[leetcode 714] best time to buy and sell stock with transaction fee

Question

Leetcode 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.

Note:

1. 0 < prices.length <= 50000.
2. 0 < prices[i] < 50000.
3. 0 <= fee < 50000.

Examples

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

Method 1

On each day, we hold two values represent our profit in two states: if we have cash, or if we hold stock.

1. cash[i] = max(cash[i-1], hold[i-1] + price[i] - fee)
2. hold[i] = max(hold[i-1], cash[i-1] - price[i])

Code

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