Package g2201_2300.s2256_minimum_average_difference

Class Solution

  • 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

    • Constructor Detail

      • Solution

        public Solution()

    • Method Detail

      • minimumAverageDifference

        public int minimumAverageDifference​(int[] nums)