What is the optimal time complexity of solving Best Time to Buy and Sell Stock with Cooldown?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Best Time to Buy and Sell Stock with Cooldown?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Best Time to Buy and Sell Stock with Cooldown?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Best Time to Buy and Sell Stock with Cooldown?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Best Time to Buy and Sell Stock with Cooldown

Learn how to solve the 'Best Time to Buy and Sell Stock with Cooldown' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Medium

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).

Write a function maxProfit(prices: List[int]) -> int.

Constraints

•1 <= len(prices) <= 5000
•0 <= prices[i] <= 1000

Examples

Example 1

Input

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

Output

Explanation

Transactions = [buy, sell, cooldown, buy, sell].

Example 2

Input

prices = [1]

Output

Explanation

No transaction can be made.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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