Problem URL: Sum of absolute differences in a sorted array

The absolute difference between two numbers a and b is:

• a - b: When a is greater than or equal to b.
• b - a: When a is less than or equal to b.

These cases overlap when a is equal to b, but in that case a - b and b - a are both equal to 0, so it's ok.

Fix some index 0 ≤ i < n. Since our array is non-decreasing, the sum of the absolute difference between nums[i] and the elements to its left will just be i times nums[i] minus the sum of the numbers to its left, and the sum of the absolute difference between nums[i] and the elements to its right will be the sum of the elements to its right minus the number of elements to its right (n - i - 1) times nums[i].

class Solution:
    def getSumAbsoluteDifferences(self, nums: List[int]) -> List[int]:
        n = len(nums)
        leftSum, rightSum = 0, sum(nums)
        res = []
        for i, num in enumerate(nums):
            res.append(rightSum-(n-i)*num+i*num-leftSum)
            rightSum -= num
            leftSum += num
        return res

Time complexity: O(n)
Space complexity: O(1)