absolute_values_sum_minimization.md

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Array Replace

https://app.codesignal.com/arcade/intro/level-7/ZFnQkq9RmMiyE6qtq

Challenge description

Given a sorted array of integers a, your task is to determine which element of a is closest to all other values of a. In other words, find the element x in a, which minimizes the following sum:

abs(a[0] - x) + abs(a[1] - x) + ... + abs(a[a.length - 1] - x)

(where abs denotes the absolute value)

If there are several possible answers, output the smallest one.

Example

• For a = [2, 4, 7], the output should be solution(a) = 4.
  • for x = 2, the value will be abs(2 - 2) + abs(4 - 2) + abs(7 - 2) = 7.
  • for x = 4, the value will be abs(2 - 4) + abs(4 - 4) + abs(7 - 4) = 5.
  • for x = 7, the value will be abs(2 - 7) + abs(4 - 7) + abs(7 - 7) = 8.

The lowest possible value is when x = 4, so the answer is 4.

• For a = [2, 3], the output should be solution(a) = 2.
  • for x = 2, the value will be abs(2 - 2) + abs(3 - 2) = 1.
  • for x = 3, the value will be abs(2 - 3) + abs(3 - 3) = 1.

Because there is a tie, the smallest x between x = 2 and x = 3 is the answer.

Solution

Solved with Rust