README.md

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

Solutions (Ruby)

1. Solution

# @param {Integer[]} nums
# @return {Integer[]}
def get_sum_absolute_differences(nums)
  total_sum = nums.sum
  left_sum = 0
  result = [0] * nums.size

  (0...nums.size).each do |i|
    result[i] = (2 * i - nums.size) * nums[i] + total_sum - 2 * left_sum
    left_sum += nums[i]
  end

  result
end

Solutions (Rust)

1. Solution

impl Solution {
    pub fn get_sum_absolute_differences(nums: Vec<i32>) -> Vec<i32> {
        let len = nums.len() as i32;
        let total_sum = nums.iter().sum::<i32>();
        let mut left_sum = 0;
        let mut result = vec![0; nums.len()];

        for i in 0..nums.len() {
            result[i] = (2 * i as i32 - len) * nums[i] + total_sum - 2 * left_sum;
            left_sum += nums[i];
        }

        result
    }
}