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Largest sum contiguous subarray having only non-negative elements
  • Difficulty Level : Medium
  • Last Updated : 14 Apr, 2021
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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 
 

 

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++




// C++ program to implement
// the above approach
#include <bits/stdc++.h>
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[0]);
     
    cout << maxNonNegativeSubArray(arr, N);
    return 0;
}
 
// This code is contributed by divyeshrabadiya07

Java




// 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




# 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#




// 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)

Simpler Approach:

Java




public class maxNonNegativeSubArray {
     
    public static void main (String[] args) throws java.lang.Exception{
 
 
        int[] arr = {1, 4, -3, 9, 5, -6};
        int max_so_far=0, max_right_here = 0;
        int start = 0, end = 0, s=0;
 
 
        for(int i=0; i<arr.length; i++){
 
            if(arr[i] < 0 ){
                s = i+1;
                max_right_here = 0;
                
            }else{
                max_right_here += arr[i];
            }
 
            if(max_right_here > max_so_far){
                max_so_far = max_right_here;
 
                start = s;
                end = i;
            }
        }
 
        System.out.print("Sub Array : ");
        for(int i = start; i <= end; i++){
            System.out.print(arr[i] + " ");
        }
 
        System.out.println();
        System.out.print("Largest Sum : " + max_so_far);
 
    }
}
Output
Sub Array : 9 5 
Largest Sum : 14

Time Complexity: O(n)

Space complexity: O(1)

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