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You are given a sequence of integers A1, A2,..., AN. You should process Q queries. In each query: • You are given two integer parameters id and v. • Change the value of Aid to v. Then, consider all ways to partition the sequence A1, A2, ..., AN into multisets M1, M2,..., MK (for an arbitrary K > 1) such that: o Each element of A is assigned to exactly one multiset. o The medians of all multisets are the same. • Find the maximum possible value of K, i.e. the maximum number of multisets in such a partition. The median of a multiset is defined as follows: Consider the multiset as a sequence sorted in non-decreasing order. If its size is odd, the median is the middle element. If it is even, there are two integers in the middle and the median is the smaller one (either one if they are equal). Note that a multiset may contain duplicate elements, so if x elements of A with identical values are assigned to the same multiset, that multiset will contain the same integer æ times.

You are given a sequence of integers A1, A2,..., AN. You should process Q queries. In each query: • You are given two integer parameters id and v. • Change the value of Aid to v. Then, consider all ways to partition the sequence A1, A2, ..., AN into multisets M1, M2,..., MK (for an arbitrary K > 1) such that: o Each element of A is assigned to exactly one multiset. o The medians of all multisets are the same. • Find the maximum possible value of K, i.e. the maximum number of multisets in such a partition. The median of a multiset is defined as follows: Consider the multiset as a sequence sorted in non-decreasing order. If its size is odd, the median is the middle element. If it is even, there are two integers in the middle and the median is the smaller one (either one if they are equal). Note that a multiset may contain duplicate elements, so if x elements of A with identical values are assigned to the same multiset, that multiset will contain the same integer æ times.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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C++ only

Example Input
1
4 3
1 1 1 2
4 1
4 2
3 2
Example Output
4
3
2

You are given a sequence of integers A1, A2,..., AN. You should process Q queries. In each query: • You are given two integer parameters id and v. Change the value of Aid to v. Then, consider all ways to partition the sequence A1, A2,..., AN into multisets M1, M2,..., MK (for an arbitrary K > 1) such that: o Each element of A is assigned to exactly one multiset. o The medians of all multisets are the same. • Find the maximum possible value of K, i.e. the maximum number of multisets in such a partition. The median of a multiset is defined as follows: Consider the multiset as a sequence sorted in non-decreasing order. If its size is odd, the median is the middle element. If it is even, there are two integers in the middle and the median is the smaller one (either one if they are equal). Note that a multiset may contain duplicate elements, so if x elements of A with identical values are assigned to the same multiset, that multiset will contain the same integer a times.
Transcribed Image Text:You are given a sequence of integers A1, A2,..., AN. You should process Q queries. In each query: • You are given two integer parameters id and v. Change the value of Aid to v. Then, consider all ways to partition the sequence A1, A2,..., AN into multisets M1, M2,..., MK (for an arbitrary K > 1) such that: o Each element of A is assigned to exactly one multiset. o The medians of all multisets are the same. • Find the maximum possible value of K, i.e. the maximum number of multisets in such a partition. The median of a multiset is defined as follows: Consider the multiset as a sequence sorted in non-decreasing order. If its size is odd, the median is the middle element. If it is even, there are two integers in the middle and the median is the smaller one (either one if they are equal). Note that a multiset may contain duplicate elements, so if x elements of A with identical values are assigned to the same multiset, that multiset will contain the same integer a times.
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