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Largest sum contiguous subarray having only non-negative elements

  • Difficulty Level : Medium
  • Last Updated : 13 Oct, 2021

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

Javascript




<script>
 
// Javascript program to implement
// the above approach
 
// Function to return Largest Sum Contiguous
// Subarray having non-negative number
function maxNonNegativeSubArray(A, N)
{
     
    // Length of given array
    var l = N;
 
    var sum = 0, i = 0;
    var 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
var arr = [1, 4, -3, 9, 5, -6];
var N = arr.length;
document.write( maxNonNegativeSubArray(arr, N));
 
// This code is contributed by famously.
</script>
Output
14

Time Complexity: O(N)

Auxiliary Space: O(1)

Simpler Approach:The idea in this approach is that when each time we add elements, then, the sum should increase. If it doesn’t, then we have encountered a negative value and the sum would be smaller.

C++




#include <iostream>
 
using namespace std;
 
int main()
{
    int arr[] = { 1, 4, -3, 9, 5, -6 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int max_so_far = 0, max_right_here = 0;
    int start = 0, end = 0, s = 0;
    for (int i = 0; i < n; 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;
        }
    }
 
    cout << ("Sub Array : ");
    for (int i = start; i <= end; i++) {
        cout << arr[i] << " ";
    }
 
    cout << endl;
    cout << "Largest Sum : " << max_so_far;
}
 
// This code is contributed by SoumikMondal

Javascript




<script>
 
let arr = [ 1, 4, -3, 9, 5, -6 ];
let n = arr.length;
let max_so_far = 0, max_right_here = 0;
let start = 0, end = 0, s = 0;
for(let i = 0; i < n; 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;
    }
}
 
// Driver code
document.write("Sub Array : ");
for(let i = start; i <= end; i++)
{
    document.write(arr[i] + " ");
}
 
document.write("<br>");
document.write("Largest Sum : " + max_so_far);
 
// This code is contributed by Potta Lokesh
 
</script>
Output
Sub Array : 9 5 
Largest Sum : 14

Time Complexity: O(n)

Space complexity: O(1)




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