Open In App

Javascript Program for Largest Sum Contiguous Subarray

Last Updated : 30 Aug, 2024
Summarize
Comments
Improve
Suggest changes
Share
Like Article
Like
Report

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 = 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

for i=1, a[1] = -3
max_ending_here = max_ending_here + (-3)
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 0 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: 

JavaScript
// JavaScript program to find maximum 
// contiguous subarray

// Function to find the maximum 
// contiguous subarray
function maxSubArraySum(a, size) {
    let maxint = Math.pow(2, 53)
    let max_so_far = -maxint - 1
    let max_ending_here = 0

    for (let 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
let a = [-2, -3, 4, -1, -2, 1, 5, -3]
console.log("Maximum contiguous sum is",
    maxSubArraySum(a, a.length))

// This code is contributed by AnkThon

Output
Maximum contiguous sum is 7

Another approach:

JavaScript
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;
}

// Example usage:
const arr = [-2, -3, 4, -1, -2, 1, 5, -3];
const size = arr.length;
const result = maxSubarraySum(arr, size);

console.log("Maximum subarray sum is:", result);

Output
Maximum subarray sum is: 7

 Complexity Analysis:

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. 

JavaScript
// 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;
console.log("Maximum contiguous sum is ", maxSubArraySum(a, n));

Output
Maximum contiguous sum is  7

To print the subarray with the maximum sum, we maintain indices whenever we get the maximum sum.  

JavaScript
// javascript program to print largest 
// contiguous array sum    
function maxSubArraySum(a, size) {
    let max_so_far = Number.MIN_VALUE;
    let 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;
        }
    }
    console.log("Maximum contiguous sum is " + max_so_far);
    console.log("Starting index " + start);
    console.log("Ending index " + end);
}

// Driver code

let a = [-2, -3, 4, -1, -2, 1, 5, -3];
let n = a.length;
maxSubArraySum(a, n);

// This code is contributed by Rajput-Ji 

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. 

Complexity Analysis:

  • 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 refer complete article on Largest Sum Contiguous Subarray for more details!


Maximum Sum subarray
Visit Course explore course icon

Similar Reads