# 714. Best Time to Buy and Sell Stock with Transaction Fee

Your are given an array of integers prices, for which the i-th element is the price of a given stock on day i; and a non-negative integer fee representing a transaction fee.

You may complete as many transactions as you like, but you need to pay the transaction fee for each transaction. You may not buy more than 1 share of a stock at a time (ie. you must sell the stock share before you buy again.)

Return the maximum profit you can make.

Example 1:

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.

# Solution

Approach 1: DP with 2 states.

# Code (Python)

Approach 1:

    def maxProfit(self, prices: List[int], fee: int) -> int:
        if len(prices) < 2:
            return 0
        
        # same definition with cooldown
        hold = [-prices[0]]
        sold = [0]
        for price in prices[1:]:
            hold.append(max(hold[-1], sold[-1] - price))
            sold.append(max(sold[-1], hold[-2] + price - fee))
        
        return sold[-1]

# Code (C++)

Approach 1:

Approach 2: