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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Array Dynamic Programming

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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;
}