188. Best Time to Buy and Sell Stock IV

HardLeetCode

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

How to solve the problem

• Dynamic Programming

class Solution:
    def maxProfit(self, k: int, prices: List[int]) -> int:
        n = len(prices)
        # f[j][0]: max profit after j transactions, no stock
        # f[j][1]: max profit after j transactions, holding stock
        f = [[-inf] * 2 for _ in range(k + 2)]
        for j in range(1, k + 2):
            f[j][0] = 0  # base case: no stock, 0 profit

        for i, p in enumerate(prices):
            for j in range(k + 1, 0, -1):
                f[j][0] = max(f[j][0], f[j - 1][1] + p)  # sell
                f[j][1] = max(f[j][1], f[j][0] - p)  # buy

        return f[k + 1][0]  # final answer

Complexity

• Time complexity: O(n * k)
• Space complexity: O(k)