动态规划_leetcode309(状态好难定义，又是买*)

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]