188. Best Time to Buy and Sell Stock IV

https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iv/

Python

Bottom Up DP

• 3維的DP

from math import inf


class Solution:
    def maxProfit(self, k: int, prices: List[int]) -> int:
        if not prices or not k:
            return 0

        dp = [
            [
                [-inf]*2 for _ in range(k+1)

            ] for _ in range(len(prices))
        ]

        dp[0][0][0] = 0
        dp[0][1][1] = -prices[0]

        for i in range(1, len(prices)):
            for j in range(k+1):
                dp[i][j][0] = max(dp[i-1][j][0], dp[i-1][j][1]+prices[i])

                if j > 0:
                    dp[i][j][1] = max(dp[i-1][j][1], dp[i-1][j-1][0]-prices[i])

        return max(dp[len(prices)-1][j][0] for j in range(k+1))