<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. There exists an array <code>arr</code> of length <code>nums.length</code>, where <code>arr[i]</code> is the sum of <code>|i - j|</code> over all <code>j</code> such that <code>nums[j] == nums[i]</code> and <code>j != i</code>. If there is no such <code>j</code>, set <code>arr[i]</code> to be <code>0</code>.</p>

<p>Return <em>the array </em><code>arr</code><em>.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,3,1,1,2]
<strong>Output:</strong> [5,0,3,4,0]
<strong>Explanation:</strong> 
When i = 0, nums[0] == nums[2] and nums[0] == nums[3]. Therefore, arr[0] = |0 - 2| + |0 - 3| = 5. 
When i = 1, arr[1] = 0 because there is no other index with value 3.
When i = 2, nums[2] == nums[0] and nums[2] == nums[3]. Therefore, arr[2] = |2 - 0| + |2 - 3| = 3. 
When i = 3, nums[3] == nums[0] and nums[3] == nums[2]. Therefore, arr[3] = |3 - 0| + |3 - 2| = 4. 
When i = 4, arr[4] = 0 because there is no other index with value 2. 

</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [0,5,3]
<strong>Output:</strong> [0,0,0]
<strong>Explanation:</strong> Since each element in nums is distinct, arr[i] = 0 for all i.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
</ul>

<p>&nbsp;</p>
<p><strong>Note:</strong> This question is the same as <a href="https://leetcode.com/problems/intervals-between-identical-elements/description/" target="_blank"> 2121: Intervals Between Identical Elements.</a></p>

from collections import defaultdict

class Solution:
    def distance(self, nums: List[int]) -> List[int]:
        # Step 1: Group indices by their values
        value_to_indices = defaultdict(list)
        for i, num in enumerate(nums):
            value_to_indices[num].append(i)
        
        # Step 2: Calculate the sum of absolute differences for each index
        result = [0] * len(nums)
        for indices in value_to_indices.values():
            prefix_sum = [0] * (len(indices) + 1)
            suffix_sum = [0] * (len(indices) + 1)
            
            # Calculate prefix sums
            for j in range(len(indices)):
                prefix_sum[j + 1] = prefix_sum[j] + indices[j]
            
            # Calculate suffix sums
            for j in range(len(indices) - 1, -1, -1):
                suffix_sum[j] = suffix_sum[j + 1] + indices[j]
            
            # Calculate the sum of absolute differences for each index
            for j, index in enumerate(indices):
                result[index] = (indices[j] * (j + 1) - prefix_sum[j + 1]) + (suffix_sum[j] - indices[j] * (len(indices) - j))
        
        return result

# Example usage:
solution = Solution()
nums = [1, 3, 1, 1, 2]
print(solution.distance(nums))  # Output: [5, 0, 3, 4, 0]

nums = [0, 5, 3]
print(solution.distance(nums))  # Output: [0, 0, 0]
50406