Say you have an array for which the ith element is the price of a given stock on day i.
Design an algorithm to find the maximum profit. You may complete at most k transactions.
Note:
You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).
Example 1:
Input: [2,4,1], k = 2
Output: 2
Explanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.
Example 2:
Input: [3,2,6,5,0,3], k = 2
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.
class Solution:
     def maxProfit(self, k, prices):
         """
         :type k: int
         :type prices: List[int]
         :rtype: int
         """
         if len(prices)<2:
             return 0
         if k<=0:
             return 0
         if k >= len(prices) / 2:
             return sum(i - j for i, j in zip(prices[1:], prices[:-1]) if i - j > 0)
         buy = []
         sell = []
         for i in range(k):
             buy.append(-float("inf"))
             sell.append(-float("inf"))
         
         for i in prices:
             for j in range(k):
                 if j== 0:
                     buy[j] = max(buy[j], -i)
                     sell[j] = max(sell[j], i+buy[j])
                 else:
                     buy[j] = max(buy[j], sell[j-1]-i)
                     sell[j] = max(sell[j], i+buy[j])
         
         return sell[-1]

class Solution:
     def maxProfit(self, k, prices):
         """
         :type k: int
         :type prices: List[int]
         :rtype: int
         """
         if len(prices)<2:
             return 0
         if k<=0:
             return 0
         if k >= len(prices) / 2:
             return sum(i - j for i, j in zip(prices[1:], prices[:-1]) if i - j > 0)
         buy = []
         sell = []
         for i in range(k):
             buy.append(-float("inf"))
             sell.append(-float("inf"))
         
         for i in prices:
             for j in range(k):
                 if j== 0:
                     buy[j] = max(buy[j], -i)
                     sell[j] = max(sell[j], i+buy[j])
                 else:
                     buy[j] = max(buy[j], sell[j-1]-i)
                     sell[j] = max(sell[j], i+buy[j])
         
         return sell[-1]
