pku2985 The k-th Largest Group

 

题意：初始化状态为N个含单一元素的集合，动态合并任意两个集合，查询第ith大的集合的大小

分析：以虚二叉树做辅助结构找出第ith大的集合的大小

 

#include <iostream>
#include <algorithm>
using namespace std;

#define MAXN 200001

int v[MAXN],N,M,pnt[MAXN],son[3*MAXN];
//v[i]第i只猫所在组的猫的数量，范围在1～N之间；son[u]表示以结点u为根的子树的结点数

void insert(int num,int k){
    int l=1,r=N,m,u=1;
    while(l<r){
        m=(l+r)/2;
        son[u]+=k;
        if(num<=m){
            r=m;
            u=u*2;
        }
        else{
            l=m+1;
            u=u*2+1;
        }
    }
    son[u]+=k;
}

int find(int ith){
    int l=1,r=N,u=1,m;
    while(l<r){
        m=(l+r)/2;
        if(son[2*u+1]>=ith){
            l=m+1;
            u=u*2+1;
        }
        else{
            ith-=son[2*u+1];
            r=m;
            u=u*2;
        }
    }
    return l;
}



void init(){
    int i;
    for(i=1;i<=N;i++){
        pnt[i]=i;
        v[i]=1;
        insert(v[i],1);
    }
}

int fs(int i){
    if(pnt[i]==i)
        return i;
    pnt[i]=fs(pnt[i]);
    return pnt[i];
}



int main(){
    int q,a,b,x,y,ith;
    while(scanf("%d%d",&N,&M)!=EOF){
        init();
        while(M--){
            scanf("%d",&q);
            if(q==0){
                scanf("%d%d",&a,&b);
                x=fs(a);
                y=fs(b);
                if(x!=y){
                    pnt[x]=y;                    
                    insert(v[x],-1);
                    insert(v[y],-1);
                    v[y]+=v[x];
                    insert(v[y],1);
                }
            }
            else{
                scanf("%d",&ith);
                printf("%d\n",find(ith));
            }
        }
    }
    return 0;
}