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

Solution

算是企图入门主席树,学习博客戳这

Code

//=============================================================
// File Name: poj-2104.cpp
// Author: Wycer
// Created Time: 2018-05-07 17:33
//=============================================================
#include <cstdio>
#include <algorithm>
const int N = 1e5 + 10;
using namespace std;
int read()
{
    int x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || '9' < ch)
    {
        if (ch == '-')
            f = -1;
        ch = getchar();
    }
    while ('0' <= ch && ch <= '9')
    {
        x = x * 10 + ch - 48;
        ch = getchar();
    }
    return x * f;
}
int n, m, a[N], tag[N], back[N], root[N];
void readin()
{
    n = read();
    m = read();
    for (int i = 1; i <= n; ++i)
    {
        a[i] = read();
        tag[i] = i;
        back[i] = a[i];
    }
}

struct node
{
    int l, r, cnt;
    node()
    {
        l = r = cnt = 0;
    }
} tr[20 * N];
int cnt = 0;
void insert(int &k, int l, int r, int x)
{
    tr[++cnt] = tr[k];
    k = cnt;
    ++tr[k].cnt;
    if (l == r)
        return;
    int mid = (l + r) >> 1;
    if (x <= mid)
        insert(tr[k].l, l, mid, x);
    else
        insert(tr[k].r, mid + 1, r, x);
}
int query(int x, int y, int l, int r, int k)
{
    if (l == r)
        return l;
    int tmp = tr[tr[y].l].cnt - tr[tr[x].l].cnt;
    int mid = (l + r) >> 1;
    if (k <= tmp)
        return query(tr[x].l, tr[y].l, l, mid, k);
    else
        return query(tr[x].r, tr[y].r, mid + 1, r, k - tmp);
}
bool cmp(int x, int y)
{
    return a[x] < a[y];
}
int r[N];
void solve()
{
    sort(tag + 1, tag + n + 1, cmp);
    for (int i = 1; i <= n; ++i)
        r[tag[i]] = i;
    for (int i = 1; i <= n; ++i)
    {
        root[i] = root[i - 1];
        insert(root[i], 1, n, r[i]);
    }

    int x, y, k;
    while (m--)
    {
        x = read();
        y = read();
        k = read();
        printf("%d\n", a[tag[query(root[x - 1], root[y], 1, n, k)]]);
    }
}

int main()
{
    readin();
    solve();
    return 0;
}