> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Maximum Sum Circular Subarray Python Solution

> Tested Python solution for LeetCode 918 with 18 pytest cases. Generate a practice environment with lcpy.

LeetCode 918, Medium. Topics: Array, Divide and Conquer, Dynamic Programming, Queue, Monotonic Queue. [View on LeetCode](https://leetcode.com/problems/maximum-sum-circular-subarray/description/).

Generate this problem as a practice environment: tested reference solution, 18 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 918   # by problem number
lcpy gen -s maximum_sum_circular_subarray   # by problem name
```

## Problem

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`.

### Examples

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

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

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

### Constraints

* `n == nums.length`
* 1 \<= n \<= 3 \* 10^4
* -3 \* 10^4 \<= nums\[i] \<= 3 \* 10^4

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/maximum_sum_circular_subarray/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/maximum_sum_circular_subarray/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(n)
    # Space: O(1)
    def max_subarray_sum_circular(self, nums: list[int]) -> int:
        total = 0
        cur_max = 0
        cur_min = 0
        max_sum = nums[0]
        min_sum = nums[0]

        for num in nums:
            total += num
            cur_max = max(num, cur_max + num)
            max_sum = max(max_sum, cur_max)
            cur_min = min(num, cur_min + num)
            min_sum = min(min_sum, cur_min)

        # If all numbers are negative, total - min_sum == 0 (empty subarray) is invalid.
        if max_sum < 0:
            return max_sum
        return max(max_sum, total - min_sum)
```

## Complexity

| Time | Space |
| ---- | ----- |
| O(n) | O(1)  |

## Tags

[NeetCode 250](/catalog/neetcode-250), [NeetCode All](/catalog/neetcode).