918. Maximum Sum Circular Subarray
[Medium] 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
題目:給定一個由整數數組 A
表示的環形數組 C
,求 C
的非空子數組的最大可能和。
思路:參考lee215。如果最大子數組和存在於環中,那麼等價於數組總和減去最小子數組和。不能簡單的將數組拼接後採用LeetCode53. Maximum Subarray,這樣會出現位置重疊的情況,如A=[1]
,那麼拼接後A'=[1,1]
,直接按照Kadane’s algorithm計算會出現最大子數組和爲2的錯誤答案。
示意圖轉自motorix:
class Solution {
public:
int maxSubarraySumCircular(vector<int>& A) {
int maxsum = INT_MIN, minsum = INT_MAX;
int curmax = INT_MIN, curmin = INT_MAX;
int total = 0;
for(int num : A){
curmax = num + max(curmax, 0);
curmin = num + min(curmin, 0);
maxsum = max(maxsum, curmax);
minsum = min(minsum, curmin);
total += num;
}
// 考慮數組中都是負數的情況
return curmax > 0 ? max(maxsum, total-minsum) : maxsum;
}
};