# https://leetcode.com/problems/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).

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

Constraints:
1 <= prices.length <= 5 * 104
1 <= prices[i] < 5 * 104
0 <= fee < 5 * 104
"""
from math import inf


def max_profit(prices: list[int], fee: int) -> int:
    n = len(prices)
    dp = [[0] * 2 for _ in range(n + 1)]

    dp[0][1] = -inf

    for i in range(1, n + 1):
        dp[i][0] = max(dp[i - 1][0], dp[i - 1][1] + prices[i - 1])
        dp[i][1] = max(dp[i - 1][1], dp[i - 1][0] - prices[i - 1] - fee)
    return dp[n][0]
