[leetcode] 918. Maximum Sum Circular Subarray

Description

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

分析

题目的意思是：求一个循环数组的子序列和的最大值，代码一是我自己包里破解的，分了三种情况，所有的都为负，所有的都为正，有正也有负。比较死板。
代码二就厉害了，用了动态规划，一个循环就搞定了,

dp[j]=max(A[i],A[i+1],...,A[j])

dp[j+1]=A[j+1]+max(dp[j],0)

大概意思dp[j]就定义为A[i]~A[j]最大的和，考虑到dp[j]可能为负数，所以最后公式就变成了dp[j+1]=A[j+1]+max(dp[j],0)了

代码一

class Solution:
    def maxSubarraySumCircular(self, A: List[int]) -> int:
        max_value=float("-inf")
        t=0
        flag=True
        for i in range(len(A)):
            if(A[i]<0):
                flag=False
                break
            t+=A[i]
        if(flag):
            return t
            
        for i in range(len(A)):
            sum_a=0
            if(A[i]>0):
                sum_a=0
                for j in range(i,i+len(A)):
                    a=j%len(A)
                    sum_a+=A[a]
                    max_value=max(sum_a,max_value)
                    if(sum_a<0):
                        break
        if(max_value==float("-inf")):
            for i in range(len(A)):
                max_value=max(max_value,A[i])
        return max_value
               

代码二

class Solution:
    def maxSubarraySumCircular(self, A: List[int]) -> int:
        ans=cur=0
        for x in A:
            cur=x+max(cur,0)
            ans=max(ans,cur)
        return ans

参考文献

[LeetCode]Notes and A Primer on Kadane’s Algorithm