Skip to content
Related Articles

Related Articles

Table of Contents

Improve Article
Save Article
Like Article

Largest Sum Contiguous Subarray

  • Difficulty Level : Medium
  • Last Updated : 06 May, 2022

Write an efficient program to find the sum of contiguous subarray within a one-dimensional array of numbers that has the largest sum. 

kadane-algorithm

 

Kadane’s Algorithm:

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

Explanation: 
The simple idea of Kadane’s algorithm is to look for all positive contiguous segments of the array (max_ending_here is used for this). And keep track of maximum sum contiguous segment among all positive segments (max_so_far is used for this). Each time we get a positive sum compare it with max_so_far and update max_so_far if it is greater than max_so_far 

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = INT_MIN
    max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0
    and set max_so_far = -2

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Since max_ending_here = -3 and max_so_far = -2, max_so_far will remain -2
    Set max_ending_here = 0 because max_ending_here < 0
      
    
    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was -2 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

Program: 

C++




// C++ program to print largest contiguous array sum
#include<iostream>
#include<climits>
using namespace std;
 
int maxSubArraySum(int a[], int size)
{
    int max_so_far = INT_MIN, max_ending_here = 0;
 
    for (int i = 0; i < size; i++)
    {
        max_ending_here = max_ending_here + a[i];
        if (max_so_far < max_ending_here)
            max_so_far = max_ending_here;
 
        if (max_ending_here < 0)
            max_ending_here = 0;
    }
    return max_so_far;
}
 
/*Driver program to test maxSubArraySum*/
int main()
{
    int a[] = {-2, -3, 4, -1, -2, 1, 5, -3};
    int n = sizeof(a)/sizeof(a[0]);
    int max_sum = maxSubArraySum(a, n);
    cout << "Maximum contiguous sum is " << max_sum;
    return 0;
}
Java



import java.io.*;
// Java program to print largest contiguous array sum
import java.util.*;
 
class Kadane
{
    public static void main (String[] args)
    {
        int [] a = {-2, -3, 4, -1, -2, 1, 5, -3};
        System.out.println("Maximum contiguous sum is " +
                                       maxSubArraySum(a));
    }
 
    static int maxSubArraySum(int a[])
    {
        int size = a.length;
        int max_so_far = Integer.MIN_VALUE, max_ending_here = 0;
 
        for (int i = 0; i < size; i++)
        {
            max_ending_here = max_ending_here + a[i];
            if (max_so_far < max_ending_here)
                max_so_far = max_ending_here;
            if (max_ending_here < 0)
                max_ending_here = 0;
        }
        return max_so_far;
    }
}
Python



# Python program to find maximum contiguous subarray
  
# Function to find the maximum contiguous subarray
from sys import maxint
def maxSubArraySum(a,size):
      
    max_so_far = -maxint - 1
    max_ending_here = 0
      
    for i in range(0, size):
        max_ending_here = max_ending_here + a[i]
        if (max_so_far < max_ending_here):
            max_so_far = max_ending_here
 
        if max_ending_here < 0:
            max_ending_here = 0  
    return max_so_far
  
# Driver function to check the above function
 
a = [-2, -3, 4, -1, -2, 1, 5, -3]
 
print "Maximum contiguous sum is", maxSubArraySum(a,len(a))
  
#This code is contributed by _Devesh Agrawal_
C#



// C# program to print largest
// contiguous array sum
using System;
 
class GFG
{
    static int maxSubArraySum(int []a)
    {
        int size = a.Length;
        int max_so_far = int.MinValue,
            max_ending_here = 0;
 
        for (int i = 0; i < size; i++)
        {
            max_ending_here = max_ending_here + a[i];
             
            if (max_so_far < max_ending_here)
                max_so_far = max_ending_here;
             
            if (max_ending_here < 0)
                max_ending_here = 0;
        }
         
        return max_so_far;
    }
     
    // Driver code
    public static void Main ()
    {
        int [] a = {-2, -3, 4, -1, -2, 1, 5, -3};
        Console.Write("Maximum contiguous sum is " +
                                maxSubArraySum(a));
    }
 
}
 
// This code is contributed by Sam007_
PHP



<?php
// PHP program to print largest
// contiguous array sum
 
function maxSubArraySum($a, $size)
{
    $max_so_far = PHP_INT_MIN;
    $max_ending_here = 0;
 
    for ($i = 0; $i < $size; $i++)
    {
        $max_ending_here = $max_ending_here + $a[$i];
        if ($max_so_far < $max_ending_here)
            $max_so_far = $max_ending_here;
 
        if ($max_ending_here < 0)
            $max_ending_here = 0;
    }
    return $max_so_far;
}
 
// Driver code
$a = array(-2, -3, 4, -1,
           -2, 1, 5, -3);
$n = count($a);
$max_sum = maxSubArraySum($a, $n);
echo "Maximum contiguous sum is " ,
                          $max_sum;
 
// This code is contributed by anuj_67.
?>
Javascript



<script>
 
// JavaScript program to find maximum
// contiguous subarray
  
// Function to find the maximum
// contiguous subarray
function maxSubArraySum(a, size)
{
    var maxint = Math.pow(2, 53)
    var max_so_far = -maxint - 1
    var max_ending_here = 0
      
    for (var i = 0; i < size; i++)
    {
        max_ending_here = max_ending_here + a[i]
        if (max_so_far < max_ending_here)
            max_so_far = max_ending_here
 
        if (max_ending_here < 0)
            max_ending_here = 0
    }
    return max_so_far
}
  
// Driver code
var a = [ -2, -3, 4, -1, -2, 1, 5, -3 ]
document.write("Maximum contiguous sum is",
               maxSubArraySum(a, a.length))
  
// This code is contributed by AnkThon
 
</script>
Output:
Maximum contiguous sum is 7
Another approach:
 
C++



int maxSubarraySum(int arr[], int size)
{
    int max_ending_here = 0, max_so_far = INT_MIN;
    for (int i = 0; i < size; i++) {
       
        // include current element to previous subarray only
        // when it can add to a bigger number than itself.
        if (arr[i] <= max_ending_here + arr[i]) {
            max_ending_here += arr[i];
        }
       
        // Else start the max subarray from current element
        else {
            max_ending_here = arr[i];
        }
        if (max_ending_here > max_so_far)
            max_so_far = max_ending_here;
    }
    return max_so_far;
} // contributed by Vipul Raj
Java



static int maxSubArraySum(int a[],int size)
{
     
    int max_so_far = a[0], max_ending_here = 0;
 
    for (int i = 0; i < size; i++)
    {
        max_ending_here = max_ending_here + a[i];
        if (max_ending_here < 0)
            max_ending_here = 0;
         
        /* Do not compare for all
           elements. Compare only
           when max_ending_here > 0 */
        else if (max_so_far < max_ending_here)
            max_so_far = max_ending_here;
         
    }
    return max_so_far;
}
 
// This code is contributed by ANKITRAI1
Python



def maxSubArraySum(a,size):
     
    max_so_far = a[0]
    max_ending_here = 0
     
    for i in range(0, size):
        max_ending_here = max_ending_here + a[i]
        if max_ending_here < 0:
            max_ending_here = 0
         
        # Do not compare for all elements. Compare only  
        # when  max_ending_here > 0
        elif (max_so_far < max_ending_here):
            max_so_far = max_ending_here
             
    return max_so_far
C#



static int maxSubArraySum(int[] a, int size)
{
    int max_so_far = a[0], max_ending_here = 0;
 
    for (int i = 0; i < size; i++) {
        max_ending_here = max_ending_here + a[i];
        if (max_ending_here < 0)
            max_ending_here = 0;
 
        /* Do not compare for all
        elements. Compare only
        when max_ending_here > 0 */
        else if (max_so_far < max_ending_here)
            max_so_far = max_ending_here;
    }
    return max_so_far;
}
 
// This code is contributed
// by ChitraNayal
PHP



<?php
function maxSubArraySum(&$a, $size)
{
$max_so_far = $a[0];
$max_ending_here = 0;
for ($i = 0; $i < $size; $i++)
{
    $max_ending_here = $max_ending_here + $a[$i];
    if ($max_ending_here < 0)
        $max_ending_here = 0;
 
    /* Do not compare for all elements.
       Compare only when max_ending_here > 0 */
    else if ($max_so_far < $max_ending_here)
        $max_so_far = $max_ending_here;
}
return $max_so_far;
 
// This code is contributed
// by ChitraNayal
?>
Javascript



<script>
        // JavaScript Program to implement
        // the above approach
 
        function maxSubarraySum(arr, size)
        {
            let max_ending_here = 0, max_so_far = Number.MIN_VALUE;
            for (let i = 0; i < size; i++) {
 
                // include current element to previous subarray only
                // when it can add to a bigger number than itself.
                if (arr[i] <= max_ending_here + arr[i]) {
                    max_ending_here += arr[i];
                }
 
                // Else start the max subarray from current element
                else {
                    max_ending_here = arr[i];
                }
                if (max_ending_here > max_so_far) {
                    max_so_far = max_ending_here;
                }
            }
            return max_so_far;
        }
         
// This code is contributed by Potta Lokesh
    </script>
Time Complexity: O(n) 
Algorithmic Paradigm: Dynamic Programming
Following is another simple implementation suggested by Mohit Kumar. The implementation handles the case when all numbers in the array are negative. 
C++



#include<iostream>
using namespace std;
 
int maxSubArraySum(int a[], int size)
{
   int max_so_far = a[0];
   int curr_max = a[0];
 
   for (int i = 1; i < size; i++)
   {
        curr_max = max(a[i], curr_max+a[i]);
        max_so_far = max(max_so_far, curr_max);
   }
   return max_so_far;
}
 
/* Driver program to test maxSubArraySum */
int main()
{
   int a[] =  {-2, -3, 4, -1, -2, 1, 5, -3};
   int n = sizeof(a)/sizeof(a[0]);
   int max_sum = maxSubArraySum(a, n);
   cout << "Maximum contiguous sum is " << max_sum;
   return 0;
}
Java



// Java program to print largest contiguous
// array sum
import java.io.*;
 
class GFG {
 
    static int maxSubArraySum(int a[], int size)
    {
    int max_so_far = a[0];
    int curr_max = a[0];
 
    for (int i = 1; i < size; i++)
    {
           curr_max = Math.max(a[i], curr_max+a[i]);
        max_so_far = Math.max(max_so_far, curr_max);
    }
    return max_so_far;
    }
 
    /* Driver program to test maxSubArraySum */
    public static void main(String[] args)
    {
    int a[] = {-2, -3, 4, -1, -2, 1, 5, -3};
    int n = a.length;  
    int max_sum = maxSubArraySum(a, n);
    System.out.println("Maximum contiguous sum is "
                       + max_sum);
    }
}
 
// This code is contributed by Prerna Saini
Python



# Python program to find maximum contiguous subarray
 
def maxSubArraySum(a,size):
     
    max_so_far =a[0]
    curr_max = a[0]
     
    for i in range(1,size):
        curr_max = max(a[i], curr_max + a[i])
        max_so_far = max(max_so_far,curr_max)
         
    return max_so_far
 
# Driver function to check the above function
a = [-2, -3, 4, -1, -2, 1, 5, -3]
print"Maximum contiguous sum is" , maxSubArraySum(a,len(a))
 
#This code is contributed by _Devesh Agrawal_
C#



// C# program to print largest
// contiguous array sum
using System;
 
class GFG
{
    static int maxSubArraySum(int []a, int size)
    {
    int max_so_far = a[0];
    int curr_max = a[0];
 
    for (int i = 1; i < size; i++)
    {
        curr_max = Math.Max(a[i], curr_max+a[i]);
        max_so_far = Math.Max(max_so_far, curr_max);
    }
 
    return max_so_far;
    }
 
    // Driver code
    public static void Main ()
    {
        int []a = {-2, -3, 4, -1, -2, 1, 5, -3};
        int n = a.Length;
        Console.Write("Maximum contiguous sum is "
                           + maxSubArraySum(a, n));
    }
 
}
 
// This code is contributed by Sam007_
PHP



<?php
function maxSubArraySum($a, $size)
{
    $max_so_far = $a[0];
    $curr_max = $a[0];
     
    for ($i = 1; $i < $size; $i++)
    {
        $curr_max = max($a[$i],
                        $curr_max + $a[$i]);
        $max_so_far = max($max_so_far,
                          $curr_max);
    }
    return $max_so_far;
}
 
// Driver Code
$a = array(-2, -3, 4, -1,
           -2, 1, 5, -3);
$n = sizeof($a);
$max_sum = maxSubArraySum($a, $n);
echo "Maximum contiguous sum is " .
                          $max_sum;
 
// This code is contributed
// by Akanksha Rai(Abby_akku)
?>
Javascript



<script>
// C# program to print largest
// contiguous array sum
 
function maxSubArraySum(a,size)
{
  let max_so_far = a[0];
  let curr_max = a[0];
 
  for (let i = 1; i < size; i++)
  {
      curr_max = Math.max(a[i], curr_max+a[i]);
      max_so_far = Math.max(max_so_far, curr_max);
  }
 
return max_so_far;
}
 
// Driver code
 
let a = [-2, -3, 4, -1, -2, 1, 5, -3];
let n = a.length;
document.write("Maximum contiguous sum is ",maxSubArraySum(a, n));
     
</script>
Output: 
Maximum contiguous sum is 7
To print the subarray with the maximum sum, we maintain indices whenever we get the maximum sum.  
C++



// C++ program to print largest contiguous array sum
#include<iostream>
#include<climits>
using namespace std;
 
int maxSubArraySum(int a[], int size)
{
    int max_so_far = INT_MIN, max_ending_here = 0,
       start =0, end = 0, s=0;
 
    for (int i=0; i< size; i++ )
    {
        max_ending_here += a[i];
 
        if (max_so_far < max_ending_here)
        {
            max_so_far = max_ending_here;
            start = s;
            end = i;
        }
 
        if (max_ending_here < 0)
        {
            max_ending_here = 0;
            s = i + 1;
        }
    }
    cout << "Maximum contiguous sum is "
        << max_so_far << endl;
    cout << "Starting index "<< start
        << endl << "Ending index "<< end << endl;
}
 
/*Driver program to test maxSubArraySum*/
int main()
{
    int a[] = {-2, -3, 4, -1, -2, 1, 5, -3};
    int n = sizeof(a)/sizeof(a[0]);
    int max_sum = maxSubArraySum(a, n);
    return 0;
}
Java



// Java program to print largest
// contiguous array sum
class GFG {
 
    static void maxSubArraySum(int a[], int size)
    {
        int max_so_far = Integer.MIN_VALUE,
        max_ending_here = 0,start = 0,
        end = 0, s = 0;
 
        for (int i = 0; i < size; i++)
        {
            max_ending_here += a[i];
 
            if (max_so_far < max_ending_here)
            {
                max_so_far = max_ending_here;
                start = s;
                end = i;
            }
 
            if (max_ending_here < 0)
            {
                max_ending_here = 0;
                s = i + 1;
            }
        }
        System.out.println("Maximum contiguous sum is "
                           + max_so_far);
        System.out.println("Starting index " + start);
        System.out.println("Ending index " + end);
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int a[] = { -2, -3, 4, -1, -2, 1, 5, -3 };
        int n = a.length;
        maxSubArraySum(a, n);
    }
}
 
// This code is contributed by  prerna saini
Python3



# Python program to print largest contiguous array sum
 
from sys import maxsize
 
# Function to find the maximum contiguous subarray
# and print its starting and end index
def maxSubArraySum(a,size):
 
    max_so_far = -maxsize - 1
    max_ending_here = 0
    start = 0
    end = 0
    s = 0
 
    for i in range(0,size):
 
        max_ending_here += a[i]
 
        if max_so_far < max_ending_here:
            max_so_far = max_ending_here
            start = s
            end = i
 
        if max_ending_here < 0:
            max_ending_here = 0
            s = i+1
 
    print ("Maximum contiguous sum is %d"%(max_so_far))
    print ("Starting Index %d"%(start))
    print ("Ending Index %d"%(end))
 
# Driver program to test maxSubArraySum
a = [-2, -3, 4, -1, -2, 1, 5, -3]
maxSubArraySum(a,len(a))
C#



// C# program to print largest
// contiguous array sum
using System;
 
class GFG
{
    static void maxSubArraySum(int []a,
                               int size)
    {
        int max_so_far = int.MinValue,
        max_ending_here = 0, start = 0,
        end = 0, s = 0;
 
        for (int i = 0; i < size; i++)
        {
            max_ending_here += a[i];
 
            if (max_so_far < max_ending_here)
            {
                max_so_far = max_ending_here;
                start = s;
                end = i;
            }
 
            if (max_ending_here < 0)
            {
                max_ending_here = 0;
                s = i + 1;
            }
        }
        Console.WriteLine("Maximum contiguous " +
                         "sum is " + max_so_far);
        Console.WriteLine("Starting index " +
                                      start);
        Console.WriteLine("Ending index " +
                                      end);
    }
 
    // Driver code
    public static void Main()
    {
        int []a = {-2, -3, 4, -1,
                   -2, 1, 5, -3};
        int n = a.Length;
        maxSubArraySum(a, n);
    }
}
 
// This code is contributed
// by anuj_67.
PHP



<?php
// PHP program to print largest
// contiguous array sum
 
function maxSubArraySum($a, $size)
{
    $max_so_far = PHP_INT_MIN;
    $max_ending_here = 0;
    $start = 0;
    $end = 0;
    $s = 0;
 
    for ($i = 0; $i < $size; $i++)
    {
        $max_ending_here += $a[$i];
 
        if ($max_so_far < $max_ending_here)
        {
            $max_so_far = $max_ending_here;
            $start = $s;
            $end = $i;
        }
 
        if ($max_ending_here < 0)
        {
            $max_ending_here = 0;
            $s = $i + 1;
        }
    }
    echo "Maximum contiguous sum is ".
                     $max_so_far."\n";
    echo "Starting index ". $start . "\n".
            "Ending index " . $end . "\n";
}
 
// Driver Code
$a = array(-2, -3, 4, -1, -2, 1, 5, -3);
$n = sizeof($a);
$max_sum = maxSubArraySum($a, $n);
 
// This code is contributed
// by ChitraNayal
?>
Javascript



<script>
// javascript program to print largest
// contiguous array sum   
function maxSubArraySum(a , size) {
        var max_so_far = Number.MIN_VALUE, max_ending_here = 0, start = 0, end = 0, s = 0;
 
        for (i = 0; i < size; i++) {
            max_ending_here += a[i];
 
            if (max_so_far < max_ending_here) {
                max_so_far = max_ending_here;
                start = s;
                end = i;
            }
 
            if (max_ending_here < 0) {
                max_ending_here = 0;
                s = i + 1;
            }
        }
        document.write("Maximum contiguous sum is " + max_so_far);
        document.write("<br/>Starting index " + start);
        document.write("<br/>Ending index " + end);
    }
 
    // Driver code
     
        var a = [ -2, -3, 4, -1, -2, 1, 5, -3 ];
        var n = a.length;
        maxSubArraySum(a, n);
 
// This code is contributed by Rajput-Ji
</script>
Output: 
Maximum contiguous sum is 7
Starting index 2
Ending index 6
Kadane’s Algorithm can be viewed both as a greedy and DP. As we can see that we are keeping a running sum of integers and when it becomes less than 0, we reset it to 0 (Greedy Part). This is because continuing with a negative sum is way more worse than restarting with a new range. Now it can also be viewed as a DP, at each stage we have 2 choices: Either take the current element and continue with previous sum OR restart a new range. These both choices are being taken care of in the implementation. 
Time Complexity: O(n)
Auxiliary Space: O(1)
Now try the below question 
Given an array of integers (possibly some elements negative), write a C program to find out the *maximum product* possible by multiplying ‘n’ consecutive integers in the array where n ≤ ARRAY_SIZE. Also, print the starting point of the maximum product subarray.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

My Personal Notes
arrow_drop_up
Previous
Find the Number Occurring Odd Number of Times
Next

Maximum Subarray Sum using Divide and Conquer algorithm
Recommended Articles
Page :
Largest sum contiguous increasing subarray
10, May 17
Range query for Largest Sum Contiguous Subarray
04, Apr 18
K-th Largest Sum Contiguous Subarray
06, Oct 17
Largest sum contiguous subarray having only non-negative elements
09, Jul 20
Largest Sum Contiguous Subarray having unique elements
08, Sep 20
C++ Program to Find the K-th Largest Sum Contiguous Subarray
06, Dec 21
Java Program to Find the K-th Largest Sum Contiguous Subarray
06, Dec 21
Python3 Program to Find the K-th Largest Sum Contiguous Subarray
06, Dec 21
Javascript Program for Largest Sum Contiguous Subarray
22, Nov 21
Largest sum contiguous subarray by adding S exactly at K different positions
09, Mar 22
Length of the largest subarray with contiguous elements | Set 1
18, Oct 14
Largest Ratio Contiguous subarray
29, Jul 20
Smallest sum contiguous subarray
30, Jul 17
Smallest sum contiguous subarray | Set-2
09, Aug 18
Find the largest contiguous pair sum in given Array
25, Jun 20
Length of longest subarray with increasing contiguous elements
25, Oct 20
Check if a non-contiguous subsequence same as the given subarray exists or not
02, Dec 20
Maximum length of longest increasing contiguous subarray after deleting exactly one element from array
27, Oct 21
First subarray having sum at least half the maximum sum of any subarray of size K
09, Sep 20
Minimum cost to convert all elements of a K-size subarray to 0 from given Ternary Array with subarray sum as cost
05, Jul 21
Maximize the subarray sum after multiplying all elements of any subarray with X
24, Apr 19
Maximum length of subarray such that sum of the subarray is even
25, Apr 19
Count of subarray that does not contain any subarray with sum 0
13, Apr 20
Maximum subarray sum possible after removing at most one subarray
07, May 21
Article Contributed By :
https://media.geeksforgeeks.org/auth/avatar.png
GeeksforGeeks
Vote for difficulty
Current difficulty :
Medium





Improved By :
Article Tags :
Practice Tags :
Report Issue

We use cookies to ensure you have the best browsing experience on our website. By using our site, you
acknowledge that you have read and understood our
Cookie Policy &
        Privacy Policy

Lightbox

Start Your Coding Journey Now!