LC309 - Best Time to Buy and Sell Stock with Cooldown

Problem

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

• After you sell your stock, you cannot buy stock on the next day (i.e., cooldown one day).

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

Example

Input: prices = [1,2,3,0,2]

Output: 3

Explanation: transactions = [buy, sell, cooldown, buy, sell]

Solution

DFS

Enumerate the entire decision tree and find the leaf node with the maximum value. This approach is really costly as there are $2^n$ possible decisions, and hence $O(2^n)$ space complexity.

Cached DFS

Use cache decorator to memoize states. Time complexity seems to be around $O(n^2)$.

def maxProfit(self, prices: List[int]) -> int:
	@cache
	def dfs(i, cool):
		# end
		if i >= len(prices):
		return 0
		# cooldown
		profit = dfs(i+1, cool)
		# buy
		if not cool:
			profit = max(profit, dfs(i+1, True) - prices[i])
		# sell
		else:
			profit = max(profit, dfs(i+2, False) + prices[i])		
		return profit
	return dfs(0, False)