Minimum Operations To Make Median Of Array Equal To K · Interview Problem

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Leetcode

Medium

Arrays

Sorting

Greedy

Minimum Operations To Make Median Of Array Equal To K

Make the median of an array equal to a target value using the minimum number of unit increments or decrements.

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Problem Statement

Problem

You are given an integer array and a target value $k$ . In one operation, you may increase or decrease any element by 1.

Return the minimum number of operations needed so that the median of the array becomes exactly $k$ .

For an array of length $n$ , the median is the element at index $\lfloor n/2 \rfloor$ after the array is sorted in nondecreasing order.

Idea

Only the values around the median matter after sorting. Your goal is to adjust the middle element to $k$ and ensure the elements on the left do not exceed it while the elements on the right do not fall below it in a way that would change the median away from $k$ .

Input Format

The first line contains an integer $n$ .
The second line contains $n$ integers representing the array.
The third line contains an integer $k$ .

Output Format

Print one integer: the minimum number of operations required.

Constraints

$1 \le n \le 10^5$
Elements can be negative or positive integers
Each operation changes one element by exactly 1

Examples

Sample cases returned by the problem API.

Example 1

Input

n = 3
nums = [2, 5, 6]
k = 5

Output

Explanation

After sorting, the median is already 5, so no operations are needed.

Example 2

Input

n = 5
nums = [2, 4, 6, 8, 10]
k = 5

Output

Explanation

After sorting, the median is 6. Decrease it by 1 to make the median equal to 5.

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Example 3

Input

n = 5
nums = [1, 2, 3, 4, 5]
k = 3

Output

Explanation

The sorted median is already 3.

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