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 n elements is the sum of the n elements divided (integer division) by n. The average of 0 elements is considered to be 0.
Input Format:
First Parameter: integer N
, length of the array nums.
Second parameter: an integer array nums
.
Output Format:
Return the number.
Example 1:
Input:
6
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:
1
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
- Time complexity: O(n)
- Space complexity: O(n)