Sure, here is a Python solution for the problem:

```python
def sum_of_absolute_differences(nums):
n = len(nums)
result = [0] * n
total_sum = sum(nums)
prefix_sum = 0

for i in range(n):
result[i] = (i * nums[i] - prefix_sum) + (total_sum - prefix_sum - (n - i) * nums[i])
prefix_sum += nums[i]

return result
```

Here is a step-by-step explanation of the solution:

1. Initialize the length of the array `n` and the result array `result` with the same length as `nums`, filled with zeros.

2. Calculate the total sum of the array `nums`.

3. Initialize a variable `prefix_sum` to keep track of the sum of the elements before the current index.

4. Iterate over the array `nums`. For each index `i`, calculate the sum of absolute differences between `nums[i]` and all the other elements in the array. This is done by subtracting the prefix sum from `i * nums[i]` (which gives the sum of absolute differences for all elements before `i`) and adding the sum of absolute differences for all elements after `i`, which is calculated as `total_sum - prefix_sum - (n - i) * nums[i]`.

5. Add `nums[i]` to the prefix sum.

6. Return the result array.

Question

Sure, here is a Python solution for the problem:

```python
def sum_of_absolute_differences(nums):
    n = len(nums)
    result = [0] * n
    total_sum = sum(nums)
    prefix_sum = 0

for i in range(n):
        result[i] = (i * nums[i] - prefix_sum) + (total_sum - prefix_sum - (n - i) * nums[i])
        prefix_sum += nums[i]

return result
```

Here is a step-by-step explanation of the solution:

1. Initialize the length of the array `n` and the result array `result` with the same length as `nums`, filled with zeros.

2. Calculate the total sum of the array `nums`.

3. Initialize a variable `prefix_sum` to keep track of the sum of the elements before the current index.

4. Iterate over the array `nums`. For each index `i`, calculate the sum of absolute differences between `nums[i]` and all the other elements in the array. This is done by subtracting the prefix sum from `i * nums[i]` (which gives the sum of absolute differences for all elements before `i`) and adding the sum of absolute differences for all elements after `i`, which is calculated as `total_sum - prefix_sum - (n - i) * nums[i]`.

5. Add `nums[i]` to the prefix sum.

6. Return the result array.

Knowee AI · Accepted Answer