2574. Left and Right Sum Differences
Description
Given a 0-indexed integer array nums
, find a 0-indexed integer array answer
where:
answer.length == nums.length
.answer[i] = |leftSum[i] - rightSum[i]|
.
Where:
leftSum[i]
is the sum of elements to the left of the indexi
in the arraynums
. If there is no such element,leftSum[i] = 0
.rightSum[i]
is the sum of elements to the right of the indexi
in the arraynums
. If there is no such element,rightSum[i] = 0
.
Return the array answer
.
Example 1:
Input: nums = [10,4,8,3] Output: [15,1,11,22] Explanation: The array leftSum is [0,10,14,22] and the array rightSum is [15,11,3,0]. The array answer is [|0 - 15|,|10 - 11|,|14 - 3|,|22 - 0|] = [15,1,11,22].
Example 2:
Input: nums = [1] Output: [0] Explanation: The array leftSum is [0] and the array rightSum is [0]. The array answer is [|0 - 0|] = [0].
Constraints:
1 <= nums.length <= 1000
1 <= nums[i] <= 105
Solutions
Solution 1: Prefix Sum
We define a variable $left$ to represent the sum of the elements to the left of index $i$ in the array nums
, and a variable $right$ to represent the sum of the elements to the right of index $i$ in the array nums
. Initially, $left = 0$, $right = \sum_{i = 0}^{n - 1} nums[i]$.
We iterate over the array nums
. For the current number $x$ we are iterating over, we update $right = right - x$. At this point, $left$ and $right$ represent the sum of the elements to the left and right of index $i$ in the array nums
, respectively. We add the absolute difference between $left$ and $right$ to the answer array ans
, and then update $left = left + x$.
After the iteration is complete, we return the answer array ans
.
The time complexity is $O(n)$, and the space complexity is $O(1)$. Where $n$ is the length of the array nums
.
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