Intervals Between Identical Elements
<p>You are given a <strong>0-indexed</strong> array of <code>n</code> integers <code>arr</code>.</p>

<p>The <strong>interval</strong> between two elements in <code>arr</code> is defined as the <strong>absolute difference</strong> between their indices. More formally, the <strong>interval</strong> between <code>arr[i]</code> and <code>arr[j]</code> is <code>|i - j|</code>.</p>

<p>Return <em>an array</em> <code>intervals</code> <em>of length</em> <code>n</code> <em>where</em> <code>intervals[i]</code> <em>is <strong>the sum of intervals</strong> between </em><code>arr[i]</code><em> and each element in </em><code>arr</code><em> with the same value as </em><code>arr[i]</code><em>.</em></p>

<p><strong>Note:</strong> <code>|x|</code> is the absolute value of <code>x</code>.</p>

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

<pre>
<strong>Input:</strong> arr = [2,1,3,1,2,3,3]
<strong>Output:</strong> [4,2,7,2,4,4,5]
<strong>Explanation:</strong>
- Index 0: Another 2 is found at index 4. |0 - 4| = 4
- Index 1: Another 1 is found at index 3. |1 - 3| = 2
- Index 2: Two more 3s are found at indices 5 and 6. |2 - 5| + |2 - 6| = 7
- Index 3: Another 1 is found at index 1. |3 - 1| = 2
- Index 4: Another 2 is found at index 0. |4 - 0| = 4
- Index 5: Two more 3s are found at indices 2 and 6. |5 - 2| + |5 - 6| = 4
- Index 6: Two more 3s are found at indices 2 and 5. |6 - 2| + |6 - 5| = 5
</pre>

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

<pre>
<strong>Input:</strong> arr = [10,5,10,10]
<strong>Output:</strong> [5,0,3,4]
<strong>Explanation:</strong>
- Index 0: Two more 10s are found at indices 2 and 3. |0 - 2| + |0 - 3| = 5
- Index 1: There is only one 5 in the array, so its sum of intervals to identical elements is 0.
- Index 2: Two more 10s are found at indices 0 and 3. |2 - 0| + |2 - 3| = 3
- Index 3: Two more 10s are found at indices 0 and 2. |3 - 0| + |3 - 2| = 4
</pre>

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

<ul>
	<li><code>n == arr.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= arr[i] &lt;= 10<sup>5</sup></code></li>
</ul>

<p>&nbsp;</p>
<p><strong>Note:</strong> This question is the same as <a href="https://leetcode.com/problems/sum-of-distances/description/" target="_blank"> 2615: Sum of Distances.</a></p>
Array; Hash Table; Prefix Sum
class Solution:
    def getDistances(self, arr: List[int]) -> List[int]:
        d = defaultdict(list)
        n = len(arr)
        for i, v in enumerate(arr):
            d[v].append(i)
        ans = [0] * n
        for v in d.values():
            m = len(v)
            val = sum(v) - v[0] * m
            for i, p in enumerate(v):
                delta = v[i] - v[i - 1] if i >= 1 else 0
                val += i * delta - (m - i) * delta
                ans[p] = val
        return ans
