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+# 123. Best Time to Buy and Sell Stock III
+
+"""
+you are given an array 'prices' where 'prices[i]' is the price of a given
+stock on the i'th day. find the maximum profit you can achieve. you may
+complete at most two transactions. note, you may not engage in multiple
+transactions simultaneously.
+"""
+
+
+class Solution(object):
+ def maxProfit(self, prices):
+ """
+ :type prices: List[int]
+ :rtype: int
+ """
+ if len(prices) == 0:
+ return 0
+ k = 2
+ states = [0] + [-float("inf") for i in range(k * 2)]
+ states[1] = -prices[0]
+ for i in range(1, len(prices)):
+ for j in range(k):
+ states[2 * j + 1] = max(states[2 * j + 1], states[2 * j] - prices[i])
+ states[2 * j + 2] = max(
+ states[2 * j + 2], states[2 * j + 1] + prices[i]
+ )
+ return max(0, states[-1])
+
+
+if __name__ == "__main__":
+ obj = Solution()
+ print(obj.maxProfit(prices=[3, 3, 5, 0, 0, 3, 1, 4]))
+ print(obj.maxProfit(prices=[1, 2, 3, 4, 5]))
+ print(obj.maxProfit(prices=[7, 6, 4, 3, 1]))