# 123. Best Time to Buy and Sell Stock III 买卖股票的最佳时机 III

@TOC

## # 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.
``````

## # 解题方法

``````class Solution(object):
def maxProfit(self, prices):
"""
:type prices: List[int]
:rtype: int
"""
if not prices: return 0
N = len(prices)
g = [ * 3 for _ in range(N)]
l = [ * 3 for _ in range(N)]
for i in range(1, N):
diff = prices[i] - prices[i - 1]
for j in range(1, 3):
l[i][j] = max(g[i - 1][j - 1] + max(diff, 0), l[i - 1][j] + diff)
g[i][j] = max(l[i][j], g[i - 1][j])
return g[-1][-1]
``````

## # 日期

2018 年 11 月 29 日 —— 时不我待