Minimum Average Difference
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
nelements is the sum of thenelements divided (integer division) byn. - The average of
0elements is considered to be0.
Example 1
Input
nums = [2,5,3,9,5,3]Output
3The average difference is minimized at index 3, where both rounded averages are 4 and the difference is 0.
Example 2
Input
nums = [0]Output
0The only index is 0, and its average difference is 0.
Constraints
- 1 <= nums.length <= 10^5
- 0 <= nums[i] <= 10^5