Leetcode 152. Maximum Product Subarray

152. Maximum Product Subarray

• Total Accepted: 65740
• Total Submissions: 286731
• Difficulty: Medium

Find the contiguous subarray within an array (containing at least one number) which has the largest product.

For example, given the array [2,3,-2,4],
the contiguous subarray [2,3] has the largest product = 6.

思路：DP。注意到乘积变化的连续性，设nums[i]所在子序列的最大值为Smax[i]，nums[i]所在子序列的最小值为Smin[i]。

那么有

1. Smax[i]=max(Smax[i]*nums[i-1],Smin[i]*nums[i-1],nums[i]);

2. Smin[i]=min(Smax[i]*nums[i-1],Smin[i]*nums[i-1],nums[i])。

所以，result=max(Smax[0]...Smax[n-1])。

代码：

class Solution {
public:
    int maxProduct(vector<int>& nums) {
        int result=nums[0],maxproduct=nums[0],minproduct=nums[0],i,n=nums.size();
        for(i=1;i<n;i++){
            int temp=maxproduct;
            maxproduct=max(max(maxproduct*nums[i],minproduct*nums[i]),nums[i]);
            minproduct=min(min(temp*nums[i],minproduct*nums[i]),nums[i]);
            result=max(maxproduct,result);
        }
        return result;
    }
};