【主席樹】 ZOJ 2112 Dynamic Rankings 區間第k小值

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題解：Empress

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <string>
#include <iostream>
#include <algorithm>
#include <sstream>
#include <cmath>
using namespace std;
#include <queue>
#include <stack>
#include <vector>
#include <deque>
#include<bitset>
#include <set>
#include <map>
#define clc(arr, val)    memset(arr, val, sizeof(arr))
#define FOR(i,a,b)  for(int i=a;i<=b;i++)
#define IN   freopen ("in.txt" , "r" , stdin);
#define OUT  freopen ("out.txt" , "w" , stdout);
typedef long long  LL;
typedef unsigned long long  ULL;
const int MAXN = 60000;
const int MAXM = 6000010;
const int INF = 0x3f3f3f3f;
const LL mod = (LL)1<<32;
const double eps= 1e-8;
const double pi=acos(-1.0);
#define lson l,m, rt<<1
#define rson m+1,r,rt<<1|1
int Hash[MAXN],a[MAXN],all,tol,n;
int T[MAXN],S[MAXN],L[MAXN<<5],R[MAXN<<5],sum[MAXN<<5];
int build(int l,int r)
{
    int rt=(++all);
    sum[rt]=0;
    if(l==r) return rt;
    int m=(l+r)>>1;
    L[rt]=build(l,m);
    R[rt]=build(m+1,r);
    return rt;
}
int update(int pre,int x,int val,int l,int r)
{
    int rt=(++all);
    L[rt]=L[pre],R[rt]=R[pre],sum[rt]=sum[pre]+val;
    if(l==r) return rt;
    int m=(l+r)>>1;
    if(x<=m)
        L[rt]=update(L[pre],x,val,l,m);
    else R[rt]=update(R[pre],x,val,m+1,r);
    return rt;
}
/***樹狀數組*****/
int use[MAXN];
int lowbit(int x)
{
    return x&(-x);
}
void add(int x, int pos, int val)
{
    while(x<=n)
    {
        S[x]=update(S[x], pos, val, 1, tol);
        x+=lowbit(x);
    }
}
int Sum(int x)
{
    int ret=0;
    while(x>0)
    {
        ret+=sum[L[use[x]]];
        x-=lowbit(x);
    }
    return ret;
}
void modify(int x, int p, int d)
{
    while(x<=n)
    {
        S[x]=update(S[x], p, d, 1, tol);
        x+=lowbit(x);
    }
}
/****query***/
int query(int left,int right,int lr,int rr,int k,int l,int r)
{
    if(l==r) return l;
    int m=(l+r)>>1;
    int num=Sum(right)-Sum(left)+sum[L[rr]]-sum[L[lr]];
    if(k<=num)
    {
        for(int i=left;i;i-=lowbit(i))
            use[i]=L[use[i]];
        for(int i=right;i;i-=lowbit(i))
            use[i]=L[use[i]];
        return query(left,right,L[lr],L[rr],k,l,m);
    }
    else
    {
        for(int i=left;i;i-=lowbit(i))
            use[i]=R[use[i]];
        for(int i=right;i;i-=lowbit(i))
            use[i]=R[use[i]];
        return query(left,right,R[lr],R[rr],k-num,m+1,r);
    }
}

/*******詢問*****/
struct node
{
    int op,l,r,k;
}Q[10100];
int main()
{
    int m,t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%d",&n,&m);
        all=0;
        for(int i=1;i<=n;++i)
        {
            scanf("%d",&a[i]);
            Hash[++all]=a[i];
        }
        for(int i=0;i<m;i++)//save query
        {
            char op[2];
            scanf("%s",op);
            if(op[0]=='Q')
            {
                scanf("%d%d%d",&Q[i].l,&Q[i].r,&Q[i].k);
                Q[i].op=1;
            }
            else 
            {
                scanf("%d%d",&Q[i].l,&Q[i].r);
                Hash[++all]=Q[i].r;
                Q[i].op=0;
            }
        }
        sort(Hash+1,Hash+all+1);
        tol=unique(Hash+1,Hash+all+1)-Hash-1;
        T[0]=build(1,tol);
        for(int i=1;i<=n;i++)//build tree
        {
            int x=lower_bound(Hash+1,Hash+tol+1,a[i])-Hash;
            T[i]=update(T[i-1],x,1,1,tol);
            S[i]=T[0];
        }
        for(int i=0;i<m;i++)//output query
        {
            if(Q[i].op)//Query
            {
                for(int j=Q[i].l-1;j;j-=lowbit(j))
                    use[j]=S[j];
                for(int j=Q[i].r;j;j-=lowbit(j))
                    use[j]=S[j];
                int x=query(Q[i].l-1,Q[i].r,T[Q[i].l-1],T[Q[i].r],Q[i].k,1,tol);
                printf("%d\n",Hash[x]);
            }
            else //Change
            {
                modify(Q[i].l, lower_bound(Hash+1, Hash+tol+1, a[Q[i].l])-Hash, -1);
                modify(Q[i].l, lower_bound(Hash+1, Hash+tol+1, Q[i].r)-Hash, 1);
                a[Q[i].l]=Q[i].r;
            }
        }
    }
    return 0;
}
/*
*/