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188. Best Time To Buy And Sell Stock IV

Array Dynamic Programming

Problem - Best Time To Buy And Sell Stock IV

Hard

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

Solutions

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class Solution:
    def maxProfit(self, k: int, prices: List[int]) -> int:
        dp = [[0] * 2 for _ in range(k + 1)]

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

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

        return dp[-1][0]

Submission Stats:

  • Runtime: 55 ms (69.91%)
  • Memory: 18 MB (75.58%)