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Given a circular array C of integers represented by A
, find the maximum possible sum of a non-empty subarray of C.
Here, a circular array means the end of the array connects to the beginning of the array. (Formally, C[i] = A[i]
when 0 <= i < A.length
, and C[i+A.length] = C[i]
when i >= 0
.)
Also, a subarray may only include each element of the fixed buffer A
at most once. (Formally, for a subarray C[i], C[i+1], ..., C[j]
, there does not exist i <= k1, k2 <= j
with k1 % A.length = k2 % A.length
.)
Example 1:
Input: [1,-2,3,-2]
Output: 3
Explanation: Subarray [3] has maximum sum 3
Example 2:
Input: [5,-3,5]
Output: 10
Explanation: Subarray [5,5] has maximum sum 5 + 5 = 10
Example 3:
Input: [3,-1,2,-1]
Output: 4
Explanation: Subarray [2,-1,3] has maximum sum 2 + (-1) + 3 = 4
Example 4:
Input: [3,-2,2,-3]
Output: 3
Explanation: Subarray [3] and [3,-2,2] both have maximum sum 3
Example 5:
Input: [-2,-3,-1]
Output: -1
Explanation: Subarray [-1] has maximum sum -1
Note:
-30000 <= A[i] <= 30000
1 <= A.length <= 30000
[Array]
Hints
Hint 1
For those of you who are familiar with the Kadane's algorithm, think in terms of that. For the newbies, Kadane's algorithm is used to finding the maximum sum subarray from a given array. This problem is a twist on that idea and it is advisable to read up on that algorithm first before starting this problem. Unless you already have a great algorithm brewing up in your mind in which case, go right ahead!
Hint 2
What is an alternate way of representing a circular array so that it appears to be a straight array?
Essentially, there are two cases of this problem that we need to take care of. Let's look at the figure below to understand those two cases:
Hint 3
The first case can be handled by the good old Kadane's algorithm. However, is there a smarter way of going about handling the second case as well?