Problem description:

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:

Input: [1,2,3,0,2]
Output: 3
Explanation: transactions = [buy, sell, cooldown, buy, sell]

Solution:

The key of solving this question is to find out the dp equation.
(1) We have to rest before we buy and
(2) we have to buy before we sell

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class Solution {
public:
    int maxProfit(vector<int>& prices) {
        //use two sets of buy& sell to check if there's cooldown
        int buy(INT_MIN), sell(0), prev_sell(0), prev_buy(0);
        
        for(int price: prices){
            prev_buy = buy; 
            buy = max(buy, prev_sell-price); //
            prev_sell = sell;
            sell = max(sell, prev_buy+price);
        }
        return sell;
    }
};

reference: