【USACO06JAN】牛的舞会The Cow Prom

题目描述

约翰的N (2 <= N <= 10,000)只奶牛非常兴奋，因为这是舞会之夜！她们穿上礼服和新鞋子，别上鲜花，她们要表演圆舞.

只有奶牛才能表演这种圆舞.圆舞需要一些绳索和一个圆形的水池.奶牛们围在池边站好，顺时针顺序由1到N编号.每只奶牛都面对水池，这样她就能看到其他的每一只奶牛.

为了跳这种圆舞，她们找了 M(2<M< 50000)条绳索.若干只奶牛的蹄上握着绳索的一端，绳索沿顺时针方绕过水池，另一端则捆在另一些奶牛身上.这样，一些奶牛就可以牵引另一些奶牛.有的奶牛可能握有很多绳索，也有的奶牛可能一条绳索都没有.

对于一只奶牛，比如说贝茜，她的圆舞跳得是否成功，可以这样检验：沿着她牵引的绳索，找到她牵引的奶牛，再沿着这只奶牛牵引的绳索，又找到一只被牵引的奶牛，如此下去，若最终能回到贝茜，则她的圆舞跳得成功，因为这一个环上的奶牛可以逆时针牵引而跳起旋转的圆舞. 如果这样的检验无法完成，那她的圆舞是不成功的.

如果两只成功跳圆舞的奶牛有绳索相连，那她们可以同属一个组合.

给出每一条绳索的描述，请找出，成功跳了圆舞的奶牛有多少个组合？

输入

Line 1: Two space-separated integers: N and M

Lines 2..M+1: Each line contains two space-separated integers A and B that describe a rope from cow A to cow B in the clockwise direction.

输出

Line 1: A single line with a single integer that is the number of groups successfully dancing the Round Dance.

样例输入

样例输出

题解

tarjan求强连通分量模版题。

#include<cmath>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define ll long longconst int maxn=10000+50;
const int maxm=50000+50;int fir[maxn],nex[maxm],to[maxm],ecnt;
int col[maxn],dfn[maxm],low[maxm],stack[maxm],vis[maxn],cnt[maxn];
int n,m,t,deep,sum,ans,x,y;void add_edge(int u,int v){nex[++ecnt]=fir[u];fir[u]=ecnt;to[ecnt]=v;
}template<typename T>void read(T& aa){char cc; ll ff;aa=0;cc=getchar();ff=1;while((cc<'0'||cc>'9')&&cc!='-') cc=getchar();if(cc=='-') ff=-1,cc=getchar();while(cc>='0'&&cc<='9') aa=aa*10+cc-'0',cc=getchar();aa*=ff;
}int tarjan(int u){dfn[u]=++deep;low[u]=deep;vis[u]=1;stack[++t]=u;for(int e=fir[u];e;e=nex[e]){int v=to[e];if(!dfn[v]){tarjan(v);low[u]=min(low[u],low[v]);}else{if(vis[v]) low[u]=min(low[u],dfn[v]);}}if(dfn[u]==low[u]){col[u]=++sum;vis[u]=0;while(stack[t]!=u){col[stack[t]]=sum;vis[stack[t--]]=0;}t--;}
}int main(){read(n),read(m);for(int i=1;i<=m;i++){read(x),read(y);add_edge(x,y);}for(int i=1;i<=n;i++){if(!dfn[i]) tarjan(i);}for(int i=1;i<=n;i++) cnt[col[i]]++;for(int i=1;i<=sum;i++){if(cnt[i]>1) ans++;}cout<<ans<<endl;return 0;
}

转载于:https://www.cnblogs.com/rlddd/p/9657121.html

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