哈理工OJ 1248 The kth great number（平衡树求第k大数）

题目链接：http://acm.hrbust.edu.cn/index.php?m=ProblemSet&a=showProblem&problem_id=1248

The kth great number
Time Limit: 1000 MS Memory Limit: 65536 K
Total Submit: 108(36 users) Total Accepted: 65(35 users) Rating: Special Judge: No
Description
Xiao Ming and Xiao Bao are playing a simple Numbers game. In a round Xiao Ming can choose to write down a number, or ask Xiao Bao what the kth great number is. Because the number written by Xiao Ming is too much, Xiao Bao is feeling giddy. Now, try to help Xiao Bao.
Input
There are several test cases. For each test case, the first line of input contains two positive integer n, k. Then n lines follow. If Xiao Ming choose to write down a number, there will be an ” I” followed by a number that Xiao Ming will write down. If Xiao Ming choose to ask Xiao Bao, there will be a “Q”, then you need to output the kth great number.
Output
The output consists of one integer representing the largest number of islands that all lie on one line.
Sample Input
8 3
I 1
I 2
I 3
Q
I 5
Q
I 4
Q
Sample Output
1
2
3
Source
The 36th ACM/ICPC Asia Regional Dalian Site —— Online Contest

【中文题意】求第k大数是多少。
【思路分析】平衡树模板题，就是写的有点麻烦。
【AC代码】

#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
#define maxn 1000005

typedef struct sbtnod
{
    int key,left,right,size;
}sbtnode;
int sbttail,sbt;

sbtnode tree[maxn];

void rrotate(int &t)
{
    int k=tree[t].left;
    if(!k)
    {
        return ;
    }
    tree[t].left=tree[k].right;
    tree[k].right=t;
    tree[k].size=tree[t].size;
    tree[t].size=tree[tree[t].left].size+tree[tree[t].right].size+1;
    t=k;
}

void lrotate(int &t)
{
    int k=tree[t].right;
    if(!k)return;
    tree[t].right=tree[k].left;
    tree[k].left=t;
    tree[k].size=tree[t].size;
    tree[t].size=tree[tree[t].left].size+tree[tree[t].right].size+1;
    t=k;
}

void maintain(int &t,bool flag)
{
    if(!t)return;
    if(!flag)
    {
        if(tree[tree[tree[t].left].left].size>tree[tree[t].right].size)
        {
            rrotate(t);
        }
        else if(tree[tree[tree[t].left].right].size>tree[tree[t].right].size)
        {
            lrotate(tree[t].left);
            rrotate(t);
        }
        else return ;
    }
    else
    {
        if(tree[tree[tree[t].right].right].size>tree[tree[t].left].size)
        {
            lrotate(t);
        }
        else if(tree[tree[tree[t].right].left].size>tree[tree[t].left].size)
        {
            rrotate(tree[t].right);
            lrotate(t);
        }
        else return ;
    }
    maintain(tree[t].left,false);
    maintain(tree[t].right,true);
    maintain(t,false);
    maintain(t,true);
}

void insert(int &t,int v)
{
    if(!t)
    {
        sbttail++;
        tree[sbttail].key=v;
        tree[sbttail].size=1;
        t=sbttail;
    }
    else
    {
        tree[t].size++;
        if(v<tree[t].key)
        {
            insert(tree[t].left,v);
        }
        else
        {
            insert(tree[t].right,v);
        }
        maintain(t,v>=tree[t].key);
    }
}

int del(int &t,int v)
{
    int ret;
    tree[t].size--;
    if(v==tree[t].key||(v<tree[t].key&&tree[t].left==0)||(v>tree[t].key&&tree[t].right==0))
    {
        ret=tree[t].key;
        if(tree[t].left==0||tree[t].right==0)
        {
            t=tree[t].left+tree[t].right;
        }
        else
        {
            tree[t].key=del(tree[t].left,tree[t].key+1);
        }
    }
    else
    {
            if(v<tree[t].key)
            {
                ret=del(tree[t].left,v);
            }
            else
            {
                ret=del(tree[t].right,v);
            }
    }
    return ret;
}

int select(int t,int k)
{
    if(k==tree[tree[t].left].size+1)
    {
        return t;
    }
    if(k<=tree[tree[t].left].size)
    {
        return select(tree[t].left,k);
    }
    else return select(tree[t].right,k-1-tree[tree[t].left].size);
}

int main()
{
    int n,k;
    while(~scanf("%d%d",&n,&k))
    {
        memset(tree,0,sizeof(tree));
        sbttail=0;
        sbt=0;

        char c;
        for(int i=1;i<=n;i++)
        {
            c=getchar();
            while(c!='I'&&c!='Q')
            {
                c=getchar();
            }
            int now;
            if(c=='I')
            {
                scanf("%d",&now);
                insert(sbt,now);
            }
            else
            {
                now=select(sbt,sbttail-k+1);
                printf("%d\n",tree[now].key);
            }
        }
    }
    return 0;
}