LeetCode Top Interview 150

918. Maximum Sum Circular Subarray

Medium

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

Solution

from typing import List

class Solution:
    def maxSubarraySumCircular(self, nums: List[int]) -> int:
        if len(nums) == 1:
            return nums[0]
        
        def kadane(nums: List[int], sign: int) -> int:
            curr_sum = float('-inf')
            max_sum = float('-inf')
            for num in nums:
                curr_sum = sign * num + max(curr_sum, 0)
                max_sum = max(max_sum, curr_sum)
            return max_sum
        
        sum_of_array = sum(nums)
        max_sum_subarray = kadane(nums, 1)
        min_sum_subarray = kadane(nums, -1) * -1
        
        if sum_of_array == min_sum_subarray:
            return max_sum_subarray
        else:
            return max(max_sum_subarray, sum_of_array - min_sum_subarray)

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