best_buy_sell.py

from typing import List
import math


class Solution:
    def maxProfit(self, k: int, prices: List[int]) -> int:
        n = len(prices)

        # solve special cases
        if not prices or k==0:
            return 0

        if 2*k > n:
            res = 0
            for i, j in zip(prices[1:], prices[:-1]):
                res += max(0, i - j)
            return res

        # dp[i][used_k][ishold] = balance
        # ishold: 0 nothold, 1 hold
        dp = [[[-math.inf]*2 for _ in range(k+1)] for _ in range(n)]

        # set starting value
        dp[0][0][0] = 0
        dp[0][1][1] = -prices[0]

        # fill the array
        for i in range(1, n):
            for j in range(k+1):
                # transition equation
                dp[i][j][0] = max(dp[i-1][j][0], dp[i-1][j][1]+prices[i])
                # you can't hold stock without any transaction
                if j > 0:
                    dp[i][j][1] = max(dp[i-1][j][1], dp[i-1][j-1][0]-prices[i])

        res = max(dp[n-1][j][0] for j in range(k+1))
        return res


# Tests:
if __name__ == '__main__':
    Sol = Solution()
    Solve = Sol.maxProfit(k = 2, prices = [2,4,1])  # k = 2, prices = [2,4,1] -> 2
    print(Solve)