0%

### 题目描述

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).

### 例子

#### 例子 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.

#### 例子 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.

#### 例子 3

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

### 解题思路

• `FirstBuy` : 第一次买入时的利润（应该是负值）
• `FirstSell`：第一次卖出时的利润
• `SecondBuy`：第二次买入时（此时第一次已卖出）的利润（可正可负）
• `SecondSell`：第二次卖出时的利润

• `SecondSell` 比较 `SecondSell + prices[i]`
• `SecondBuy` 比较 `FirstSell - prices[i]` (买入，所以利润相减)
• `FirstSell` 比较 `FirstBuy + prices[i]`
• `FirstBuy` 比较 `-prices[i]`

• 时间复杂度：O(n)
• 空间复杂度：O(1)