MKTHNUM - K-th Number
English | Vietnamese |
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 contains n — the size of the array, and m — the number of questions to answer (1 ≤ n ≤ 100000, 1 ≤ m ≤ 5000).
The second line contains n different integer numbers not exceeding 10^9 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.
Example
Input: 7 3 1 5 2 6 3 7 4 2 5 3 4 4 1 1 7 3 Output: 5 6 3
Note: a naive solution will not work!!!
hide comments
kesh4281:
2020-03-24 09:07:34
no.s can be -ve, beware
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zufius:
2020-02-01 15:09:50
this problem is easier than (& similar) problem COT (use persistent IT to solve) Last edit: 2020-02-01 15:10:14 |
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fardin_abir:
2019-12-20 09:28:54
solved it on O(log^3 * N).... nice problem... |
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piasroy071:
2019-10-21 20:11:07
Somehow my solution of merge sort tree with O(log^3 * N) got AC in 1.04s, although the time limit is 0.115s-0.667s. Can someone explain this?
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zhaopeng:
2019-05-20 12:25:28
Merge Seg + Binary Search + compress(TLE if without), AC.
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caro_linda2018:
2019-04-26 02:16:28
ACed it in one go :) Last edit: 2019-04-26 02:17:03 |
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golu20174024:
2019-03-21 03:47:47
use persistent segment tree and i-th order statistics
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ab_biswas09:
2019-03-16 20:11:15
Finally AC |
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kukreja_vlk:
2019-03-09 04:27:35
Any solutions in Java ? Getting TLE after some cases |
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gormint7777:
2019-03-05 19:21:50
weak test cases!!
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Added by: | psetter |
Date: | 2009-02-24 |
Time limit: | 1s |
Source limit: | 50000B |
Memory limit: | 1536MB |
Cluster: | Cube (Intel G860) |
Languages: | All except: ERL JS-RHINO |
Resource: | Northeastern Europe 2004 Northern Subregion |