Maximum Sum Circular Subarray

The key idea

The best subarray is either a normal (non-wrapping) one, found by ordinary Kadane, OR a wrapping one. A wrapping subarray's sum equals the total of the array minus the minimum non-wrapping subarray (the middle slice you leave out). So the answer is max(maxKadane, total - minKadane). Edge case: when every element is negative, total - minKadane would pick the empty middle, so just return maxKadane.

Problem

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.

Constraints

n == nums.length
1 <= n <= 3 * 10^4
-3 * 10^4 <= nums[i] <= 3 * 10^4

Examples

Input: nums = [1,-2,3,-2] Output: 3

Input: nums = [5,-3,5] Output: 10

Input: nums = [-3,-2,-3] Output: -2

Complexity

Time: O(n) Space: O(1)

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