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 = |2-2| + |2-3| + |2-5| = 0 + 1 + 3 = 4,
result = |3-2| + |3-3| + |3-5| = 1 + 0 + 2 = 3,
result = |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`

1685. Sum of Absolute Differences in a Sorted Array
``````struct Solution;

impl Solution {
fn get_sum_absolute_differences(nums: Vec<i32>) -> Vec<i32> {
let n = nums.len();
let mut prev = nums;
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);
}
``````