# Count the subarray with sum strictly greater than the sum of remaining elements

Given an array arr[] of N positive integers, the task is to count all the subarrays where the sum of subarray elements is strictly greater than the sum of remaining elements.

Examples:

Input: arr[] = {1, 2, 3, 4, 5}
Output: 6
Explanation:
Subarrays are:
{1, 2, 3, 4} – sum of subarray = 10, sum of remaining elements {5} = 5
{1, 2, 3, 4, 5} – sum of subarray =15, sum of remaining element = 0
{2, 3, 4} – sum of subarray = 9, sum of remaining elements {1, 5} = 6
{2, 3, 4, 5} – sum of subarray = 14, sum of remaining elements {1} = 1
{3, 4, 5} – sum of subarray = 12, sum of remaining elements {1, 2} = 3
{4, 5} – sum of subarray = 9, sum of remaining elements {1, 2, 3} = 6

Input: arr[] = {10, 9, 12, 6}
Output: 5
Explanation:
Sub arrays are :
{10, 9} – sum of subarray = 19, sum of remaining elements {12, 6} = 18
{10, 9, 12} – sum of subarray = 31, sum of remaining elements {6} = 6
{10, 9, 12, 6} – sum of subarray = 37, sum of remaining elements = 0
{9, 12} – sum of subarray = 21, sum of remaining elements {10, 6} = 16
{9, 12, 6} – sum of subarray =27, sum of remaining element {10} = 10

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

Naive Approach:
A naive approach is to generate the sum of every subarray using three nested loops and check the calculated subarray sum with the sum of remaining array elements.

1. The first loop indicates the beginning of the subarray.
2. The second loop indicate the ending of the subarray.
3. Inside the second loop, we have for loops to calculate the subarray_sum and remaining array element sum.
4. Increment the counter, when subarray_sum is strictly greater than remaining_sum.

Below is the implementation of the above approach:

## CPP

 `// C++ implementation of the above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to count the number of ` `// sub-arrays with sum strictly greater ` `// than the remaining elements of array ` `int` `Count_subarray(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `subarray_sum, remaining_sum, count = 0; ` ` `  `    ``// For loop for begining point of a subarray ` `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// For loop for ending point of the subarray ` `        ``for` `(``int` `j = i; j < n; j++) { ` ` `  `            ``// Initialise subarray_sum and ` `            ``// remaining_sum to 0 ` `            ``subarray_sum = 0; ` `            ``remaining_sum = 0; ` ` `  `            ``// For loop to calculate ` `            ``// the sum of generated subarray ` `            ``for` `(``int` `k = i; k <= j; k++) { ` `                ``subarray_sum += arr[k]; ` `            ``} ` `            ``// For loop to calculate the ` `            ``// sum remaining array element ` `            ``for` `(``int` `l = 0; l < i; l++) { ` `                ``remaining_sum += arr[l]; ` `            ``} ` `            ``for` `(``int` `l = j + 1; l < n; l++) { ` `                ``remaining_sum += arr[l]; ` `            ``} ` `            ``// Checking for condition when ` `            ``// subarray sum is strictly greater than ` `            ``// remaining sum of array element ` `            ``if` `(subarray_sum > remaining_sum) { ` `                ``count += 1; ` `            ``} ` `        ``} ` `    ``} ` `    ``return` `count; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 10, 9, 12, 6 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` `    ``cout << Count_subarray(arr, n); ` `    ``return` `0; ` `} `

## Java

 `// Java implementation of the above approach ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to count the number of ` `// sub-arrays with sum strictly greater ` `// than the remaining elements of array ` `static` `int` `Count_subarray(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `subarray_sum, remaining_sum, count = ``0``; ` ` `  `    ``// For loop for begining point of a subarray ` `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `    ``{ ` ` `  `        ``// For loop for ending point of the subarray ` `        ``for` `(``int` `j = i; j < n; j++) ` `        ``{ ` ` `  `            ``// Initialise subarray_sum and ` `            ``// remaining_sum to 0 ` `            ``subarray_sum = ``0``; ` `            ``remaining_sum = ``0``; ` ` `  `            ``// For loop to calculate ` `            ``// the sum of generated subarray ` `            ``for` `(``int` `k = i; k <= j; k++) ` `            ``{ ` `                ``subarray_sum += arr[k]; ` `            ``} ` `             `  `            ``// For loop to calculate the ` `            ``// sum remaining array element ` `            ``for` `(``int` `l = ``0``; l < i; l++)  ` `            ``{ ` `                ``remaining_sum += arr[l]; ` `            ``} ` `            ``for` `(``int` `l = j + ``1``; l < n; l++) ` `            ``{ ` `                ``remaining_sum += arr[l]; ` `            ``} ` `             `  `            ``// Checking for condition when ` `            ``// subarray sum is strictly greater than ` `            ``// remaining sum of array element ` `            ``if` `(subarray_sum > remaining_sum) ` `            ``{ ` `                ``count += ``1``; ` `            ``} ` `        ``} ` `    ``} ` `    ``return` `count; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `arr[] = { ``10``, ``9``, ``12``, ``6` `}; ` `    ``int` `n = arr.length; ` `    ``System.out.print(Count_subarray(arr, n)); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

## Python3

 `# Python implementation of the above approach ` ` `  `# Function to count the number of ` `# sub-arrays with sum strictly greater ` `# than the remaining elements of array ` `def` `Count_subarray(arr, n): ` `    ``subarray_sum, remaining_sum, count ``=` `0``, ``0``, ``0``; ` ` `  `    ``# For loop for begining poof a subarray ` `    ``for` `i ``in` `range``(n): ` ` `  `        ``# For loop for ending poof the subarray ` `        ``for` `j ``in` `range``(i, n): ` ` `  `            ``# Initialise subarray_sum and ` `            ``# remaining_sum to 0 ` `            ``subarray_sum ``=` `0``; ` `            ``remaining_sum ``=` `0``; ` ` `  `            ``# For loop to calculate ` `            ``# the sum of generated subarray ` `            ``for` `k ``in` `range``(i, j ``+` `1``): ` `                ``subarray_sum ``+``=` `arr[k]; ` `             `  ` `  `            ``# For loop to calculate the ` `            ``# sum remaining array element ` `            ``for` `l ``in` `range``(i): ` `                ``remaining_sum ``+``=` `arr[l]; ` `            ``for` `l ``in` `range``(j ``+` `1``, n): ` `                ``remaining_sum ``+``=` `arr[l]; ` `             `  `            ``# Checking for condition when ` `            ``# subarray sum is strictly greater than ` `            ``# remaining sum of array element ` `            ``if` `(subarray_sum > remaining_sum): ` `                ``count ``+``=` `1``; ` `             `  `    ``return` `count; ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``arr ``=` `[ ``10``, ``9``, ``12``, ``6``]; ` `    ``n ``=` `len``(arr); ` `    ``print``(Count_subarray(arr, n)); ` `     `  `# This code is contributed by 29AjayKumar `

## C#

 `// C# implementation of the above approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to count the number of ` `// sub-arrays with sum strictly greater ` `// than the remaining elements of array ` `static` `int` `Count_subarray(``int` `[]arr, ``int` `n) ` `{ ` `    ``int` `subarray_sum, remaining_sum, count = 0; ` ` `  `    ``// For loop for begining point of a subarray ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `    ``{ ` ` `  `        ``// For loop for ending point of the subarray ` `        ``for` `(``int` `j = i; j < n; j++) ` `        ``{ ` ` `  `            ``// Initialise subarray_sum and ` `            ``// remaining_sum to 0 ` `            ``subarray_sum = 0; ` `            ``remaining_sum = 0; ` ` `  `            ``// For loop to calculate ` `            ``// the sum of generated subarray ` `            ``for` `(``int` `k = i; k <= j; k++) ` `            ``{ ` `                ``subarray_sum += arr[k]; ` `            ``} ` `             `  `            ``// For loop to calculate the ` `            ``// sum remaining array element ` `            ``for` `(``int` `l = 0; l < i; l++)  ` `            ``{ ` `                ``remaining_sum += arr[l]; ` `            ``} ` `            ``for` `(``int` `l = j + 1; l < n; l++) ` `            ``{ ` `                ``remaining_sum += arr[l]; ` `            ``} ` `             `  `            ``// Checking for condition when ` `            ``// subarray sum is strictly greater than ` `            ``// remaining sum of array element ` `            ``if` `(subarray_sum > remaining_sum) ` `            ``{ ` `                ``count += 1; ` `            ``} ` `        ``} ` `    ``} ` `    ``return` `count; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `[]arr = { 10, 9, 12, 6 }; ` `    ``int` `n = arr.Length; ` `    ``Console.Write(Count_subarray(arr, n)); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```5
```

Time Complexity: O(N3)

Efficient Approach:

An efficient solution is to use total_sum of given array arr[] that help in calculating subarray_sum and remaining_sum.

1. The total sum of the given array is calculated.
2. Run a for loop where the loop variable i indicate the beginning index of subarray.
3. Another loop, where every j indicate the ending index of the subarray and calculate subarray_sum for every j th index.
4. subarray_sum=arr[i]+arr[i+1]+…..+arr[j]
remaining_sum=total_sum – subarray_sum
5. Then, check for condition and increment counter when subarray sum is strictly greater than the remaining sum of array elements.

Below is the implementation of the above approach.

## C++

 `// C++ implementation of the above approach ` `#include ` `using` `namespace` `std; ` ` `  `int` `Count_subarray(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `total_sum = 0, subarray_sum, ` `        ``remaining_sum, count = 0; ` ` `  `    ``// Calculating total sum of given array ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``total_sum += arr[i]; ` `    ``} ` ` `  `    ``// For loop for begining point of a subarray ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``// initialise subarray_sum to 0 ` `        ``subarray_sum = 0; ` ` `  `        ``// For loop for calculating ` `        ``// subarray_sum and remaining_sum ` `        ``for` `(``int` `j = i; j < n; j++) { ` ` `  `            ``// Calculating subarray_sum ` `            ``// and corresponding remaining_sum ` `            ``subarray_sum += arr[j]; ` `            ``remaining_sum = total_sum - subarray_sum; ` ` `  `            ``// Checking for the condition when ` `            ``// subarray sum is strictly greater than ` `            ``// the remaining sum of the array element ` `            ``if` `(subarray_sum > remaining_sum) { ` `                ``count += 1; ` `            ``} ` `        ``} ` `    ``} ` `    ``return` `count; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 10, 9, 12, 6 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` `    ``cout << Count_subarray(arr, n); ` `    ``return` `0; ` `} `

## Java

 `// Java implementation of the above approach ` `class` `GFG ` `{ ` ` `  `static` `int` `Count_subarray(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `total_sum = ``0``, subarray_sum, ` `        ``remaining_sum, count = ``0``; ` ` `  `    ``// Calculating total sum of given array ` `    ``for` `(``int` `i = ``0``; i < n; i++) ` `    ``{ ` `        ``total_sum += arr[i]; ` `    ``} ` ` `  `    ``// For loop for begining point of a subarray ` `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `    ``{ ` `        ``// initialise subarray_sum to 0 ` `        ``subarray_sum = ``0``; ` ` `  `        ``// For loop for calculating ` `        ``// subarray_sum and remaining_sum ` `        ``for` `(``int` `j = i; j < n; j++) ` `        ``{ ` ` `  `            ``// Calculating subarray_sum ` `            ``// and corresponding remaining_sum ` `            ``subarray_sum += arr[j]; ` `            ``remaining_sum = total_sum - subarray_sum; ` ` `  `            ``// Checking for the condition when ` `            ``// subarray sum is strictly greater than ` `            ``// the remaining sum of the array element ` `            ``if` `(subarray_sum > remaining_sum)  ` `            ``{ ` `                ``count += ``1``; ` `            ``} ` `        ``} ` `    ``} ` `    ``return` `count; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `arr[] = { ``10``, ``9``, ``12``, ``6` `}; ` `    ``int` `n = arr.length; ` `    ``System.out.print(Count_subarray(arr, n)); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

## Python3

 `# Python3 implementation of the above approach  ` ` `  `def` `Count_subarray(arr, n) :  ` ` `  `    ``total_sum ``=` `0``;  ` `    ``count ``=` `0``;  ` ` `  `    ``# Calculating total sum of given array  ` `    ``for` `i ``in` `range``(n) : ` `        ``total_sum ``+``=` `arr[i];  ` `     `  `    ``# For loop for begining point of a subarray  ` `    ``for` `i ``in` `range``(n) :  ` ` `  `        ``# initialise subarray_sum to 0  ` `        ``subarray_sum ``=` `0``;  ` ` `  `        ``# For loop for calculating  ` `        ``# subarray_sum and remaining_sum  ` `        ``for` `j ``in` `range``(i, n) :  ` ` `  `            ``# Calculating subarray_sum  ` `            ``# and corresponding remaining_sum  ` `            ``subarray_sum ``+``=` `arr[j];  ` `            ``remaining_sum ``=` `total_sum ``-` `subarray_sum;  ` ` `  `            ``# Checking for the condition when  ` `            ``# subarray sum is strictly greater than  ` `            ``# the remaining sum of the array element  ` `            ``if` `(subarray_sum > remaining_sum) : ` `                ``count ``+``=` `1``;  ` `         `  `    ``return` `count;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``arr ``=` `[ ``10``, ``9``, ``12``, ``6` `];  ` `    ``n ``=` `len``(arr);  ` `    ``print``(Count_subarray(arr, n));  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the above approach  ` `using` `System; ` ` `  `class` `GFG  ` `{  ` `     `  `    ``static` `int` `Count_subarray(``int` `[]arr, ``int` `n)  ` `    ``{  ` `        ``int` `total_sum = 0, subarray_sum,  ` `            ``remaining_sum, count = 0;  ` `     `  `        ``// Calculating total sum of given array  ` `        ``for` `(``int` `i = 0; i < n; i++)  ` `        ``{  ` `            ``total_sum += arr[i];  ` `        ``}  ` `     `  `        ``// For loop for begining point of a subarray  ` `        ``for` `(``int` `i = 0; i < n; i++)  ` `        ``{  ` `            ``// initialise subarray_sum to 0  ` `            ``subarray_sum = 0;  ` `     `  `            ``// For loop for calculating  ` `            ``// subarray_sum and remaining_sum  ` `            ``for` `(``int` `j = i; j < n; j++)  ` `            ``{  ` `     `  `                ``// Calculating subarray_sum  ` `                ``// and corresponding remaining_sum  ` `                ``subarray_sum += arr[j];  ` `                ``remaining_sum = total_sum - subarray_sum;  ` `     `  `                ``// Checking for the condition when  ` `                ``// subarray sum is strictly greater than  ` `                ``// the remaining sum of the array element  ` `                ``if` `(subarray_sum > remaining_sum)  ` `                ``{  ` `                    ``count += 1;  ` `                ``}  ` `            ``}  ` `        ``}  ` `        ``return` `count;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main()  ` `    ``{  ` `        ``int` `[]arr = { 10, 9, 12, 6 };  ` `        ``int` `n = arr.Length;  ` `        ``Console.WriteLine(Count_subarray(arr, n));  ` `    ``}  ` `}  ` ` `  `// This code is contributed by AnkitRai01 `

Output:

```5
```

Time Complexity: O(N2)

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