Day 15 Maximum Sum Circular Subarray.cpp

PROBLEM:


Given a circular array C of integers represented by A, find the maximum possible sum of a non-empty subarray of C.
Here, a circular array means the end of the array connects to the beginning of the array.  (Formally, C[i] = A[i] when
0 <= i < A.length, and C[i+A.length] = C[i] when i >= 0.)
Also, a subarray may only include each element of the fixed buffer A at most once.  (Formally, for a subarray C[i],
C[i+1], ..., C[j], there does not exist i <= k1, k2 <= j with k1 % A.length = k2 % A.length.)

 
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
 
Note:

1. -30000 <= A[i] <= 30000
2. 1 <= A.length <= 30000



SOLUTION:


class Solution {
    private:
    
    int kadane(vector<int>& A)
    {
        int ans=INT_MIN,s=0;
        
        for(auto k:A)
        {
            s=max(s+k,k);
            ans=max(ans,s);
        }
        
        return ans;
    }
    
public:
    int maxSubarraySumCircular(vector<int>& A) {
        
        int s1,s2,i,n,s=0,ans;
        s1=kadane(A);       // if max subarray is in middle
        
        n=A.size();
        
        for(i=0;i<n;i++)
        {
            s+=A[i];
            A[i]=-A[i];
        }
        
        s2=kadane(A);      //max subarray sum with negative elements
        
        if(s+s2==0)
            ans=s1;
        else
            ans=max(s1,s+s2);
        
        return ans;
        
    }
};