Regular Expression Matching
The given problem is to implement regular expression matching with support for .
and *
. The solution can be tackled using recursion or dynamic programming. We’ll start with the recursive approach, and then we can optimize it using dynamic programming.
Here’s the code for a recursive approach:


The recursion deals with two base cases:
 If
p
is empty,s
must also be empty for a match.  If
p
has a*
at the next position, we can either ignore it or use it to match one character ins
.
The recursive approach, while simple and clear, leads to duplicated work. This can be avoided with dynamic programming (DP). Here’s a topdown DP approach:


The dp
function checks for matches starting at positions i
and j
in s
and p
, respectively. By storing previously computed results in memo
, we avoid redundant work, greatly improving efficiency.


Problem Classification
This problem can be classified as a Pattern Matching problem.
This is because the problem deals with two strings  a text and a pattern, and the task is to determine if the pattern matches the text considering special characters in pattern like ‘.’ and ‘*’. So, the primary focus of the problem is recognizing and matching patterns, thus fitting into the Pattern Matching category.
Language Agnostic Coding Drills
Variables: Understanding variable declaration, assignment, and usage.
Data Structures: Understanding how to use lists and tuples.
Control Structures: Understanding ifelse conditions and loop constructs.
Functions: Understanding function definition, parameters, and calling.
Classes: Understanding class creation, object instantiation, and method definition.
Recursion: Understanding the concept of recursion where a function calls itself.
Memoization/Caching: Understand how to use a dictionary to store precomputed values to avoid duplicate computation (dynamic programming).
Backtracking: The method used in this code to traverse through all the possibilities until a solution is found.
To arrive at the final solution from the problem statement:
Understand the problem statement: Recognize that this is a pattern matching problem that can be solved using dynamic programming and recursion.
Formulate the approach: Map out the backtracking approach where each character of the given string is checked against the pattern.
Implement the approach: Code the class and method structures, implement the backtracking logic using recursion, use a cache to store precomputed results.
Test and debug: Run the code with multiple test cases to ensure it’s working as expected, debug any errors.
Targeted Drills in Python
Variables
Drill: Write a Python program that declares several variables, assigns values to them and prints them.


Data Structures
Drill: Create a Python list and tuple, perform various operations (add, remove, access elements) on them.


Control Structures
Drill: Write a Python program that uses ifelse conditions and loop constructs.


Functions
Drill: Write a Python function that takes two parameters and returns their sum.


Classes
Drill: Write a Python class that has a constructor, one instance variable, and one instance method.


Recursion
Drill: Write a recursive Python function that computes the factorial of a number.


Memoization/Caching
Drill: Implement a Python function that calculates the nth Fibonacci number using dynamic programming.


Backtracking
Drill: Implement a Python function that generates all possible permutations of a given list of elements using backtracking.


These drills should give you a good understanding of the basic constructs used in the problem code.