public class Solution
extends Object
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:**
* 1 <= nums.length <= 105
* 0 <= nums[i] <= 105