Maximum Sum Circular Subarray
Given a circular array (the last element is connected to the first element), find the maximum contiguous subarray sum.
Constraints:
- 1 <= nums.length <= 10^4
- -10^5 <= nums[i] <= 10^5
Examples:
Input: [5,-3,5]
Output: 10
Explanation: The maximum sum is obtained by taking the subarray [5, -3, 5] which has a sum of 5 + (-3) + 5 = 7. However, since the array is circular, we can also consider the subarray [5, -3, 5] as [5] + [-3, 5] which has a sum of 5 + (-3 + 5) = 7. But the maximum sum is actually obtained by taking the subarray [5, -3, 5] as [-3, 5] + [5] which has a sum of (-3 + 5) + 5 = 7. So the maximum sum is 10 which is obtained by taking the subarray [5, -3, 5] as [5] + [5, -3].
Solutions
Kadane's Algorithm
The solution uses Kadane's algorithm to find the maximum sum of a subarray. It first calculates the maximum sum of a subarray using Kadane's algorithm. Then it calculates the maximum sum of a wrapped subarray by subtracting the minimum sum of a subarray from the total sum of the array.
def maxSubarraySumCircular(nums):
max_kadane = kadane(nums) max_wrapped = [0] * len(nums) max_wrapped[0] = nums[0] for i in range(1, len(nums)):
max_wrapped[i] = max_wrapped[i - 1] + nums[i] max_sum = max(max_wrapped) return max(max_kadane, max_sum)
def kadane(nums):
max_so_far = nums[0] max_ending_here = nums[0] for i in range(1, len(nums)):
max_ending_here = max(nums[i], max_ending_here + nums[i]) max_so_far = max(max_so_far, max_ending_here) return max_so_farFollow-up:
What if the array is not circular?
