Best Time to Buy and Sell Stock II
“Best Time to Buy and Sell Stock II” involves making as many transactions as you like (i.e., buy one and sell one share of the stock multiple times) to maximize profit, given a list of stock prices for different days. The task is to find a strategy that maximizes the total profit.
A problem that can be considered isomorphic, in terms of problemsolving strategy and not the actual problem context, is “Maximum Subarray” (LeetCode #53). In this problem, you are given an integer array nums, and you need to find a contiguous subarray (containing at least one number) which has the largest sum.
Here’s the reasoning:
In “Best Time to Buy and Sell Stock II”, you want to maximize the total profit by buying and selling the stock. Essentially, you add all positive differences between the price of the stock for two consecutive days (i.e., sell it today if the price is higher than yesterday). This effectively translates to adding all positive integers in a subarray in “Maximum Subarray”.
In “Maximum Subarray”, you want to find a contiguous subarray that has the largest sum. This problem requires a similar strategy—add all positive integers in a subarray—to solve it.
So, while the context of the problems is quite different—one deals with stock prices and the other deals with subarray sums—the problemsolving strategy applied to them is quite similar. Therefore, they are isomorphic in terms of problemsolving strategy.
“Best Time to Buy and Sell Stock II” does not have constraints on the number of transactions, whereas the subarray problem might have constraints on the length of the subarray, which could slightly modify the approach you would take to solve it.
“Best Time to Buy and Sell Stock II” is a problem that involves understanding the stock market transactions with the ability to execute as many transactions as desired (buy one and sell one share of the stock multiple times). Here are 10 problems to prepare for it:
121. Best Time to Buy and Sell Stock: This problem is the simpler version where you are only allowed to complete at most one transaction.
53. Maximum Subarray: Understanding this problem is key to realizing that the problem of buying and selling stock can be transformed into a maximum subarray problem.
122. Best Time to Buy and Sell Stock III: This is a slightly more complex version where you are only allowed to complete at most two transactions.
198. House Robber: This problem involves choosing the maximum amount of money, similar to choosing the maximum profit in stock transactions.
134. Gas Station: This problem also requires an understanding of circular sequences and choosing the right starting point, much like choosing when to buy and sell stocks.
189. Rotate Array: This problem is about array manipulation, which is helpful to understand for solving stock problems.
217. Contains Duplicate: Understanding this problem can help with grasping the concept of handling and processing arrays.
283. Move Zeroes: This problem is about array manipulation, which can help in solving stock problems.
628. Maximum Product of Three Numbers: This problem helps you practice array manipulation and finding maximum values.
714. Best Time to Buy and Sell Stock with Transaction Fee: This problem involves a similar scenario as buying and selling stocks but includes a transaction fee.
These involve array manipulation and dynamic programming, which are beneficial for tackling “Best Time to Buy and Sell Stock II”.


Clarification Questions
What are the clarification questions we can ask about this problem?
Identifying Problem Isomorphism
Can you help me with finding the isomorphism for this problem?
Which problem does this problem map to the corresponding isomorphic problem on Leetcode ?
Language Agnostic Coding Drills
Here are the learning units that the code can be broken down into, arranged from simpler to more complex concepts:
Variable Assignments and Arithmetic Operations: Basic knowledge of how to assign values to variables and how to perform simple arithmetic operations.
Lists: Understanding how to define lists and access their elements, and understanding the length of a list.
Conditional Statements (if): Learning how to use
if
statements to control program flow based on certain conditions.Defining Functions: Understanding how to define a function and how to call it, along with the concept of function recursion.
Decorators: Learning what decorators are and how to use them. In this case, the
@cache
decorator is used to improve the efficiency of the recursive function.Tuples: Understanding how to use tuples to store multiple values and how to access the individual elements in a tuple.
Classes and Methods: Learning how to define a class and a method within the class.
Type Hinting: Understanding how to use type hinting to specify the expected type of function arguments and the return type.
Dynamic Programming: An understanding of the dynamic programming approach to problem solving, where subproblems are solved and their solutions stored for use in larger problems. This concept is key to understanding how the recursive function
trade
works in the provided code.Memoization: Understanding the concept of memoization, a technique often used in dynamic programming to store the results of expensive function calls and reusing them when the same inputs occur. This is being used here with the
@cache
decorator.Problem Solving and Algorithmic Thinking: An understanding of how to approach a problem in a systematic way, break it down into smaller parts, and translate the solution into a set of stepbystep instructions (an algorithm). This includes being able to understand the problem that the code is solving (maximizing profit from buying and selling stocks) and how it is solving it.
Targeted Drills in Python
Here are Python drills targeting each of the learning units identified:
 Variable Assignments and Arithmetic Operations:


 Lists:


 Conditional Statements (if):


 Defining Functions:


 Decorators:


 Tuples:


 Classes and Methods:


 Type Hinting:


 Dynamic Programming:


 Memoization:


 Problem Solving and Algorithmic Thinking:

