Leetcode 2121: Intervals Between Identical Elements

In this problem, we should return an array which, for each index, contains the sum of intervals for this index, for the indices that contain the same value as arr[i]. This is the problem statement:

You are given a 0-indexed array of n integers arr.
The interval between two elements in arr is defined as the absolute difference between their indices. More formally, the interval between arr[i] and arr[j] is |i - j|.
Return an array intervals of length n where intervals[i] is the sum of intervals between arr[i] and each element in arr with the same value as arr[i].
Note: |x| is the absolute value of x.

We are given a couple of examples to make sure we understood the problem and for testing:

Examples

Solution design

Since we are working with indices with the same value in the array, it is actually more practical to reverse the array to a Map, that maps value to the set of indices with this value.

For example, in the first example, we would obtain the following map:

1 -> [0,4] 
2 -> [1,3]
3 -> [2,5,6]

In addition, I would like the sets in the map to be ordered, for instance [2,5,6]. The reason for that will appear later.