【LeetCode】【152. Maximum Product Subarray】（python版)

Description：
Given an integer array nums, find the contiguous subarray within an array (containing at least one number) which has the largest product.

Example 1:

Input: [2,3,-2,4]
Output: 6
Explanation: [2,3] has the largest product 6.

Example 2:

Input: [-2,0,-1]
Output: 0
Explanation: The result cannot be 2, because [-2,-1] is not a subarray.

思路：
本题要求连续子数组的最大乘积，思路与求连续子数组的最大和相似，都是采用动态规划，$maxvalue[i]$表示以$a[i]$为结尾的子数组中最大乘积，同时维护一个全局最大值$globalmax$，记录$maxvalue[i]$中的最大值。与求子数组的最大和不同的是，还需要维记录子数组最小乘积$minvalue[i]$，因为可能会出现 负 × 负 = 正的情况。并且最大最小乘积只可能出现在
$(maxvalue[i-1] ×a[i], minvalue[i-1] ×a[i], a[i])$三者之间。

下面以[2,3,-2,4]演示求解过程

子数组末尾数字	最大乘积	最小乘积
2	2	2
3	6	3
-2	-2	-12
4	4	-48

代码实现如下：

    class Solution(object):
    def maxProduct(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        maxvalue = minvalue = nums[0]
        globalmax = nums[0]
        for i in range(1, len(nums)):
            lastmax = maxvalue
            maxvalue = max(minvalue * nums[i], lastmax * nums[i], nums[i])
            minvalue = min(minvalue * nums[i], lastmax * nums[i], nums[i])
            globalmax = max(globalmax, maxvalue)
        return globalmax