46.Maximum Product Subarray（最大乘积子数组）

Level：

  Medium

题目描述：

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.

思路分析：

  因为是乘积的最大值，可能是若干个正数相乘得到，也可能是若干个负数相乘得到；因此，必须保留前一阶段的最大值和最小值k+1在内结尾的最小乘积序列为：

min(k+1) = min(min(k) * a[k+1], max(k) * a[k+1], a[k+1])

代码：

public class Solution{
    public int maxProduct(int []nums){
        int dp=nums[0];
        int maxk=nums[0]; //第K阶段的最大值
        int mink=nums[0]; //第K阶段的最小值
        int maxcur=maxk;
        int mincur=mink;
        for(int i=1;i<nums.length;i++){
        maxk=Math.max(Math.max(maxcur*nums[i],mincur*nums[i]),nums[i]);
          mink=Math.min(Math.min(maxcur*nums[i],mincur*nums[i]),nums[i]);
            maxcur=maxk;
            mincur=mink;
            dp=Math.max(dp,maxcur);
        }
        return dp;
    }
}