Algorithm

Problem Name: 918. Maximum Sum Circular Subarray

Given a circular integer array `nums` of length `n`, return the maximum possible sum of a non-empty subarray of `nums`.

A circular array means the end of the array connects to the beginning of the array. Formally, the next element of `nums[i]` is `nums[(i + 1) % n]` and the previous element of `nums[i]` is `nums[(i - 1 + n) % n]`.

A subarray may only include each element of the fixed buffer `nums` at most once. Formally, for a subarray `nums[i], nums[i + 1], ..., nums[j]`, there does not exist `i <= k1`, `k2 <= j` with `k1 % n == k2 % n`.

Example 1:

```Input: nums = [1,-2,3,-2]
Output: 3
Explanation: Subarray [3] has maximum sum 3.
```

Example 2:

```Input: nums = [5,-3,5]
Output: 10
Explanation: Subarray [5,5] has maximum sum 5 + 5 = 10.
```

Example 3:

```Input: nums = [-3,-2,-3]
Output: -2
Explanation: Subarray [-2] has maximum sum -2.
```

Constraints:

• `n == nums.length`
• `1 <= n <= 3 * 104`
• `-3 * 104 <= nums[i] <= 3 * 104`

Code Examples

#1 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const maxSubarraySumCircular = function(A) {
let minSum = Infinity, sum = 0, maxSum = -Infinity, curMax = 0, curMin = 0
for(let a of A) {
sum += a
curMax = Math.max(curMax + a, a);
maxSum = Math.max(maxSum, curMax);
curMin = Math.min(curMin + a, a);
minSum = Math.min(minSum, curMin);
}
return  maxSum > 0 ? Math.max(maxSum, sum - minSum) : maxSum;
};
``````
Copy The Code &

Input

cmd
nums = [1,-2,3,-2]

Output

cmd
3

#2 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def maxSubarraySumCircular(self, A):
lMn, rMx, res, lSm, rSm, preSm = float("inf"), [-float("inf")] * (len(A) + 1), -float("inf"), 0, 0, 0
for i in range(len(A) - 1, -1, -1):
rSm += A[i]
rMx[i] = max(rMx[i + 1], rSm)
for i in range(len(A)):
preSm += A[i]
lMn = min(lMn, lSm)
res = max(res, preSm, preSm - lMn, preSm + rMx[i + 1])
lSm += A[i]
return res
``````
Copy The Code &

Input

cmd
nums = [1,-2,3,-2]

Output

cmd
3

#3 Code Example with C# Programming

```Code - C# Programming```

``````
using System;
using System.Linq;

namespace LeetCode
{
public class _0918_MaximumSumCircularSubarray
{
public int MaxSubarraySumCircular(int[] A)
{
int n = A.Length;
if (n == 1) return A[0];

int curr = int.MinValue, result1 = int.MinValue;
for (int i = 0; i  <  n; i++)
{
curr = A[i] + Math.Max(curr, 0);
result1 = Math.Max(result1, curr);
}

int total = A.Sum();

curr = int.MaxValue;
int result2 = int.MaxValue;
for (int i = 1; i  <  n; i++)
{
curr = A[i] + Math.Min(curr, 0);
result2 = Math.Min(result2, curr);
}
result2 = total - result2;

curr = int.MaxValue;
int result3 = int.MaxValue;
for (int i = 0; i  <  n - 1; i++)
{
curr = A[i] + Math.Min(curr, 0);
result3 = Math.Min(result3, curr);
}
result3 = total - result3;

return Math.Max(result1, Math.Max(result2, result3));
}
}
}
``````
Copy The Code &

Input

cmd
nums = [5,-3,5]

Output

cmd
10