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188. Best Time to Buy and Sell Stock IV

Difficulty Topics

Description

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.

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

Solution

best-time-to-buy-and-sell-stock-iv.py
class Solution:
    def maxProfit(self, k: int, prices: List[int]) -> int:
        n = len(prices)

        if k >= n // 2:
            res = 0

            for i in range(1, n):
                if prices[i] > prices[i - 1]:
                    res += prices[i] - prices[i - 1]

            return res

        dp = [[0] * (n) for _ in range(k + 1)]

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

            for j in range(1, n):
                dp[i][j] = max(dp[i][j - 1], prices[j] + tempMax)
                tempMax = max(tempMax, dp[i - 1][j - 1] - prices[j])

        return dp[k][n - 1]