[LeetCode]Maximum Product Subarray

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.

还是动态规划的问题，由于负数的存在，这儿要维护3个变量，local_min,local_max,global。思路可以参考博客。

DP问题的关键是写出递推公式。

1 int copy_max = local_max;
2 local_max = max(max(local_max*nums[i],local_min*nums[i]),nums[i]);
3 local_min = min(min(local_min*nums[i],copy_max*nums[i]),nums[i]);
4 global = max(global,local_max);

这就是这道题的递推公式。

 1 class Solution {
 2 public:
 3     int maxProduct(vector<int>& nums) {
 4         if(nums.size()==0) return 0;
 5         int global=nums[0],local_min=nums[0],local_max=nums[0];
 6         for(int i=1;i<nums.size();i++)
 7         {
 8             int copy_max = local_max;
 9             local_max = max(max(local_max*nums[i],local_min*nums[i]),nums[i]);
10             local_min = min(min(local_min*nums[i],copy_max*nums[i]),nums[i]);
11             global = max(global,local_max);
12         }
13         return global;
14     }
15 };