题目描述

或许你并不知道，你的某个朋友是你的亲戚。他可能是你的曾祖父的外公的女婿的外甥女的表姐的孙子。如果能得到完整的家谱，判断两个人是否亲戚应该是可行的，但如果两个人的最近公共祖先与他们相隔好几代，使得家谱十分庞大，那么检验亲戚关系实非人力所能及。在这种情况下，最好的帮手就是计算机。为了将问题简化，你将得到一些亲戚关系的信息，如Marry和Tom是亲戚，Tom和Ben是亲戚，等等。从这些信息中，你可以推出Marry和Ben是亲戚。请写一个程序，对于我们的关于亲戚关系的提问，以最快的速度给出答案。

输入格式

输入由两部分组成。

第一部分以N，M开始。N为问题涉及的人的个数(1  N  20000)。这些人的编号为1,2,3,…, N。下面有M行(1  M  1 000 000)，每行有两个数ai, bi，表示已知ai和bi是亲戚。第二部分以Q开始。以下Q行有Q个询问(1 <=  Q < = 1 000 000)，每行为ci, di，表示询问ci和di是否为亲戚。

输出格式

对于每个询问ci, di，输出一行：若ci和di为亲戚，则输出“Yes”，否则输出“No”。

闲来无事肝一肝并查集......

明显的并查集裸题。其思路是：对于每对亲戚关系，我们都将两人所在的集合合并为一个集合，查询时若两人再同一个集合就说明是亲戚了。

 
 
 
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#include<iostream>
#include<cstring>
#include<cstdio>
#define maxn 1000001
using namespace std;


int fa[maxn],n,m,q;




inline int read(){


    register int x(0),f(1); register char c(getchar());


    while(c<'0'||'9'<c){ if(c=='-') f=-1; c=getchar(); }


    while('0'<=c&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();


    return x*f;


}




int get(int x){


    if(fa[x]==x) return x;


    return fa[x]=get(fa[x]);


}




int main(){


    n=read(),m=read();


    for(register int i=1;i<=n;i++) fa[i]=i;


    for(register int i=1;i<=m;i++){


        int u=read(),v=read();


        u=get(u),v=get(v);


        fa[u]=v;


    }


     


    q=read();


    for(register int i=1;i<=q;i++){


        int u=read(),v=read();


        if(get(u)==get(v)) puts("Yes");


        else puts("No");


    }


    return 0;




}














 


 






时间复杂度为O((m+q)logn)


虽然是log级别，但这是上界，实际是远远达不到的




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