1685. Sum of Absolute Differences in a Sorted Array

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

Rust Solution

struct Solution;

impl Solution {
    fn get_sum_absolute_differences(nums: Vec<i32>) -> Vec<i32> {
        let n = nums.len();
        let mut prev = nums[0];
        let mut prev_sum = 0;
        let mut res = vec![0; n];
        for i in 0..n {
            let diff = nums[i] - prev;
            prev_sum += diff * i as i32;
            res[i] += prev_sum;
            prev = nums[i];
        }
        prev = nums[n - 1];
        prev_sum = 0;
        for i in (0..n).rev() {
            let diff = (nums[i] - prev).abs();
            prev_sum += diff * (n - 1 - i) as i32;
            res[i] += prev_sum;
            prev = nums[i];
        }
        res
    }
}

#[test]
fn test() {
    let nums = vec![2, 3, 5];
    let res = vec![4, 3, 5];
    assert_eq!(Solution::get_sum_absolute_differences(nums), res);
    let nums = vec![1, 4, 6, 8, 10];
    let res = vec![24, 15, 13, 15, 21];
    assert_eq!(Solution::get_sum_absolute_differences(nums), res);
}

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