152. Maximum Product Subarray

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.

这道题需要注意的是当一个整数，后面有一个负数时，相乘会变小，再乘以一个负数又会变大，所以需要记录这个极小数。动态方程如下：

1、maxDP = max(maxDP*nums[n+1], nums[i+1], minDP*nums[n+1]);

2、minDP = min(maxDP*nums[n+1], nums[i+1], minDP*nums[n+1]);

3、max = max(max, maxDP);

从0开始，代码如下：

public class Solution {    public int maxProduct(int[] nums) {        if (nums.length == 0 || nums == null) {            return 0;        }        int minDP = nums[0], maxDP = nums[0], max = nums[0];        for (int i = 1; i < nums.length; i ++) {            int premaxDP = maxDP;            maxDP = Math.max(Math.max(maxDP * nums[i], nums[i]), minDP * nums[i]);            minDP = Math.min(Math.min(premaxDP * nums[i], nums[i]), minDP * nums[i]);            max = Math.max(max, maxDP);        }        return max;    }}