Say you have an array for which the i^th element is the price of a given stock on day i.

Design an algorithm to find the maximum profit. You may complete at most two transactions.

Note:

You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).

1 class Solution { 2 public: 3     int maxProfit(vector
     
       &prices) { 4         // Start typing your C/C++ solution below 5         // DO NOT write int main() function 6         if (prices.size() == 0) 7             return 0; 8              9         vector
      
        f1(prices.size());10         vector
       
         f2(prices.size());11         12         int minV = prices[0];13         f1[0] = 0;14         for(int i = 1; i < prices.size(); i++)15         {16             minV = min(minV, prices[i]);17             f1[i] = max(f1[i-1], prices[i] - minV);18         }19         20         int maxV = prices[prices.size()-1];21         f2[f2.size()-1] = 0;22         for(int i = prices.size() - 2; i >= 0; i--)23         {24             maxV = max(prices[i], maxV);25             f2[i] = max(f2[i+1], maxV - prices[i]);26         }27         28         int sum = 0;29         for(int i = 0; i < prices.size(); i++)30             sum = max(sum, f1[i] + f2[i]);31             32         return sum;33     }34 };