README_EN.md

1685. Sum of Absolute Differences in a Sorted Array

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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 <= 105
• 1 <= nums[i] <= nums[i + 1] <= 104

Solutions

Python3

class Solution:
    def getSumAbsoluteDifferences(self, nums: List[int]) -> List[int]:
        n = len(nums)
        presum = [0] * (n + 1)
        for i in range(n):
            presum[i + 1] = presum[i] + nums[i]
        res = []
        for i, num in enumerate(nums):
            t = num * i - presum[i] + presum[n] - presum[i + 1] - num * (n - i - 1)
            res.append(t)
        return res

Java

class Solution {
    public int[] getSumAbsoluteDifferences(int[] nums) {
        int n = nums.length;
        int[] presum = new int[n + 1];
        for (int i = 0; i < n; ++i) {
            presum[i + 1] = presum[i] + nums[i];
        }
        int[] res = new int[n];
        for (int i = 0; i < n; ++i) {
            res[i] = nums[i] * i - presum[i] + presum[n] - presum[i + 1] - nums[i] * (n - i - 1);
        }
        return res;
    }
}

C++

class Solution {
public:
    vector<int> getSumAbsoluteDifferences(vector<int>& nums) {
        int n = nums.size();
        vector<int> presum(n + 1);
        for (int i = 0; i < n; ++i) {
            presum[i + 1] = presum[i] + nums[i];
        }
        vector<int> res;
        for (int i = 0; i < n; ++i) {
            int t = nums[i] * i - presum[i] + presum[n] - presum[i + 1] - nums[i] * (n - i - 1);
            res.push_back(t);
        }
        return res;
    }
};

Go

func getSumAbsoluteDifferences(nums []int) []int {
	n := len(nums)
	presum := make([]int, n+1)
	for i := 0; i < n; i++ {
		presum[i+1] = presum[i] + nums[i]
	}
	var res []int
	for i := 0; i < n; i++ {
		t := nums[i]*i - presum[i] + presum[n] - presum[i+1] - nums[i]*(n-i-1)
		res = append(res, t)
	}
	return res
}

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