3.Maximum Sum Circular Subarray

Given a circular array C of integers represented by A, find the maximum possible sum of a non-empty subarray of C.

Example 1:
Input: [1,-2,3,-2]
Output: 3
Explanation: Subarray [3] has maximum sum 3

Example 2:
Input: [5,-3,5]
Output: 10
Explanation: Subarray [5,5] has maximum sum 5 + 5 = 10

Example 3:
Input: [3,-1,2,-1]
Output: 4
Explanation: Subarray [2,-1,3] has maximum sum 2 + (-1) + 3 = 4

Example 4:
Input: [3,-2,2,-3]
Output: 3
Explanation: Subarray [3] and [3,-2,2] both have maximum sum 3

Example 5:
Input: [-2,-3,-1]
Output: -1
Explanation: Subarray [-1] has maximum sum -1

Solution: (Kadane algorithm)

Approach: We find the max subarray sum We find the sum of non-contributing element by inverting array and finding max sum. Compare the sum obtained by both cases and return the maximum of the two sums.

class Solution
{
public:
    int kadane(vector<int> v)
    {

        int s = 0;
        int maxS = INT_MIN;

        for (int i = 0; i < v.size(); i++)
        {
            s = s + v[i];

            if (s > maxS)
            {
                maxS = s;
            }

            if (s < 0)
            {
                s = 0;
            }
        }
        return maxS;
    }

    int maxSubarraySumCircular(vector<int> &A)
    {

        int maxSum = kadane(A);
        
        int sumArr = 0;
        for (int i = 0; i < A.size(); i++)
        {
            sumArr = sumArr + A[i];
            A[i] = A[i] * -1;
        }

        int minSum = -kadane(A);
        
        if(minSum == sumArr){
            return maxSum;
        }
        
        return max(maxSum, sumArr - minSum);
    }
};

Time Complexity: O(n)