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买卖股票的最佳时机 IV

Best Time to Buy and Sell Stock IV

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 IV

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-iv/

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

Find the maximum profit you can achieve. You may complete at most k transactions: i.e. you may buy at most k times and sell at most k times.

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

 

Example 1:

Input: k = 2, prices = [2,4,1]
Output: 2
Explanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.

Example 2:

Input: k = 2, prices = [3,2,6,5,0,3]
Output: 7
Explanation: Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6-2 = 4. Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.

 

Constraints:

  • 1 <= k <= 100
  • 1 <= prices.length <= 1000
  • 0 <= prices[i] <= 1000
解析

思路：用动态规划维护第 j 次买入和第 j 次卖出后的最大收益。若 k 大于 n/2，可退化成无限次交易；否则每天按交易次数更新状态。

复杂度：时间 O(nk)，空间 O(k)。