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买卖股票的最佳时机 III

Best Time to Buy and Sell Stock III

专题
Algorithmic Programming / 算法编程
难度
L4
来源
Citadel

题目详情

问题：买卖股票的最佳时机 III

考察：数组、动态规划

来源：Citadel

链接：https://www.jointaro.com/interviews/questions/best-time-to-buy-and-sell-stock-iii/

You are given an array prices where prices[i] is the price of a given stock on the ith day.

Find the maximum profit you can achieve. You may complete at most two transactions.

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

 

Example 1:

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

 

Constraints:

  • 1 <= prices.length <= 105
  • 0 <= prices[i] <= 105
解析

思路：维护四个状态：第一次买入、第一次卖出、第二次买入、第二次卖出后的最大收益。每天用当前价格依次更新这些状态，最后第二次卖出状态即最多两笔交易的答案。

复杂度：时间 O(n)，空间 O(1)。