(DP 线性DP) leetcode 152. Maximum Product Subarray

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.

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这个题与最大连续和比较相似，不过这个是最大乘积子序列，所以，如果最后得到负数的话，不能舍弃掉，因为这个负数乘上接下来的数，也有可能得到最大正数。

所以，这次要建立两个变量，分别记录最小乘积和最大乘积。

C++代码：

class Solution {
public:
    int maxProduct(vector<int>& nums) {
        if(nums.size() == 0)return 0;
        if(nums.size() == 1)return nums[0];
        int n = nums.size();
        int negative = 1,positive = 1;
        vector<int> dp(n,1);
        int res = -0x3f3f3f3f;
        for(int num : nums){
            positive *= num;
            negative *= num;
            if(positive < negative){
                swap(positive,negative);
            }
            positive = max(positive,num);
            negative = min(negative,num);
            res = max(positive,res);
        }
        return res;
    }
};