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Solution: Regular Expression Matching

Explore how to solve the regular expression matching problem using dynamic programming. Understand how to handle special characters '.' and '*' with recursion and memoization to efficiently match patterns to strings. Gain insights into optimizing time and space complexity by avoiding repeated computations and applying optimal substructure concepts.

Statement

You are given an input string, s, and a pattern string, p. Your task is to implement regular expression matching between s and p, where the pattern may include the special characters '.' and '*':

  • '.' matches any single character.

  • '*' matches zero or more occurrences of the preceding character.

The match must cover the entire input string, not just part of it.

Constraints:

  • 11 \leq s.length 20\leq 20

  • 11 \leq p.length 20\leq 20

  • s contains only lowercase English letters.

  • p contains only lowercase English letters, '.', and '*'.

  • It is guaranteed that for each appearance of the character '*', there will be a previous valid character to match.

Solution

One of the first ideas that comes to ...