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 <= 1051 <= nums[i] <= nums[i + 1] <= 104
Solution
Python3
class Solution:
def getSumAbsoluteDifferences(self, nums: List[int]) -> List[int]:
N = len(nums)
total = sum(nums)
prefix = 0
res = []
for i, x in enumerate(nums):
total -= x
leftCount = i if i > 0 else 0
rightCount = N - i - 1 if i != N - 1 else 0
left = x * leftCount - prefix
right = total - x * rightCount
res.append(left + right)
prefix += x
return res