LeetCode #309 - Best Time to Buy and Sell Stock with Cooldown

最新推荐文章于 2020-06-07 23:35:49 发布

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本文介绍了一个股票交易场景下的动态规划算法实现，该算法允许多次买入卖出，并在每次卖出后强制冷却一天。通过构建三种状态（无股票无暂停、无股票有暂停、有股票无暂停）及其相互转移关系，实现了最大利润的计算。

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 as many transactions as you like (ie, buy one and sell one share of the stock multiple times) with the following restrictions:

You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).
After you sell your stock, you cannot buy stock on next day. (ie, cooldown 1 day)

Example:

prices = [1, 2, 3, 0, 2]
maxProfit = 3
transactions = [buy, sell, cooldown, buy, sell]

每次卖出股票必须暂停一轮，求最大盈利金额。由于情况较复杂，可以画出股票买卖的状态转移图，从而进行动态规划。

令s0表示无股票且无暂停的状态，s1表示无股票且有暂停的状态，s2表示有股票且无暂停的状态，从而可以构建三个状态之间的状态转移关系，具体见代码。

class Solution {
public:
    int maxProfit(vector<int>& prices) {
        if(prices.size()==0) return 0;
        vector<int> s0(prices.size(),0);
        vector<int> s1(prices.size(),0);
        vector<int> s2(prices.size(),0);
        s0[0]=0;
        s1[0]=0;
        s2[0]=-prices[0];
        for(int i=1;i<prices.size();i++)
        {
            s0[i]=max(s1[i-1],s0[i-1]);
            s1[i]=s2[i-1]+prices[i];
            s2[i]=max(s2[i-1],s0[i-1]-prices[i]);
        }
        return max(s0.back(),s1.back());
    }
};