POJ 2104 K-th Number 主席树

K-th Number

 

Description

You are working for Macrohard company in data structures department. After failing your previous task about key insertion you were asked to write a new data structure that would be able to return quickly k-th order statistics in the array segment. 
That is, given an array a[1...n] of different integer numbers, your program must answer a series of questions Q(i, j, k) in the form: "What would be the k-th number in a[i...j] segment, if this segment was sorted?" 
For example, consider the array a = (1, 5, 2, 6, 3, 7, 4). Let the question be Q(2, 5, 3). The segment a[2...5] is (5, 2, 6, 3). If we sort this segment, we get (2, 3, 5, 6), the third number is 5, and therefore the answer to the question is 5.

Input

The first line of the input file contains n --- the size of the array, and m --- the number of questions to answer (1 <= n <= 100 000, 1 <= m <= 5 000). 
The second line contains n different integer numbers not exceeding 10⁹ by their absolute values --- the array for which the answers should be given. 
The following m lines contain question descriptions, each description consists of three numbers: i, j, and k (1 <= i <= j <= n, 1 <= k <= j - i + 1) and represents the question Q(i, j, k).

Output

For each question output the answer to it --- the k-th number in sorted a[i...j] segment.

Sample Input

7 3
1 5 2 6 3 7 4
2 5 3
4 4 1
1 7 3

Sample Output

5
6
3

Hint

This problem has huge input,so please use c-style input(scanf,printf),or you may got time limit exceed.

 

题意：

　　给你n个数，q次询问

　　每次询问l,r之间的第k小的数是多少

题解：

　　不理解就去套板子啊

 

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 1e5+10, M = 1e5, mod = 1e9, inf = 1e9+9;
typedef long long ll;

int n,q,a[N],pos[N],c[N];
struct cooltree{
    struct node {int l,r,v;}tr[N*20];
    int sz,root[N];
    void init() {
        sz = 0, root[0] = 0;
    }
    void update(int &k,int l,int r,int x) {
        tr[++sz] = tr[k], k = sz;
        ++tr[k].v;
        if(l==r) return ;
        int mid = (l+r)>>1;
        if(x <= mid) update(tr[k].l,l,mid,x);
        else update(tr[k].r,mid+1,r,x);
    }
    int ask(int x,int y,int k) {
        int l = 1, r = n;
        x = root[x-1], y = root[y];
        while(l!=r) {
            int mid = (l+r)>>1, now = tr[tr[y].l].v - tr[tr[x].l].v;
            if(k <= now) x = tr[x].l,y = tr[y].l, r = mid;
            else x =tr[x].r , y = tr[y].r, l = mid + 1, k-=now;
        }
        return a[l];
    }
}T;
int main() {
    T.init();
    scanf("%d%d",&n,&q);
    for(int i=1;i<=n;i++) scanf("%d",&a[i]), c[i] = a[i];
    sort(a+1,a+n+1);
    int cnt = unique(a+1,a+n+1) - a - 1;
    //cout<<cnt<<endl;
    for(int i=1;i<=n;i++) pos[i] = lower_bound(a+1,a+cnt+1,c[i]) - a;
    for(int i=1;i<=n;i++) T.update(T.root[i] = T.root[i-1],1,n,pos[i]);
    for(int i=1;i<=q;i++) {
            int x,y,z;
        scanf("%d%d%d",&x,&y,&z);
        printf("%d
",T.ask(x,y,z));
    }
    return 0;
}