[Leetcode]188. Best Time to Buy and Sell Stock IV@python

题目

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).

题目要求

给定一个数组，数组中的元素是n天中每天的股票价格。设计一个算法，如果最多允许交易k次（一次交易指一次完整的买入和卖出），能够得到的最大利润。

解题思路

此题参考了书影博客的解题思路。
k次交易，意味着k次的买入和卖出，如果2 k > n,说明我们可以获取所有交易过程中的利润。如果2 * k <= n,采用动态规划来计算。dp[j]表示进行 j次交易获得的最大利润。第一次交易为买入，以后的交易为卖出和买入的交替。总收益为交易序列中偶数项之和减去奇数项之和。

代码

class Solution(object):    def maxProfit(self, k, prices):        """        :type k: int        :type prices: List[int]        :rtype: int        """        if 2 * k > len(prices):            return self.quickProfit(prices)        dp = [None] * (2 * k + 1)        dp[0] = 0        for i in range(len(prices)):            for j in range(1,min(2 * k,i + 1) + 1):                dp[j] = max(dp[j],dp[j - 1] + prices[i] * [1,-1][j % 2])        return max(dp)    def quickProfit(self,prices):        sum = 0        for i in range(1,len(prices)):            if prices[i] - prices[i - 1] > 0:                sum += prices[i] - prices[i - 1]        return sum