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() <= 1)
            return 0;
            
        vector<int> max_forward;
        int lowest = prices[0];
        int max_profit = 0;
        max_forward.push_back(0);
        for(int i = 1; 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() - 1];
        vector<int> max_backward;
        int largest = prices[prices.size() - 1];
        max_profit = 0;
        for(int i = prices.size() - 2; i >= 0; 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;
    }