# 2256. Minimum Average Difference

T: O(n)

S: O(1)

````java
```java
class Solution {
    public int minimumAverageDifference(int[] nums) {
        long total = 0;
        for (int num : nums) {
            total += num;
        }
        
        int n = nums.length;
        long result = Integer.MAX_VALUE;
        int resultIdx = -1;
        
        long prefixSum = 0;
        long preCount = 0;
        for (int i = 0 ; i < n; i++) {
            prefixSum += nums[i];
            preCount++;
        
            long preAvg = (prefixSum/preCount);
            long postAvg = n - preCount == 0 ? 0 : (total - prefixSum)/(n - preCount);
            long avgDiff = Math.abs(preAvg - postAvg);
            if (result > avgDiff) {
                result = avgDiff;
                resultIdx = i;
            }
        }
        return resultIdx;
    }
}

/**

i
  i+1    n-i-1

abs(diff)

avg(first i+1 elements)
avg(last n - i - 1)

i = 1
0 1 2

first i+1 ->  first 2
  0 1 2
  [ ]

last (3 - 1 - 1 = 1) -> last 1
 0 1 2
     []

rounded down means 
2.9 -> 2
2.4 -> 2
2.5 -> 2

find the index for min avg diff 

ps = prefix sum of i
last_ps = sum - ps

ps / (0 to i) = ps / i+1

last_ps / n - i - 1

Min(Math.abs(ps - last_ps))
 */
```
````
