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.

对于Product Subarray，要考虑到一种特殊情况，即负数和负数相乘：如果前面得到一个较小的负数，和后面一个较大的负数相乘，得到的反而是一个较大的数，如{2，-3，-7}，所以，我们在处理乘法的时候，除了需要维护一个局部最大值，同时还要维护一个局部最小值，由此，可以写出如下的转移方程式：

max_copy[i] = max_local[i]
max_local[i + 1] = Max(Max(max_local[i] * A[i], A[i]), min_local * A[i])

min_local[i + 1] = Min(Min(max_copy[i] * A[i], A[i]), min_local * A[i])

</pre><pre>

class Solution {
public:int maxProduct(vector<int>& nums) {int n=nums.size();int pmax = nums[0];int pmin = nums[0];int ans = nums[0];for (int i = 1; i < n; i++) {int tmax = nums[i] * pmax;int tmin = nums[i] * pmin;pmax = max(nums[i], max(tmax, tmin));pmin = min(nums[i], min(tmax, tmin));ans = max(pmax, ans);}return ans;}
};

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