Best Time to Buy and Sell Stock III [LeetCode]

Say you have an array for which the ith 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).

Solution: DP,  caculate max profit both forward and backward, then return the max sum of them.

     int maxProfit(vector<int> &prices) {
         if(prices.size() <= )
             return ;

         vector<int> max_forward;
         int lowest = prices[];
         int max_profit = ;
         max_forward.push_back();
         for(int i = ; i < prices.size(); i ++ ){
             int profit = prices[i] - lowest;
             if(profit > max_profit)
                 max_profit = profit;

             max_forward.push_back(max_profit);
             lowest = min(prices[i], lowest);
         }

         int result = max_forward[max_forward.size() - ];
         vector<int> max_backward;
         int largest = prices[prices.size() - ];
         max_profit = ;
         for(int i = prices.size() - ; i >= ; i --) {
             int profit = largest - prices[i];
             max_profit = max(profit, max_profit);

             result = max(result, max_profit + max_forward[i]);

             largest = max(largest, prices[i]);
         }
         return result;
     }