feat(dp): buy & sell stock

Author: BrianLusina

puzzles/arrays/max_profit/README.md renamed to algorithms/dynamic_programming/buy_sell_stock/README.md

@@ -85,3 +85,46 @@ Input: prices = [7,6,4,3,1]
 Output: 0
 Explanation: In this case, no transaction is done, i.e. max profit = 0.
 ```
+
+---
+
+# Best Time To Buy and Sell Stock With Transaction Fee
+
+You are given an array prices where prices[i] is the price of a given stock on the ith day, and an integer fee
+representing a transaction fee.
+
+Find the maximum profit you can achieve. You may complete as many transactions as you like, but you need to pay the
+transaction fee for each transaction.
+
+Note:
+
+You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).
+The transaction fee is only charged once for each stock purchase and sale.
+
+Example 1:
+
+```text
+Input: prices = [1,3,2,8,4,9], fee = 2
+Output: 8
+Explanation: The maximum profit can be achieved by:
+- Buying at prices[0] = 1
+- Selling at prices[3] = 8
+- Buying at prices[4] = 4
+- Selling at prices[5] = 9
+The total profit is ((8 - 1) - 2) + ((9 - 4) - 2) = 8.
+```
+
+Example 2:
+
+```text
+Input: prices = [1,3,7,5,10,3], fee = 3
+Output: 6
+```
+
+# Related topics
+
+- Arrays
+- Dynamic Programming
+- Greedy
+
+

puzzles/arrays/max_profit/__init__.py renamed to algorithms/dynamic_programming/buy_sell_stock/__init__.py

@@ -1,3 +1,4 @@
+import math
 from typing import List
 
 
@@ -93,3 +94,29 @@ def max_profit_3(prices: List[int]) -> int:
         profit = max(profit, forward_profit[day] + backward_profit[day])
 
     return profit
+
+
+def max_profit_with_fee(prices: List[int], fee: int) -> int:
+    # initially, there is no cash
+    initial_cash = -math.inf
+    # initial profit is 0
+    current_profit = 0
+
+    for price in prices:
+        # Maximum cash in hand with shares
+        # Either
+        # 1. withold prev share in which case your cash in hand will not change,
+        # 2. or assume there was no currently bought share but you want to buy it today -
+        #         In this case: your current cash in hand with shares will be your previous cash
+        #         in hand without shares minus buying price of the share today.
+        initial_cash = max(initial_cash, current_profit - price)
+
+        # Maximum cash in hand without shares
+        # Either
+        # 1. withold money without shares in which case your cash in hand will not change,
+        # 2. or assume you previously bought the share and you are going to sell that today -
+        #         In this case : your current cash in hand without shares will be your previous cash
+        #         in hand with shares plus the current selling price minus transaction fee
+        current_profit = max(current_profit, initial_cash + price - fee)
+
+    return current_profit

puzzles/arrays/max_profit/test_max_profit.py renamed to algorithms/dynamic_programming/buy_sell_stock/test_max_profit.py

@@ -0,0 +1,51 @@
+import unittest
+
+from . import max_profit_with_fee
+
+
+class MaxProfitWithFeeTestCases(unittest.TestCase):
+    def test_empty_array(self):
+        nums = []
+        expected = 0
+        actual = max_profit_with_fee(nums, 4)
+        self.assertEqual(expected, actual)
+
+    def test_prices_are_same(self):
+        nums = [1, 1, 1, 1]
+        expected = 0
+        actual = max_profit_with_fee(nums, 4)
+        self.assertEqual(expected, actual)
+
+    def test_single_element_array(self):
+        nums = [1]
+        expected = 0
+        actual = max_profit_with_fee(nums, 1)
+        self.assertEqual(expected, actual)
+
+    def test_4(self):
+        """should return 8 for prices=1,3,2,8,4,9 and fee of 2"""
+        nums = [1, 3, 2, 8, 4, 9]
+        fee = 2
+        expected = 8
+        actual = max_profit_with_fee(nums, fee)
+        self.assertEqual(expected, actual)
+
+    def test_5(self):
+        """should return 6 for prices=1,3,7,5,10,3 and fee of 3"""
+        nums = [1, 3, 7, 5, 10, 3]
+        fee = 3
+        expected = 6
+        actual = max_profit_with_fee(nums, fee)
+        self.assertEqual(expected, actual)
+
+    def test_6(self):
+        """should return 13 for prices=[1,4,6,2,8,3,10,14] and fee of 3"""
+        nums = [1, 4, 6, 2, 8, 3, 10, 14]
+        fee = 3
+        expected = 13
+        actual = max_profit_with_fee(nums, fee)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()