动态规划_leetcode309(状态好难定义，又是买彩票)

class Solution(object):
    def maxProfit(self, prices):
        """
 :type prices: List[int]
 :rtype: int
 """


 length = len(prices)

 if length <= 1:
 return 0

 hold = [-1 for i in range(length)]
 cash = [0 for i in range(length)]

 hold[0] = -prices[0]
 hold[1] = max(hold[0],-prices[1])
 cash[1] = max(cash[0],hold[0] + prices[1])

 for i in range(2,length):
 cash[i] = max(cash[i-1],hold[i-1]+prices[i])
 hold[i] = max(hold[i-1],cash[i-2]-prices[i])



 return cash.pop()




# 好难
# sell[i]表示截至第i天，最后一个操作是卖时的最大收益；
# buy[i]表示截至第i天，最后一个操作是买时的最大收益；
# cool[i]表示截至第i天，最后一个操作是冷冻期时的最大收益；
# 递推公式：
# sell[i] = max(buy[i-1]+prices[i], sell[i-1]) (第一项表示第i天卖出，第二项表示第i天冷冻)
# buy[i] = max(cool[i-1]-prices[i], buy[i-1]) （第一项表示第i天买进，第二项表示第i天冷冻）
# cool[i] = max(sell[i-1], buy[i-1], cool[i-1])
# python:

class Solution2:
 def maxProfit(self, prices):
 n = len(prices)
 if n == 0:
 return 0
 sell = [0 for _ in range(n)]
 buy = [0 for _ in range(n)]
 cool = [0 for _ in range(n)]
 buy[0] = -prices[0]
 for i in range(1,n):
 sell[i] = max(buy[i-1] + prices[i], sell[i-1])
 buy[i] = max(cool[i-1] - prices[i], buy[i-1])
 cool[i] = max(sell[i-1], buy[i-1],cool[i-1])
 return sell[-1]