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Size of The Subarray With Maximum Sum

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  • Difficulty Level : Easy
  • Last Updated : 09 Dec, 2022
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Given an array arr[] of size N, the task is to find the length of the subarray having maximum sum.

Examples : 

Input :  a[] = {1, -2, 1, 1, -2, 1}
Output : Length of the subarray is 2
Explanation : Subarray with consecutive elements 
and maximum sum will be {1, 1}. So length is 2

Input : ar[] = { -2, -3, 4, -1, -2, 1, 5, -3 }
Output : Length of the subarray is 5
Explanation : Subarray with consecutive elements 
and maximum sum will be {4, -1, -2, 1, 5}. 

Method 1: This problem is mainly a variation of Largest Sum Contiguous Subarray Problem
The idea is to update starting index whenever the sum ending here becomes less than 0.

Below is the implementation of the above approach:

C++




// C++ program to print length of the largest
// contiguous array sum
#include<bits/stdc++.h>
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;
        }
    }
     
    return (end - start + 1);
}
 
/*Driver program to test maxSubArraySum*/
int main()
{
    int a[] = {-2, -3, 4, -1, -2, 1, 5, -3};
    int n = sizeof(a)/sizeof(a[0]);
    cout << maxSubArraySum(a, n);
    return 0;
}

Java




// Java program to print length of the largest
// contiguous array sum
import java.io.*;
 
class GFG {
 
    static int 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;
            }
        }
        return (end - start + 1);
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int a[] = { -2, -3, 4, -1, -2, 1, 5, -3 };
        int n = a.length;
        System.out.println(maxSubArraySum(a, n));
    }
}

Python3




# Python3 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
 
    return (end - start + 1)
 
# Driver program to test maxSubArraySum
a = [-2, -3, 4, -1, -2, 1, 5, -3]
print(maxSubArraySum(a,len(a)))

C#




// C# program to print length of the
// largest contiguous array sum
using System;
 
class GFG {
 
    // Function to find maximum subarray sum
    static int 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;
            }
        }
        return (end - start + 1);
    }
 
    // Driver code
    public static void Main(String[] args)
    {
        int []a = {-2, -3, 4, -1, -2, 1, 5, -3};
        int n = a.Length;
        Console.Write(maxSubArraySum(a, n));
    }
}
 
// This code is contributed by parashar...

PHP




<?php
// PHP program for Bresenham’s
// Line Generation Assumptions :
 
// 1) Line is drawn from
// left to right.
// 2) x1 < x2 and y1 < y2
// 3) Slope of the line is
// between 0 and 1.
// We draw a line from lower
// left to upper right.
 
// function for line generation
function bresenham($x1, $y1, $x2, $y2)
{
$m_new = 2 * ($y2 - $y1);
$slope_error_new = $m_new - ($x2 - $x1);
for ($x = $x1, $y = $y1; $x <= $x2; $x++)
{
    echo "(" ,$x , "," , $y, ")\n";
 
    // Add slope to increment
    // angle formed
    $slope_error_new += $m_new;
 
    // Slope error reached limit,
    // time to increment y and
    // update slope error.
    if ($slope_error_new >= 0)
    {
        $y++;
        $slope_error_new -= 2 * ($x2 - $x1);
    }
}
}
 
// Driver Code
$x1 = 3; $y1 = 2; $x2 = 15; $y2 = 5;
bresenham($x1, $y1, $x2, $y2);
 
// This code is contributed by nitin mittal.
?>

Javascript




<script>
 
// JavaScript program to print length
// of the largest contiguous array sum
function maxSubArraySum(a, size)
{
    let max_so_far = Number.MIN_VALUE,
    max_ending_here = 0,start = 0,
    end = 0, s = 0;
 
    for(let 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;
        }
    }
    return (end - start + 1);
}
 
// Driver code
let a = [ -2, -3, 4, -1, -2, 1, 5, -3 ];
let n = a.length;
 
document.write(maxSubArraySum(a, n));
 
// This code is contributed by splevel62
 
</script>

Output : 

5

 

Time Complexity: O(n)
Auxiliary Space: O(1)


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