BestTimetoBuyandSellStockIV.py

"""
You are given an integer array prices where prices[i] is the price of a given stock on the ith day, and an integer k.

Find the maximum profit you can achieve. You may complete at most k transactions: i.e. you may buy at most k times and sell at most k times.

Note: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).



Example 1:

Input: k = 2, prices = [2,4,1]
Output: 2
Explanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.
Example 2:

Input: k = 2, prices = [3,2,6,5,0,3]
Output: 7
Explanation: Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6-2 = 4. Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.


Constraints:

1 <= k <= 100
1 <= prices.length <= 1000
0 <= prices[i] <= 1000
"""


class Solution:
    def maxProfit(self, k: int, prices: List[int]) -> int:
        n = len(prices)
        if n == 0:
            return 0

        # If k is large or equal to n/2, we can perform unlimited transactions
        if k >= n // 2:
            max_profit = 0
            for i in range(1, n):
                if prices[i] > prices[i - 1]:
                    max_profit += prices[i] - prices[i - 1]
            return max_profit

        # Initialize variables to represent the buy and sell states for k transactions
        buy = [float('-inf')] * (k + 1)
        sell = [0] * (k + 1)

        for price in prices:
            for j in range(1, k + 1):
                buy[j] = max(buy[j], sell[j - 1] - price)
                sell[j] = max(sell[j], buy[j] + price)

        return sell[k]


# Test code
solution = Solution()

# Test case 1
k1, prices1 = 2, [2,4,1]
result1 = solution.maxProfit(k1, prices1)
print("Test case 1 result:", result1)  # Expected output: 2

# Test case 2
k2, prices2 = 2, [3,2,6,5,0,3]
result2 = solution.maxProfit(k2, prices2)
print("Test case 2 result:", result2)  # Expected output: 7