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
sfialok98:
2017-06-06 21:16:24
Finally Accepted,Learned Persistent Segment Trees....!!!!
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joseluisacv2:
2017-06-06 03:01:15
The number of queries is wrong. It is M<= 1e5
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leafbebop:
2017-05-31 05:16:35
Note: sometimes it is not the algorithms blocks you from AC, but the I/O speed.
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mddaud001:
2017-05-20 21:26:13
Trying to solve from last week
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rihaz_zahir:
2017-02-15 20:12:33
why array compression with sqrt decomposition + segment tree is giving tle?
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crazymax:
2016-10-31 15:01:26
Mo+ordered_set_tree (complexity with - Q*sqrt(N)*log(N)+N*sqrt(N)) solution gives TLE. :( |
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Ravi kumar:
2016-10-25 15:57:06
Increase time limit for java. there is not even a single accepted solution.
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i_m_a_coder:
2016-09-07 22:35:48
i did it using vectors and iterators bt getting wrong answer!!!
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tamionv:
2016-08-27 03:56:22
I think I'm the first one to solve it in O((N+Q) * sqrt(N)) :)
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kiwi1995:
2016-07-21 08:08:37
learnt a lot from this problem...:D |
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 |