2256 - Minimum Average Difference.

Medium

You are given a 0-indexed integer array nums of length n.

The average difference of the index i is the absolute difference between the average of the first i + 1 elements of nums and the average of the last n - i - 1 elements. Both averages should be rounded down to the nearest integer.

Return the index with the minimum average difference. If there are multiple such indices, return the smallest one.

Note:

• The absolute difference of two numbers is the absolute value of their difference.

• The average of n elements is the sum of the n elements divided ( integer division ) by n.

• The average of 0 elements is considered to be 0.

Example 1:

Input: nums = 2,5,3,9,5,3

Output: 3

Explanation:

• The average difference of index 0 is: |2 / 1 - (5 + 3 + 9 + 5 + 3) / 5| = |2 / 1 - 25 / 5| = |2 - 5| = 3.

• The average difference of index 1 is: |(2 + 5) / 2 - (3 + 9 + 5 + 3) / 4| = |7 / 2 - 20 / 4| = |3 - 5| = 2.

• The average difference of index 2 is: |(2 + 5 + 3) / 3 - (9 + 5 + 3) / 3| = |10 / 3 - 17 / 3| = |3 - 5| = 2.

• The average difference of index 3 is: |(2 + 5 + 3 + 9) / 4 - (5 + 3) / 2| = |19 / 4 - 8 / 2| = |4 - 4| = 0.

• The average difference of index 4 is: |(2 + 5 + 3 + 9 + 5) / 5 - 3 / 1| = |24 / 5 - 3 / 1| = |4 - 3| = 1.

• The average difference of index 5 is: |(2 + 5 + 3 + 9 + 5 + 3) / 6 - 0| = |27 / 6 - 0| = |4 - 0| = 4.

The average difference of index 3 is the minimum average difference so return 3.

Example 2:

Input: nums = 0

Output: 0

Explanation:

The only index is 0 so return 0.

The average difference of index 0 is: |0 / 1 - 0| = |0 - 0| = 0.

Constraints:

• <code>1 <= nums.length <= 10⁵</code>

• <code>0 <= numsi<= 10⁵</code>