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# LeetCode 918. 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**.

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

[English Version in Youtube](https://youtu.be/oCDQ3JMZXw4)

[中文版解答Youtube Link](https://youtu.be/o_qM8AJUjt4)

[中文版解答Bilibili Link](https://www.bilibili.com/video/BV1G5411A7H3/)

```
class Solution {
public:
    int maxSubarraySumCircular(vector<int>& A) {
        int sum = 0;
        int cur_max = 0;
        int max_so_far = INT_MIN;
        int cur_min = 0;
        int min_so_far = INT_MAX;
        
        for (int v : A) {
            cur_max = max(cur_max + v, v);
            max_so_far = max(max_so_far, cur_max);
            cur_min = min(cur_min + v, v);
            min_so_far = min(min_so_far, cur_min);
            
            sum += v;
        }
        
        if (max_so_far <= 0) return max_so_far;
        return max(max_so_far, sum - min_so_far);
    }
};
```