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

""" 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).

 

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.
Example 2:

Input: prices = [1,3,7,5,10,3], fee = 3
Output: 6

 """

 #cash是第一笔出价不买的现金， 是0， hold是-(arr[0]+fee)
 #对之后的每一笔出价， 如果卖出 cash = max(cash, hold + arr[i]), 如果买入 hold = max(cash - arr[i] - fee, hold)

class Solution:
    def maxProfit(self, prices: List[int], fee: int) -> int:
        cash, hold = 0, -prices[0]-fee
        for i in range(1, len(prices)):
            cash = max(cash, hold+prices[i])
            hold = max(hold, cash-prices[i]-fee)
        return cash