Maximum Sum Circular Subarray

class Solution {
public:
    int maxSumCircularSubarray(vector<int>& arr) {
        int currentMax = 0;
        int currentMin = 0;
        int highestSum = arr[0];
        int lowestSum = arr[0];
        int sumTotal = 0;
        
        for (int value: arr) {
            // Standard Kadane's to find maximum subarray sum
            currentMax = max(currentMax, 0) + value;
            highestSum = max(highestSum, currentMax);
            
            // Inverse Kadane's to find the minimum subarray sum
            currentMin = min(currentMin, 0) + value;
            lowestSum = min(lowestSum, currentMin);
            
            sumTotal += value;  
        }

        if (sumTotal == lowestSum) {
            return highestSum;
        }
        
        return max(highestSum, sumTotal - lowestSum);
    }
};

The given C++ code implementation addresses the problem of finding the maximum sum of a circular subarray from a given list of integers. Here's how the algorithm effectively tackles this problem:

• Initialize variables to keep track of the maximum and minimum subarray sums (currentMax, currentMin), the highest and lowest sums found (highestSum, lowestSum), and the total sum of the array (sumTotal).
• Iterate through each element in the array:
  • Update currentMax using a variation of Kadane’s algorithm to capture the maximum subarray sum without wrapping.
  • Update currentMin simultaneously, implementing an inverted form of Kadane’s algorithm to determine the minimum subarray sum.
  • Accumulate the total sum of the array in sumTotal.
• Establish a check-condition to ensure the entire array sum is not a minimum subarray sum, which could happen if all elements are negative.
• Return the maximum value between highestSum and the difference of sumTotal and lowestSum. This step takes into consideration both the non-wrapped and wrapped subarrays.

This approach ensures the solution handles both scenarios where the maximum sum subarray is either contiguous in the regular order or spans the circular boundary of the array. Make sure the input vector is non-empty to avoid undefined behavior.

class Solution {
    public int maximumCircularSubarraySum(int[] array) {
        int currentMax = 0;
        int currentMin = 0;
        int highestSum = array[0];
        int lowestSum = array[0];
        int sum = 0;
        
        for (int value : array) {
            // Implementing maximum subarray sum using Kadane's Algorithm
            currentMax = Math.max(currentMax, 0) + value;
            highestSum = Math.max(highestSum, currentMax);
            
            // Implementing minimum subarray sum to find out the minimum subarray
            currentMin = Math.min(currentMin, 0) + value;
            lowestSum = Math.min(lowestSum, currentMin);
            
            sum += value;
        }

        if (sum == lowestSum) {
            return highestSum;
        }
        
        return Math.max(highestSum, sum - lowestSum);
    }
}

The problem at hand aims to solve the Maximum Sum Circular Subarray using Java. The provided solution implements a variation of Kadane's Algorithm to find both the maximum subarray sum in linear runtime and handle the circular nature of the problem. Below are the breakdowns and pertinent details of the solution:

1. Initialization:

   • Initialize variables to track maximum and minimum sums (highestSum and lowestSum) as well as the current maximum and minimum during iteration (currentMax and currentMin).
   • The starting values for highestSum and lowestSum are the first element of the array to ensure proper comparison across the single-element array case.

2. Iteration over the Array:

   • For each element in the array, update the currentMax sum, which represents the sum of the subarray ending at the current index. If currentMax drops below zero, reset it to zero (Kadane's reset step).
   • Simultaneously, track the currentMin sum for finding the minimum subarray sum to compute the maximum circular sum later.
   • Maintain an overall sum of the array elements for later calculations.

3. Circular Subarray Handling:

   • After iterating through the array, extract the subarray contributing the least to the overall array sum (using sum - lowestSum).
   • This helps in managing the circular aspect where the maximum sum subarray might span from the end of the array back to the beginning.

4. Edge Case:

   • If the total sum of the array and the minimum subarray sum are the same, this indicates that all elements are either the same, or the only maximum sum subarray option available isn't improved by any circular computation. Thus, return the highest sum from the standard Kadane's result.

5. Result Calculation:

   • Determine the result by comparing highestSum (from standard Kadane's algorithm) and sum - lowestSum (considering circular subarray possibilities).

This solution efficiently computes the maximum circular subarray sum in O(n) time by cleverly utilizing the modifications to Kadane's Algorithm and handling unique aspects brought about by the circular array constraint.