Maximum Sum Circular Subarray

curr_max = max(num, curr_max + num)

Update current maximum subarray sum ending at this element.

This line embodies Kadane's algorithm's core logic, deciding whether to start a new subarray at the current element or extend the existing one, which is essential for finding the maximum subarray sum efficiently.

curr_min = min(num, curr_min + num)

Update current minimum subarray sum ending at this element.

This line applies the minimum variant of Kadane's algorithm, deciding whether to start a new minimum subarray or extend the existing one, which is crucial for computing the wrapped subarray sum.

if best_max < 0:

Check if the maximum subarray sum is negative (all elements negative).

This condition identifies the all-negative scenario, ensuring the algorithm returns the correct maximum subarray sum without incorrectly using the wrapped sum formula.

return max(best_max, total - best_min)

Return the maximum between the linear max subarray sum and the wrapped subarray sum.

This return statement captures the core insight of the problem: the maximum circular subarray sum is either the maximum linear subarray sum or the total sum minus the minimum subarray sum, covering both non-wrapping and wrapping cases.

curr_max = nums[0]

Initialize current maximum subarray sum to the first element.

This initialization is critical for Kadane's algorithm to correctly track the maximum subarray sum starting from the first element.

best_max = nums[0]

Initialize best maximum subarray sum to the first element.

This variable stores the global maximum subarray sum found so far, starting with the first element to handle edge cases.

curr_min = nums[0]

Initialize current minimum subarray sum to the first element.

Tracking the minimum subarray sum is necessary to find the subarray that, when excluded, yields the maximum wrapped subarray sum.

best_min = nums[0]

Initialize best minimum subarray sum to the first element.

This variable stores the global minimum subarray sum found so far, starting with the first element to handle edge cases.

best_max = max(best_max, curr_max)

Update global maximum subarray sum if current max is greater.

Maintains the best maximum subarray sum found so far, ensuring the final answer considers all subarrays.

best_min = min(best_min, curr_min)

Update global minimum subarray sum if current min is smaller.

Keeps track of the smallest subarray sum found so far, which is necessary to compute the maximum wrapped subarray sum.

return best_max

Return the maximum subarray sum if all elements are negative.

Returns the correct result for the all-negative case, avoiding incorrect wrapped sum calculations.

total += num

Add current element to total sum.

Accumulates the sum of all elements, which is essential for calculating the wrapped subarray sum.

for i in range(1, len(nums)):

Start iterating over nums from the second element.

The loop processes each element to update total, maximum, and minimum subarray sums, enabling a single-pass solution.

total = nums[0]

Initialize total sum with the first element of nums.

Starting total with the first element sets the baseline for accumulating the sum of all elements, which is essential for calculating the wrapped subarray sum later.

num = nums[i]

Assign current element to num for clarity.

Using a descriptive variable name improves readability and reduces repeated indexing.