1685. Sum of Absolute Differences in a Sorted Array - Explanation

class Solution:
    def getSumAbsoluteDifferences(self, nums: List[int]) -> List[int]:
        res = []

        for i in nums:
            sum = 0
            for j in nums:
                sum += abs(i - j)
            res.append(sum)

        return res

class Solution:
    def getSumAbsoluteDifferences(self, nums: List[int]) -> List[int]:
        n = len(nums)
        prefix_sum = [0] * n
        suffix_sum = [0] * n
        res = [0] * n

        prefix_sum[0] = nums[0]
        for i in range(1, n):
            prefix_sum[i] = prefix_sum[i - 1] + nums[i]

        suffix_sum[n - 1] = nums[n - 1]
        for i in range(n - 2, -1, -1):
            suffix_sum[i] = suffix_sum[i + 1] + nums[i]

        for i in range(n):
            left_sum = (i * nums[i]) - (prefix_sum[i - 1] if i > 0 else 0)
            right_sum = (suffix_sum[i + 1] if i < n - 1 else 0) - ((n - i - 1) * nums[i])
            res[i] = left_sum + right_sum

        return res

class Solution:
    def getSumAbsoluteDifferences(self, nums: List[int]) -> List[int]:
        n = len(nums)
        res = [0] * n

        res[n - 1] = nums[n - 1]
        for i in range(n - 2, -1, -1):
            res[i] = res[i + 1] + nums[i]

        prefix_sum = 0
        for i in range(n):
            left_sum = (i * nums[i]) - prefix_sum
            right_sum = (res[i + 1] if i < n - 1 else 0) - ((n - i - 1) * nums[i])
            res[i] = left_sum + right_sum
            prefix_sum += nums[i]

        return res

class Solution:
    def getSumAbsoluteDifferences(self, nums: List[int]) -> List[int]:
        n = len(nums)
        res = [0] * n

        total_sum = sum(nums)
        prefix_sum = 0

        for i, num in enumerate(nums):
            total_sum -= nums[i]
            left_sum = i * nums[i] - prefix_sum
            right_sum = total_sum - (n - i - 1) * nums[i]
            res[i] = left_sum + right_sum
            prefix_sum += nums[i]

        return res