Could you outline the steps for writing a JavaScript function that finds the highest sum of any contiguous subarray in an integer array?

Question Analysis

The question asks you to write a JavaScript function that identifies the highest sum of any contiguous subarray in a given integer array. This is a classic problem known as the "Maximum Subarray Problem," and it can be efficiently solved using Kadane's Algorithm. The challenge is to iterate through the array while maintaining a running sum of the subarray and updating the maximum sum found so far. The solution should handle edge cases, such as when all numbers are negative.

Answer

To solve this problem using Kadane's Algorithm, follow these steps:

1. Initialize Variables:

   • Start by initializing two variables: maxSoFar and maxEndingHere. Set both to the first element of the array. maxSoFar will keep track of the highest sum found, while maxEndingHere will track the current subarray sum.

2. Iterate Through the Array:

   • Loop through the array starting from the second element.
   • For each element, update maxEndingHere to be the maximum of the current element itself or the current element plus maxEndingHere. This step decides whether to add the current element to the existing subarray or start a new subarray.

3. Update Maximum Sum:

   • Update maxSoFar to be the maximum of maxSoFar and maxEndingHere. This ensures you always have the highest sum encountered so far.

4. Return the Result:

   • After iterating through the array, maxSoFar will contain the highest sum of any contiguous subarray.

Here's the JavaScript function implementing the above logic:

function maxSubArraySum(arr) {
    if (arr.length === 0) return 0; // Handle the edge case of an empty array

    let maxSoFar = arr[0];
    let maxEndingHere = arr[0];

    for (let i = 1; i < arr.length; i++) {
        maxEndingHere = Math.max(arr[i], maxEndingHere + arr[i]);
        maxSoFar = Math.max(maxSoFar, maxEndingHere);
    }

    return maxSoFar;
}

Key Points:

• This solution runs in O(n) time complexity, making it efficient for large arrays.
• It only uses O(1) extra space, as it updates the sums in place.
• The function assumes the input array has at least one number. If the array could be empty, additional checks would be needed.