LeetCode918. 環形子數組的最大和

工程代碼下載 Github

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:

1. -30000 <= A[i] <= 30000
2. 1 <= A.length <= 30000

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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;
    }
};