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package g2201_2300.s2256_minimum_average_difference;

// #Medium #Array #Prefix_Sum #2022_06_12_Time_15_ms_(97.85%)_Space_71.2_MB_(84.53%)

/**
 * 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
**/
public class Solution {
    public int minimumAverageDifference(int[] nums) {
        long numsSum = 0;
        for (int num : nums) {
            numsSum += num;
        }
        long minAverageDiff = Long.MAX_VALUE;
        long sumFromFront = 0;
        int index = 0;
        for (int i = 0; i < nums.length; i++) {
            sumFromFront += nums[i];
            int numbersRight = i == nums.length - 1 ? 1 : nums.length - i - 1;
            long averageDiff =
                    Math.abs(sumFromFront / (i + 1) - (numsSum - sumFromFront) / numbersRight);
            if (minAverageDiff > averageDiff) {
                minAverageDiff = averageDiff;
                index = i;
            }
            if (averageDiff == 0) {
                break;
            }
        }
        return index;
    }
}