1685. Sum of Absolute Differences in a Sorted Array

Description

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

Solution

sum-of-absolute-differences-in-a-sorted-array.py

class Solution:
    def getSumAbsoluteDifferences(self, nums: List[int]) -> List[int]:
        res = []
        n = len(nums)
        prefix = [0]
        for num in nums:
            prefix.append(prefix[-1] + num)

        for i,x in enumerate(nums):
            left = prefix[i]
            right = prefix[-1] - prefix[i+1]

            ans = (x*i - left) + (-x*(n-i-1) + right)
            res.append(ans)

        return res