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 (i.e., you must sell the stock before you buy again).
Example 1:
Input: [3,3,5,0,0,3,1,4]
Output: 6
Explanation: Buy on day 4 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.
             Then buy on day 7 (price = 1) and sell on day 8 (price = 4), profit = 4-1 = 3.
Example 2:
Input: [1,2,3,4,5]
Output: 4
Explanation: Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4.
             Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are
             engaging multiple transactions at the same time. You must sell before buying again.
Example 3:
Input: [7,6,4,3,1]
Output: 0
Explanation: In this case, no transaction is done, i.e. max profit = 0.
class Solution:
     def maxProfit(self, prices):
         """
         :type prices: List[int]
         :rtype: int
         """
         if not prices:
             return 0
         sell_date = [0] * len(prices)
         min_price = prices[0]
         for i in range(1, len(prices)):
             sell_date[i] = max(sell_date[i - 1], prices[i] - min_price)
             min_price = min(prices[i], min_price)
         
         max_price, profit = prices[-1], 0
         for i in range(len(prices) - 1, 0, -1):
             profit = max(profit, max_price - prices[i] + sell_date[i])
             max_price = max(max_price, prices[i])
         
         return profit
class Solution:
     def maxProfit(self, prices):
         """
         :type prices: List[int]
         :rtype: int
         """
         if not prices:
             return 0
         sell_date = [0] * len(prices)
         min_price = prices[0]
         for i in range(1, len(prices)):
             sell_date[i] = max(sell_date[i - 1], prices[i] - min_price)
             min_price = min(prices[i], min_price)
         
         max_price, profit = prices[-1], 0
         for i in range(len(prices) - 1, 0, -1):
             profit = max(profit, max_price - prices[i] + sell_date[i])
             max_price = max(max_price, prices[i])
         
         return profit