LeetCode - 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

 

ChatGPT's Solution:

class Solution:
    def maxSubarraySumCircular(self, nums: List[int]) -> int:
        def kadane(nums: List[int]) -> int:
            max_sum = curr_sum = nums[0]
            for num in nums[1:]:
                curr_sum = max(num, curr_sum + num)
                max_sum = max(max_sum, curr_sum)
            return max_sum
        
        total_sum = sum(nums)
        max_kadane = kadane(nums)  # Max subarray sum in non-circular case

        # Min subarray sum to find max circular sum
        min_sum = curr_min = nums[0]
        for num in nums[1:]:
            curr_min = min(num, curr_min + num)
            min_sum = min(min_sum, curr_min)
        
        max_circular = total_sum - min_sum if total_sum != min_sum else max_kadane

        return max(max_kadane, max_circular)

 

 

Explanation:

1. Kadane’s Algorithm (kadane(nums)):

   • Finds the maximum subarray sum for the non-circular case.

2. Total Sum (total_sum):

   • Computes the sum of all elements in nums.

3. Min Subarray Sum (min_sum):

   • Finds the minimum subarray sum using a variation of Kadane’s Algorithm.

4. Max Circular Sum:

   • If the whole array isn't the min subarray, calculate total_sum - min_sum.

   • Otherwise, return max_kadane (to avoid an empty subarray).

5. Return the Maximum of the Two Cases:

   • The maximum subarray sum is the greater of max_kadane (non-circular) and max_circular (circular).