# 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).

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.

# 我的解法

## 思路分析

dp[3][2][1]的含义就是：今天是第三天，我现在手上持有着股票，至今最多进行2次交易。再比如dp[2][3][0] 的含义：今天是第二天，我现在手上没有持有股票，至今最多进行3次交易。

## 实现代码

Runtime: 28 ms, faster than 9.85% of C++ online submissions for Best Time to Buy and Sell Stock III.
Memory Usage: 18.2 MB, less than 7.14% of C++ online submissions for Best Time to Buy and Sell Stock III.