1685. Sum of Absolute Differences in a Sorted Array

Medium

30 Points

Array

Math

Prefix Sum

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).

Examples

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