# Largest sum contiguous subarray having only non-negative elements

Given an integer array arr[], the task is to find the largest sum contiguous subarray of non-negative elements and return its sum.

Examples:

Input: arr[] = {1, 4, -3, 9, 5, -6}
Output: 14
Explanation:
Subarray [9, 5] is the subarray having maximum sum with all non-negative elements.

Input: arr[] = {12, 0, 10, 3, 11}
Output: 36

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

Naive Approach:
The simplest approach is to generate all subarrays having only non-negative elements while traversing the subarray and calculating the sum of every valid subarray and updating the maximum sum.
Time Complexity: O(N^2)

Efficient Approach:
To optimize the above approach, traverse the array, and for every non-negative element encountered, keep calculating the sum. For every negative element encountered, update the maximum sum after comparison with the current sum. Reset the sum to 0 and proceed to the next element.

Below is the implementation of the above approach:

 `// C++ program to implement  ` `// the above approach  ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return Largest Sum Contiguous  ` `// Subarray having non-negative number  ` `int` `maxNonNegativeSubArray(``int` `A[], ``int` `N)  ` `{ ` `     `  `    ``// Length of given array  ` `    ``int` `l = N; ` ` `  `    ``int` `sum = 0, i = 0;  ` `    ``int` `Max = -1;  ` ` `  `    ``// Traversing array  ` `    ``while` `(i < l) ` `    ``{  ` `         `  `        ``// Increment i counter to avoid  ` `        ``// negative elements  ` `        ``while` `(i < l && A[i] < 0) ` `        ``{  ` `            ``i++;  ` `            ``continue``;  ` `        ``}  ` ` `  `        ``// Calculating sum of contiguous  ` `        ``// subarray of non-negative  ` `        ``// elements  ` `        ``while` `(i < l && 0 <= A[i]) ` `        ``{  ` `            ``sum += A[i++];  ` ` `  `            ``// Update the maximum sum  ` `            ``Max = max(Max, sum);  ` `        ``}  ` ` `  `        ``// Reset sum  ` `        ``sum = 0;  ` `    ``}  ` ` `  `    ``// Return the maximum sum  ` `    ``return` `Max;  ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 4, -3, 9, 5, -6 };  ` `     `  `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr); ` `     `  `    ``cout << maxNonNegativeSubArray(arr, N); ` `    ``return` `0; ` `} ` ` `  `// This code is contributed by divyeshrabadiya07 `

 `// Java program to implement ` `// the above approach ` `import` `java.util.*; ` ` `  `class` `GFG { ` ` `  `    ``// Function to return Largest Sum Contiguous ` `    ``// Subarray having non-negative number ` `    ``static` `int` `maxNonNegativeSubArray(``int``[] A) ` `    ``{ ` `        ``// Length of given array ` `        ``int` `l = A.length; ` ` `  `        ``int` `sum = ``0``, i = ``0``; ` ` `  `        ``int` `max = -``1``; ` ` `  `        ``// Traversing array ` `        ``while` `(i < l) { ` ` `  `            ``// Increment i counter to avoid ` `            ``// negative elements ` `            ``while` `(i < l && A[i] < ``0``) { ` `                ``i++; ` `                ``continue``; ` `            ``} ` ` `  `            ``// Calculating sum of contiguous ` `            ``// subarray of non-negative ` `            ``// elements ` `            ``while` `(i < l && ``0` `<= A[i]) { ` ` `  `                ``sum += A[i++]; ` ` `  `                ``// Update the maximum sum ` `                ``max = Math.max(max, sum); ` `            ``} ` ` `  `            ``// Reset sum ` `            ``sum = ``0``; ` `        ``} ` ` `  `        ``// Return the maximum sum ` `        ``return` `max; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` ` `  `        ``int``[] arr = { ``1``, ``4``, -``3``, ``9``, ``5``, -``6` `}; ` ` `  `        ``System.out.println(maxNonNegativeSubArray( ` `            ``arr)); ` `    ``} ` `} `

 `# Python3 program for the above approach ` `import` `math ` ` `  `# Function to return Largest Sum Contiguous  ` `# Subarray having non-negative number  ` `def` `maxNonNegativeSubArray(A, N): ` `     `  `    ``# Length of given array  ` `    ``l ``=` `N ` `     `  `    ``sum` `=` `0` `    ``i ``=` `0` `    ``Max` `=` `-``1` ` `  `    ``# Traversing array  ` `    ``while` `(i < l): ` `         `  `        ``# Increment i counter to avoid  ` `        ``# negative elements ` `        ``while` `(i < l ``and` `A[i] < ``0``): ` `            ``i ``+``=` `1` `            ``continue` `         `  `        ``# Calculating sum of contiguous  ` `        ``# subarray of non-negative  ` `        ``# elements  ` `        ``while` `(i < l ``and` `0` `<``=` `A[i]): ` `            ``sum` `+``=` `A[i] ` `            ``i ``+``=` `1` `             `  `            ``# Update the maximum sum  ` `            ``Max` `=` `max``(``Max``, ``sum``) ` `         `  `        ``# Reset sum  ` `        ``sum` `=` `0``;  ` `     `  `    ``# Return the maximum sum  ` `    ``return` `Max` `     `  `# Driver code ` `arr ``=` `[ ``1``, ``4``, ``-``3``, ``9``, ``5``, ``-``6` `] ` ` `  `# Length of array ` `N ``=` `len``(arr) ` ` `  `print``(maxNonNegativeSubArray(arr, N)) ` ` `  `# This code is contributed by sanjoy_62     `

 `// C# program to implement ` `// the above approach ` `using` `System; ` ` `  `class` `GFG{ ` ` `  `// Function to return Largest Sum Contiguous ` `// Subarray having non-negative number ` `static` `int` `maxNonNegativeSubArray(``int``[] A) ` `{ ` `     `  `    ``// Length of given array ` `    ``int` `l = A.Length; ` ` `  `    ``int` `sum = 0, i = 0; ` `    ``int` `max = -1; ` ` `  `    ``// Traversing array ` `    ``while` `(i < l) ` `    ``{ ` `         `  `        ``// Increment i counter to avoid ` `        ``// negative elements ` `        ``while` `(i < l && A[i] < 0) ` `        ``{ ` `            ``i++; ` `            ``continue``; ` `        ``} ` ` `  `        ``// Calculating sum of contiguous ` `        ``// subarray of non-negative ` `        ``// elements ` `        ``while` `(i < l && 0 <= A[i]) ` `        ``{ ` `            ``sum += A[i++]; ` `             `  `            ``// Update the maximum sum ` `            ``max = Math.Max(max, sum); ` `        ``} ` ` `  `        ``// Reset sum ` `        ``sum = 0; ` `    ``} ` ` `  `    ``// Return the maximum sum ` `    ``return` `max; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main() ` `{ ` `    ``int``[] arr = { 1, 4, -3, 9, 5, -6 }; ` ` `  `    ``Console.Write(maxNonNegativeSubArray(arr)); ` `} ` `} ` ` `  `// This code is contributed by chitranayal `

Output:
```14
```

Time Complexity: O(N)

Auxiliary Space : O(1)

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