# LeetCode 123. Best Time to Buy and Sell Stock III--Python解法--动态规划--数学题

2020/01/30 共 1666 字，约 5 分钟

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 two transactions.

Note: You may not engage in multiple transactions at the same time (i.e., you must sell the stock before you buy again).

Example 1:

``````Input: [3,3,5,0,0,3,1,4]
Output: 6
Explanation: Buy on day 4 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.
Then buy on day 7 (price = 1) and sell on day 8 (price = 4), profit = 4-1 = 3.
``````

Example 2:

``````Input: [1,2,3,4,5]
Output: 4
Explanation: Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4.
Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are
engaging multiple transactions at the same time. You must sell before buying again.
``````

Example 3:

``````Input: [7,6,4,3,1]
Output: 0
Explanation: In this case, no transaction is done, i.e. max profit = 0.
``````

``````[1,3,2,7]
``````

Python解法如下：

``````class Solution:
def maxProfit(self, prices: List[int]) -> int:
if prices == []:
return 0
SellOne = 0
SellTwo = 0
for p in prices:
SellOne = max(SellOne, p - buyOne)
SellTwo = max(SellTwo, p - buyTwo)
return SellTwo

``````

`buyTwo`变量表示的是用获利的钱(只买卖一次的全局最多的钱)购买当天股票后剩余的钱，`SellTwo`变量代表买卖股票2次获利最多的钱。