How do you solve Maximum Sum Circular Subarray on LeetCode?

Maximum Sum Circular Subarray (LeetCode #918) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Kadane's algorithm is a powerful technique for finding maximum subarray sums efficiently.

What is the brute force solution for Maximum Sum Circular Subarray?

The brute force approach for Maximum Sum Circular Subarray is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible subarray to find the maximum sum. This is done by iterating through all possible starting and ending points of subarrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Sum Circular Subarray?

Maximum Sum Circular Subarray uses the following concepts: Array, Divide and Conquer, Dynamic Programming, Queue, Monotonic Queue. The recommended patterns to study are: Kadane's Algorithm, Dynamic Programming, Sliding Window.

What are the interview tips for Maximum Sum Circular Subarray?

Always clarify the problem constraints and edge cases before diving into coding. Think about how you can break down the problem using known algorithms like Kadane's. Practice explaining your thought process as you code, as this shows your understanding to the interviewer.

What are common mistakes when solving Maximum Sum Circular Subarray?

Forgetting to handle cases where all elements are negative, which can lead to incorrect results. Not considering the circular nature of the array properly, leading to missed maximum sums.

#918

Maximum Sum Circular Subarray

Medium

ArrayDivide and ConquerDynamic ProgrammingQueueMonotonic QueueKadane's AlgorithmDynamic ProgrammingSliding Window

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Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution leverages Kadane's algorithm to find the maximum sum of a non-circular subarray and the maximum sum of a circular subarray by calculating the total sum and the minimum subarray sum. The result is the maximum of these two values.

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Algorithm

5 steps

1Step 1: Use Kadane's algorithm to find the maximum subarray sum (max_kadane).
2Step 2: Calculate the total sum of the array.
3Step 3: Use Kadane's algorithm to find the minimum subarray sum (min_kadane).
4Step 4: Calculate the maximum circular sum as total_sum - min_kadane.
5Step 5: Return the maximum of max_kadane and max_circular_sum, ensuring to handle cases where all numbers are negative.

solution.py13 lines

1def maxSubarraySumCircular(nums):
2    def kadane(arr):
3        max_sum = current_sum = arr[0]
4        for num in arr[1:]:
5            current_sum = max(num, current_sum + num)
6            max_sum = max(max_sum, current_sum)
7        return max_sum
8
9    max_kadane = kadane(nums)
10    total_sum = sum(nums)
11    min_kadane = kadane([-num for num in nums])
12    max_circular = total_sum + min_kadane
13    return max(max_kadane, max_circular) if max_kadane > 0 else max_kadane

ℹ

Complexity note: This complexity is linear because we only traverse the array a constant number of times (twice in total) to calculate the maximum and minimum subarray sums.

1Kadane's algorithm is a powerful technique for finding maximum subarray sums efficiently.
2Circular subarrays can be handled by considering both the maximum non-circular and circular cases.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.