Introduction

In this blog post, we will explore how to solve the LeetCode problem "918" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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

Explanation

Here's the breakdown of the approach and the Python code:

• Key Idea: The maximum subarray sum in a circular array is either the maximum subarray sum in the normal array, or the total sum of the array minus the minimum subarray sum. The latter represents wrapping around the array.

• Kadane's Algorithm: Utilize Kadane's algorithm to find both the maximum and minimum subarray sums efficiently.

• Handle All Negatives: If all elements are negative, the maximum sum is the largest negative number.

• Complexity:

  • Runtime: O(n)
  • Storage: O(1)

Code

    def maxSubarraySumCircular(nums: list[int]) -> int:
    """
    Finds the maximum possible sum of a non-empty subarray of a circular integer array.
    """
    total_sum = 0
    max_so_far = float('-inf')
    min_so_far = float('inf')
    current_max = 0
    current_min = 0

    for num in nums:
        total_sum += num

        current_max += num
        max_so_far = max(max_so_far, current_max)
        if current_max < 0:
            current_max = 0

        current_min += num
        min_so_far = min(min_so_far, current_min)
        if current_min > 0:
            current_min = 0

    if max_so_far < 0:
        return max_so_far

    return max(max_so_far, total_sum - min_so_far)