1685-sum-of-absolute-differences-in-a-sorted-array.rb

# frozen_string_literal: true

# 1685. Sum of Absolute Differences in a Sorted Array
# Medium
# https://leetcode.com/problems/sum-of-absolute-differences-in-a-sorted-array

=begin
You are given an integer array nums sorted in non-decreasing order.
Build and return an integer array result with the same length as nums such that result[i] is equal to the summation of absolute differences between nums[i] and all the other elements in the array.
In other words, result[i] is equal to sum(|nums[i]-nums[j]|) where 0 <= j < nums.length and j != i (0-indexed).

Example 1:
Input: nums = [2,3,5]
Output: [4,3,5]
Explanation: Assuming the arrays are 0-indexed, then
result[0] = |2-2| + |2-3| + |2-5| = 0 + 1 + 3 = 4,
result[1] = |3-2| + |3-3| + |3-5| = 1 + 0 + 2 = 3,
result[2] = |5-2| + |5-3| + |5-5| = 3 + 2 + 0 = 5.

Example 2:
Input: nums = [1,4,6,8,10]
Output: [24,15,13,15,21]

Constraints:
2 <= nums.length <= 105
1 <= nums[i] <= nums[i + 1] <= 104
=end

# @param {Integer[]} nums
# @return {Integer[]}
def get_sum_absolute_differences(nums)
  n = nums.size
  sum = nums.sum
  prev = nums[0]
  total = sum - prev * n
  result = [total]

  1.upto(n - 1) do |i|
    num = nums[i]
    total += (2 * i - n) * (num - prev)
    result << total
    prev = num
  end

  result
end

# **************** #
#       TEST       #
# **************** #

require "test/unit"
class Test_get_sum_absolute_differences < Test::Unit::TestCase
  def test_
    assert_equal [4, 3, 5], get_sum_absolute_differences([2, 3, 5])
    assert_equal [24, 15, 13, 15, 21], get_sum_absolute_differences([1, 4, 6, 8, 10])
  end
end