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]

一刷
題解：
buy[i] means before day i what is the maxProfit for any sequence end with buy.
sell[i] means before day i what is the maxProfit for any sequence end with sell.
rest[i] means before day i what is the maxProfit for any sequence end with rest.
Then we want to deduce the transition functions for buy sell and rest. By definition we have:

buy[i]  = max(rest[i-1]-price, buy[i-1]) 
sell[i] = max(buy[i-1]+price, sell[i-1])
rest[i] = max(sell[i-1], buy[i-1], rest[i-1])

由于buy[i] <= rest[i] <= sell[i] is also true, 因此：

buy[i] = max(sell[i-2]-price, buy[i-1])
sell[i] = max(buy[i-1]+price, sell[i-1])

class Solution {
    public int maxProfit(int[] prices) {
        //sell: sell[i-1], prev_sell: sell[i-2]
        int sell = 0, prev_sell = 0, buy = Integer.MIN_VALUE, prev_buy;
        for(int price : prices){
            prev_buy = buy;
            buy = Math.max(prev_sell - price, prev_buy);
            prev_sell = sell;
            sell = Math.max(prev_buy + price, sell);
        }
        return sell;
    }
}