leetcode_152题——Maximum Product Subarray（动态规划）

Maximum Product Subarray

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Question  Solution 

 

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.

 

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而对于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])

#include<iostream>

#include<vector>

#include<math.h>

using namespace std;





int maxProduct(vector<int>& nums)

{

	int len=nums.size();

	if(len==1)

		return nums[0];



	int maxm=nums[0];

	int minm=nums[0];

	int re=nums[0];

	for(int i=1;i<len;i++)

	{

		int a=max(max(maxm*nums[i],nums[i]),minm*nums[i]);

		int b=min(min(maxm*nums[i],nums[i]),minm*nums[i]);

		if(a>re)

			re=a;

		if(b>re)

			re=b;

		maxm=a;

		minm=b;

	}

	return re;

}



int main()

{

	int ary[4]={2,3,-2,4};

	vector<int> vec(ary,ary+4);

	cout<<maxProduct(vec)<<endl;

}