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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 index i in the array nums. If there is no such element, leftSum[i] = 0.
  • rightSum[i] is the sum of elements to the right of the index i in the array nums. 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.

  • class Solution {
    public int[] leftRigthDifference(int[] nums) {
        int left = 0, right = Arrays.stream(nums).sum();
        int n = nums.length;
        int[] ans = new int[n];
        for (int i = 0; i < n; ++i) {
            right -= nums[i];
            ans[i] = Math.abs(left - right);
            left += nums[i];
        }
        return ans;
    }
}

  • class Solution {
public:
    vector<int> leftRigthDifference(vector<int>& nums) {
        int left = 0, right = accumulate(nums.begin(), nums.end(), 0);
        vector<int> ans;
        for (int& x : nums) {
            right -= x;
            ans.push_back(abs(left - right));
            left += x;
        }
        return ans;
    }
};

  • class Solution:
    def leftRigthDifference(self, nums: List[int]) -> List[int]:
        left, right = 0, sum(nums)
        ans = []
        for x in nums:
            right -= x
            ans.append(abs(left - right))
            left += x
        return ans


  • func leftRigthDifference(nums []int) (ans []int) {
	var left, right int
	for _, x := range nums {
		right += x
	}
	for _, x := range nums {
		right -= x
		ans = append(ans, abs(left-right))
		left += x
	}
	return
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

  • function leftRigthDifference(nums: number[]): number[] {
    let left = 0,
        right = nums.reduce((a, b) => a + b);
    const ans: number[] = [];
    for (const x of nums) {
        right -= x;
        ans.push(Math.abs(left - right));
        left += x;
    }
    return ans;
}


  • impl Solution {
    pub fn left_rigth_difference(nums: Vec<i32>) -> Vec<i32> {
        let mut left = 0;
        let mut right = nums.iter().sum::<i32>();
        nums.iter()
            .map(|v| {
                right -= v;
                let res = (left - right).abs();
                left += v;
                res
            })
            .collect()
    }
}

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