# Count the number of sub-arrays such that the average of elements present in the sub-array is greater than that not present in the sub-array

Given an array of integers arr[], the task is to count the number of sub-arrays such that the average of elements present in the sub-array is greater than the average of elements that are not present in the sub-array.

Examples:

Input: arr[] = {6, 3, 5}
Output: 3
The sub-arrays are {6}, {5} and {6, 3, 5} because their averages
are greater than {3, 5}, {6, 3} and {} respectively.

Input: arr[] = {2, 1, 4, 1}
Output: 5

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The problem can be solved easily by calculating the prefix sum array of the given array. The ith element of the prefix sum array will contain sum of elements up to i. So, the sum of elements between any two indexes i and j can be found using the prefix sum array. Using a nested loop, find all the possible sub-arrays such that its average sum is greater than average of elements not present in the array.

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the count of sub-arrays ` `// such that the average of elements present ` `// in the sub-array is greater than the ` `// average of the elements not present ` `// in the sub-array ` `int` `countSubarrays(``int` `a[], ``int` `n) ` `{ ` `    ``// Initialize the count variable ` `    ``int` `count = 0; ` ` `  `    ``// Initialize prefix sum array ` `    ``int` `pre[n + 1] = { 0 }; ` ` `  `    ``// Preprocessing prefix sum ` `    ``for` `(``int` `i = 1; i < n + 1; i++) { ` `        ``pre[i] = pre[i - 1] + a[i - 1]; ` `    ``} ` ` `  `    ``for` `(``int` `i = 1; i < n + 1; i++) { ` `        ``for` `(``int` `j = i; j < n + 1; j++) { ` ` `  `            ``// Calculating sum and count ` `            ``// to calculate averages ` `            ``int` `sum1 = pre[j] - pre[i - 1], count1 = j - i + 1; ` `            ``int` `sum2 = pre[n] - sum1, count2 = ((n - count1) == 0) ? 1 : (n - count1); ` ` `  `            ``// Calculating averages ` `            ``int` `includ = sum1 / count1; ` `            ``int` `exclud = sum2 / count2; ` ` `  `            ``// Increment count if including avg ` `            ``// is greater than excluding avg ` `            ``if` `(includ > exclud) ` `                ``count++; ` `        ``} ` `    ``} ` ` `  `    ``return` `count; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 6, 3, 5 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` `    ``cout << countSubarrays(arr, n); ` ` `  `    ``return` `0; ` `} `

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to return the count of sub-arrays ` `// such that the average of elements present ` `// in the sub-array is greater than the ` `// average of the elements not present ` `// in the sub-array ` `static` `int` `countSubarrays(``int` `a[], ``int` `n) ` `{ ` `    ``// Initialize the count variable ` `    ``int` `count = ``0``; ` ` `  `    ``// Initialize prefix sum array ` `    ``int` `[]pre = ``new` `int``[n + ``1``]; ` `    ``Arrays.fill(pre, ``0``); ` ` `  `    ``// Preprocessing prefix sum ` `    ``for` `(``int` `i = ``1``; i < n + ``1``; i++) ` `    ``{ ` `        ``pre[i] = pre[i - ``1``] + a[i - ``1``]; ` `    ``} ` ` `  `    ``for` `(``int` `i = ``1``; i < n + ``1``; i++) ` `    ``{ ` `        ``for` `(``int` `j = i; j < n + ``1``; j++)  ` `        ``{ ` ` `  `            ``// Calculating sum and count ` `            ``// to calculate averages ` `            ``int` `sum1 = pre[j] - pre[i - ``1``], count1 = j - i + ``1``; ` `            ``int` `sum2 = pre[n] - sum1, count2 =  ` `                ``((n - count1) == ``0``) ? ``1` `: (n - count1); ` ` `  `            ``// Calculating averages ` `            ``int` `includ = sum1 / count1; ` `            ``int` `exclud = sum2 / count2; ` ` `  `            ``// Increment count if including avg ` `            ``// is greater than excluding avg ` `            ``if` `(includ > exclud) ` `                ``count++; ` `        ``} ` `    ``} ` `    ``return` `count; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``int` `arr[] = { ``6``, ``3``, ``5` `}; ` `    ``int` `n = arr.length; ` `    ``System.out.println(countSubarrays(arr, n)); ` `} ` `} ` ` `  `// This code is contributed by SURENDRA_GANGWAR `

 `# Python3 implementation of the approach ` ` `  `# Function to return the count of sub-arrays ` `# such that the average of elements present ` `# in the sub-array is greater than the ` `# average of the elements not present ` `# in the sub-array ` `def` `countSubarrays(a, n): ` `     `  `    ``# Initialize the count variable ` `    ``count ``=` `0` ` `  `    ``# Initialize prefix sum array ` `    ``pre ``=` `[``0` `for` `i ``in` `range``(n ``+` `1``)] ` ` `  `    ``# Preprocessing prefix sum ` `    ``for` `i ``in` `range``(``1``, n ``+` `1``): ` `        ``pre[i] ``=` `pre[i ``-` `1``] ``+` `a[i ``-` `1``] ` ` `  `    ``for` `i ``in` `range``(``1``, n ``+` `1``): ` `        ``for` `j ``in` `range``(i, n ``+` `1``): ` ` `  `            ``# Calculating sum and count ` `            ``# to calculate averages ` `            ``sum1 ``=` `pre[j] ``-` `pre[i ``-` `1``] ` `            ``count1 ``=` `j ``-` `i ``+` `1` `            ``sum2 ``=` `pre[n] ``-` `sum1 ` ` `  `            ``if` `n``-``count1 ``=``=` `0``: ` `                ``count2 ``=` `1` `            ``else``: ` `                ``count2 ``=` `n ``-` `count1 ` ` `  `            ``# Calculating averages ` `            ``includ ``=` `sum1 ``/``/` `count1 ` `            ``exclud ``=` `sum2 ``/``/` `count2 ` ` `  `            ``# Increment count if including avg ` `            ``# is greater than excluding avg ` `            ``if` `(includ > exclud): ` `                ``count ``+``=` `1` `         `  `    ``return` `count ` ` `  `# Driver code ` `arr ``=` `[``6``, ``3``, ``5` `] ` `n ``=` `len``(arr) ` `print``(countSubarrays(arr, n)) ` ` `  `# This code is contributed by mohit kumar `

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to return the count of sub-arrays ` `// such that the average of elements present ` `// in the sub-array is greater than the ` `// average of the elements not present ` `// in the sub-array ` `static` `int` `countSubarrays(``int` `[]a, ``int` `n) ` `{ ` `    ``// Initialize the count variable ` `    ``int` `count = 0; ` ` `  `    ``// Initialize prefix sum array ` `    ``int` `[]pre = ``new` `int``[n + 1]; ` `    ``Array.Fill(pre, 0); ` ` `  `    ``// Preprocessing prefix sum ` `    ``for` `(``int` `i = 1; i < n + 1; i++) ` `    ``{ ` `        ``pre[i] = pre[i - 1] + a[i - 1]; ` `    ``} ` ` `  `    ``for` `(``int` `i = 1; i < n + 1; i++) ` `    ``{ ` `        ``for` `(``int` `j = i; j < n + 1; j++)  ` `        ``{ ` ` `  `            ``// Calculating sum and count ` `            ``// to calculate averages ` `            ``int` `sum1 = pre[j] - pre[i - 1], count1 = j - i + 1; ` `            ``int` `sum2 = pre[n] - sum1, count2 =  ` `                ``((n - count1) == 0) ? 1 : (n - count1); ` ` `  `            ``// Calculating averages ` `            ``int` `includ = sum1 / count1; ` `            ``int` `exclud = sum2 / count2; ` ` `  `            ``// Increment count if including avg ` `            ``// is greater than excluding avg ` `            ``if` `(includ > exclud) ` `                ``count++; ` `        ``} ` `    ``} ` `    ``return` `count; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main() ` `{ ` `    ``int` `[]arr = { 6, 3, 5 }; ` `    ``int` `n = arr.Length; ` `    ``Console.WriteLine(countSubarrays(arr, n)); ` `} ` `} ` ` `  `// This code is contributed by Akanksha Rai `

 ` ``\$exclud``)  ` `                ``\$count``++;  ` `        ``}  ` `    ``}  ` ` `  `    ``return` `\$count``;  ` `}  ` ` `  `// Driver code  ` `\$arr` `= ``array``( 6, 3, 5 );  ` ` `  `\$n` `= ``count``(``\$arr``) ; ` ` `  `echo` `countSubarrays(``\$arr``, ``\$n``);  ` ` `  `// This code is contributed by Ryuga ` `?> `

Output:
```3
```

Time Complexity: O(N^2) where N is the length of the array.

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