Maximum Sum Circular Subarray

This blog series attempts to solve the 500 Top Leet Code Interview Questions with the help of AI Code Assistance, such as Gemini and GPT.

Question 128:

Maximum Sum Circular Subarray

We are given a circular integer array nums, and we need to determine the maximum possible sum of a non-empty subarray. The circular property means that elements at the end of the array are adjacent to elements at the beginning.

• The subarray must be contiguous in the original array order.
• The subarray can wrap around (i.e., take elements from the end and the beginning).
• We need to consider both normal subarrays and circular subarrays.

Breakdown:

To find the maximum sum subarray in a circular array, we need to consider two cases:

1. The maximum subarray is a normal subarray (does not wrap around). This can be found using Kadane’s Algorithm.
2. The maximum subarray is a circular subarray, meaning it wraps around. This is equivalent to:
   - Taking the sum of all elements in nums, total_sum.
   - Finding the minimum sum subarray using Kadane’s Algorithm and subtracting it from total_sum.

Approach:

1. Find the maximum subarray sum using Kadane’s Algorithm (max_kadane).
2. Find the minimum subarray sum using Kadane’s Algorithm (min_kadane).