LC_Best_Time_to_Buy_and_Sell_Stock_with_Fee.py

"""
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.

Note:
0 < prices.length <= 50000.
0 < prices[i] < 50000.
0 <= fee < 50000.

"""
class Solution(object):
    def maxProfit(self, prices, fee):
        """
        :type prices: List[int]
        :type fee: int
        :rtype: int
        """
        # At every i+1 th day, we either sell or dont sell.
        # At the end we return cash
        cash, hold = 0, -prices[0]
        for i in range(1,len(prices)):
            # hold - holds the -buyprice so hold+prices[i] will give us the profit
            # subtract the fees.
            # sell stock
            cash = max(cash, hold + prices[i] - fee)
            # day one we dont have any cash. so it will be -prices
            # buy stock
            hold = max(hold, cash - prices[i])
        return cash