <= n; i++) scanf("%d",&val[i]);
    for (int i = 1; i <= m; i++)
    {
        int a,b;
        scanf("%d%d",&a,&b);
        AddEdge(a,b);
    }
    for (int i = 1; i <= n; i++)
    {
        if (!dfn[i]) tarjan(i);
    }
    for (int k = 1; k <= n; k++)
    {
        for (int i = front[k]; i; i = e[i].next)
        {
            int xx = e[i].v;
            if(co[xx] != co[k]) AddEdge1(co[k],co[xx]);
        }
    }

    int cur,res = 0;
    memset(f,0,sizeof f);
    for (int k = 1; k <= tot; k++)
    {
        //cout<< vl[k] <<endl;
        //cout<<vl[k]<<endl;
        if (!f[k]) search(k);
    //	cout<< k <<" "<<f[k]<<endl;
        res = max(res, f[k]);
    }
    printf("%dn", res);
    return 0;
}
 

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

const int N = 10005;
int n,p,r;
struct 
{
    int v,next;
}e[N],e1[N];

int cnt = 0, cnt1 = 0;
int front[N],front1[N];
int val[N],vl[N];
int stk[N],dfn[N],low[N],co[N],num[N],rudu[N];
int tot = 0, t = 0, tp = 0;
bool instk[N],vis[N];
int inf;
pair<int,int> node[N];

void AddEdge(int u,int v)
{
    e[++cnt].v = v;
    e[cnt].next = front[u];
    front[u] = cnt;
}
void AddEdge1(int u,int v)
{
    e1[++cnt1].v = v;
    e1[cnt1].next = front1[u];
    front1[u] = cnt1;
}

void tarjan(int now)
{
    dfn[now] = low[now] = ++t;
    instk[now] = true;
    stk[++tp] = now;
    for (int i = front[now]; i; i = e[i].next)
    {
        int xx = e[i].v;
        if (!dfn[xx])
        {
            tarjan(xx);
            low[now] = min(low[now],low[xx]);
        }
        else if(instk[xx])
        {
            low[now] = min(low[now],dfn[xx]);
        }
    }
    if(dfn[now] == low[now])
    {
        tot++;
        while(stk[tp + 1] != now)
        {
            int xx = stk[tp];
            tp--;
            instk[xx] = false;
            co[xx] = tot;
            num[tot] = min(num[tot],xx);
            vl[tot] = min(vl[tot],val[xx]);
        }
    }
}
bool cmp(pair<int,int> a, pair<int,int> b)
{
    return a.second < b.second;
}
int main()
{
    scanf("%d%d",&n,&p);
    memset(val,127,sizeof val);
    memset(vl,127,sizeof vl);
    memset(num,127,sizeof num);
    for (int i = 1; i <= p; i++)
    {
        int t = 0;
        scanf("%d",&t);
        scanf("%d",&val[t]);
    }
    scanf("%d",&r);
    for (int i = 1; i <= r; i++)
    {
        int a,b;
        scanf("%d%d",&a,&b);
        AddEdge(a,b);
    }

    inf = vl[1];
    for (int i = 1; i <= n; i++)
    {
        if (!dfn[i]) tarjan(i);
    }
    for (int k = 1; k <= n; k++)
    {
        for (int i = front[k]; i; i = e[i].next)
        {
            int xx = e[i].v;
            if(co[k] != co[xx])
            {
            //	cout<<num[co[k]]<<"-->"<<num[co[xx]]<<endl;
                AddEdge1(co[k],co[xx]);
                rudu[co[xx]]++;
            }
        }
    }
    int res = 0;
    bool flg = false;
    for (int i = 1; i <= tot; i++)
    {
    //	cout<<num[i]<<" "<<rudu[i]<<" "<<vl[i]<<endl;
    	if (rudu[i] == 0 && vl[i] != inf)
    	{
    		res += vl[i];
    		vis[i] = true;
    		for (int j = front1[i]; j; j = e1[j].next)
    		{
    			int xx = e1[j].v;
    			vis[xx] = true;
    		}
    	}
    	else if (rudu[i] == 0 && vl[i] == inf) {
    	//	cout<< "NO_i "<<i<<endl;
    		flg = true;
    	}
    }
    int foo = inf;
    if(!flg) printf("YESn%d",res);
    else
    {
    	for (int i = 1; i <= tot; i++)
    	{
    		if (rudu[i] == 0 && vl[i] == inf)
    		{
    			foo = min(foo,num[i]);
    			for (int j = front1[i]; j; j = e[j].next)
    			{
    				int xx = e[j].v;
    				if(vis[xx]) continue;
    				else foo = min(foo,num[xx]);
    			}
    		}
    	}
    	printf("NOn%d",foo);
    }
    return 0;
}
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