POJ2985 The k-th Largest Group[树状数组求第k大值+并查集||treap+并查集]

The k-th Largest Group

Time Limit: 2000MS		Memory Limit: 131072K
Total Submissions: 8807		Accepted: 2875

Description

Newman likes playing with cats. He possesses lots of cats in his home. Because the number of cats is really huge, Newman wants to group some of the cats. To do that, he first offers a number to each of the cat (1, 2, 3, …, n). Then he occasionally combines the group cat i is in and the group cat j is in, thus creating a new group. On top of that, Newman wants to know the size of the k-th biggest group at any time. So, being a friend of Newman, can you help him?

Input

1st line: Two numbers N and M (1 ≤ N, M ≤ 200,000), namely the number of cats and the number of operations.

2nd to (m + 1)-th line: In each line, there is number C specifying the kind of operation Newman wants to do. If C = 0, then there are two numbers i and j (1 ≤ i, j ≤ n) following indicating Newman wants to combine the group containing the two cats (in case these two cats are in the same group, just do nothing); If C = 1, then there is only one number k (1 ≤ k ≤ the current number of groups) following indicating Newman wants to know the size of the k-th largest group.

Output

For every operation “1” in the input, output one number per line, specifying the size of the kth largest group.

Sample Input

10 10
0 1 2
1 4
0 3 4
1 2
0 5 6
1 1
0 7 8
1 1
0 9 10
1 1

Sample Output

1
2
2
2
2

Hint

When there are three numbers 2 and 2 and 1, the 2nd largest number is 2 and the 3rd largest number is 1.

Source

POJ Monthly--2006.08.27, zcgzcgzcg

---

并查集维护连通分量大小，树状数组求cc中第k大值

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
const int N=2e5+5;
inline int read(){
    char c=getchar();int x=0,f=1;
    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
    return x*f;
}
int n,m,op,x,y,k;
int fa[N],size[N],tot=0;
inline int find(int x){return x==fa[x]?x:fa[x]=find(fa[x]);}

int c[N];
inline int lowbit(int x){return x&-x;}
inline void add(int p,int v){
    for(;p<=n;p+=lowbit(p)) c[p]+=v;
}
inline int sum(int p){
    int res=0;
    for(;p>0;p-=lowbit(p)) res+=c[p];
    return res;
}
inline int kth(int k){
    int x=0,cnt=0;
    for(int i=16;i>=0;i--){
        x+=(1<<i);
        if(x>=n||cnt+c[x]>=k) x-=(1<<i);
        else cnt+=c[x];
    }
    return x+1;
}

int main(){
    n=read();m=read();
    for(int i=1;i<=n;i++) fa[i]=i,size[i]=1,tot++;
    add(1,n);
    for(int i=1;i<=m;i++){
        op=read();
        if(!op){
            x=read();y=read();
            int f1=find(x),f2=find(y);
            if(f1!=f2){
                fa[f1]=f2;
                add(size[f1],-1);
                add(size[f2],-1);
                size[f2]+=size[f1];
                add(size[f2],1);
                tot--;
            }
        //    printf("%d %d %d %d
",f1,f2,size[f1],size[f2]);
        }else{
            k=tot-read()+1;//printf("k %d
",k);
            printf("%d
",kth(k));
        }
    }
}

当然treap也可以 注意是第k大

//
//  main.cpp
//  poj2985_treap
//
//  Created by Candy on 27/11/2016.
//  Copyright © 2016 Candy. All rights reserved.
//
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
#define lc t[x].l
#define rc t[x].r
const int N=2e5+5;
inline int read(){
    char c=getchar();int x=0,f=1;
    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
    return x*f;
}
int n,m,op,x,y,k;
int fa[N],size[N];
inline int find(int x){return x==fa[x]?x:fa[x]=find(fa[x]);}
struct node{
    int l,r,v,w,rnd,size;
}t[N];
int cnt,root;
inline void update(int x){t[x].size=t[lc].size+t[rc].size+t[x].w;}
inline void rturn(int &x){
    int c=lc;lc=t[c].r;t[c].r=x;
    t[c].size=t[x].size;update(x);x=c;
}
inline void lturn(int &x){
    int c=rc;rc=t[c].l;t[c].l=x;
    t[c].size=t[x].size;update(x);x=c;
}
void ins(int &x,int v){//printf("ins %d %d
",x,v);
    if(x==0){
        cnt++;x=cnt;
        t[cnt].l=t[cnt].r=0;t[cnt].w=t[cnt].size=1;
        t[cnt].v=v;t[cnt].rnd=rand();
    }else{
        t[x].size++;
        if(t[x].v==v) t[x].w++;
        else if(v<t[x].v){
            ins(lc,v);
            if(t[lc].rnd<t[x].rnd) rturn(x);
        }else{
            ins(rc,v);
            if(t[rc].rnd<t[x].rnd) lturn(x);
        }
    }
}
void del(int &x,int v){
    if(x==0) return;
    if(t[x].v==v){
        if(t[x].w>1){t[x].w--;t[x].size--;return;}
        if(lc*rc==0) x=lc+rc;
        else if(t[lc].rnd<t[rc].rnd) rturn(x),del(x,v);
        else lturn(x),del(x,v);
    }else{
        t[x].size--;
        if(v<t[x].v) del(lc,v);
        else del(rc,v);
    }
}
//int kth(int x,int k){
//    if(x==0)return 0;
//    if(k<=t[lc].size) return kth(lc,k);
//    else if(k>t[lc].size+t[x].w) return kth(rc,k-t[lc].size-t[x].w);
//    else return t[x].v;
//}
int kth(int x,int k){
    if(x==0) return 0;
    if(k<=t[rc].size) return kth(rc,k);
    else if(k>t[rc].size+t[x].w) return kth(lc,k-t[rc].size-t[x].w);
    else return t[x].v;
}
int main(){
    n=read();m=read();
    for(int i=1;i<=n;i++) fa[i]=i,size[i]=1;
    while(m--){
        op=read();
        if(!op){
            x=read();y=read();
            int f1=find(x),f2=find(y);
            if(f1!=f2){
                fa[f1]=f2;
                if(size[f1]!=1) del(root,size[f1]);
                if(size[f2]!=1) del(root,size[f2]);
                size[f2]+=size[f1];
                ins(root,size[f2]);
            }
        }else{
            k=read();//printf("kth %d %d
",k,t[root].size);
            if(k>t[root].size) puts("1");
            else printf("%d
",kth(root,k));
        }
    }
}