Best Time to Buy and Sell Stock III

Author: gavinfish

123 Best Time to Buy and Sell Stock III.py

@@ -0,0 +1,37 @@
+'''
+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).
+'''
+
+class Solution(object):
+    def maxProfit(self, prices):
+        """
+        :type prices: List[int]
+        :rtype: int
+        """
+        total_max_profit = 0
+        n = len(prices)
+        first_profits = [0] * n
+        min_price = float('inf')
+
+        for i in range(n):
+            min_price = min(min_price, prices[i])
+            total_max_profit = max(total_max_profit, prices[i] - min_price)
+            first_profits[i] = total_max_profit
+
+        max_profit = 0
+        max_price = float('-inf')
+        for i in range(n - 1, 0, -1):
+            max_price = max(max_price, prices[i])
+            max_profit = max(max_profit, max_price - prices[i])
+            total_max_profit = max(total_max_profit, max_profit + first_profits[i - 1])
+        return total_max_profit
+
+
+if __name__ == "__main__":
+    assert Solution().maxProfit([2, 4, 6, 1, 3, 8, 3]) == 11
+    assert Solution().maxProfit([1, 2]) == 1