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Tested Python solution for LeetCode 1685 with 18 pytest cases. Generate a practice environment with lcpy.
lcpy gen -n 1685 # by problem number
lcpy gen -s sum_of_absolute_differences_in_a_sorted_array # by problem name
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).
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.
Input: nums = [1,4,6,8,10]
Output: [24,15,13,15,21]
class Solution:
# Time: O(n)
# Space: O(n)
def get_sum_absolute_differences(self, nums: list[int]) -> list[int]:
n = len(nums)
prefix = [0] * (n + 1)
for i, value in enumerate(nums):
prefix[i + 1] = prefix[i] + value
total = prefix[n]
result = []
for i, value in enumerate(nums):
left_sum = i * value - prefix[i]
right_sum = (total - prefix[i + 1]) - (n - i - 1) * value
result.append(left_sum + right_sum)
return result
| Time | Space |
|---|---|
| O(n) | O(n) |