1685.getSumAbsolutteDifferences.py

"""
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

"""

from typing import List


class Solution:
    def getSumAbsoluteDifferences(self, nums: List[int]) -> List[int]:
        # get total sum, for later subtraction
        total_sum = sum(nums)
        # left sum start at index 0 so sum of 0
        left_sum = 0
        res = []

        # loop array, get the right rum
        for i, n in enumerate(nums):
            right_sum = total_sum - n - left_sum

            left_size, right_size = i, len(nums) - i - 1

            # NOTE: calculate the absolute differences
            res.append(
                # taking the left subarray, subtract left sum
                (left_size * n - left_sum)
                +
                # right_sum
                (right_sum - right_size * n)
            )

            # update left sum
            left_sum += n

        return res