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Regular Expression Matching

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C++ program to implement regular expression matching with support for '.' and '*' where:
- '.' Matches any single character.
- '*' Matches zero or more of the preceding element.
The matching should cover the entire input string (not partial).

Example 1
    
  
  • Input: s = "aa", p = "a*"
    • 
  
  • Output: true
    • 
  
  • Explanation: 
      
      
    • '*' means zero or more of the preceding element, 'a'.
      • 
      
    • Therefore, by repeating 'a' once, it becomes "aa".
      • 
    
    •
Example 2
    
  
  • Input: s = "mississippi", p = "mis*is*p*."
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  • Output: false
    • 
  
  • Explanation: 
      
      
    • The pattern doesn't match the entire string because the final '.' needs to match the last 'i' in "mississippi".
      • 
      
    • But there's still a 'p' and 'i' left unmatched.
      • 
    
    •
Constraints
    
  
  • 1 ≤ s.length ≤ 20
    • 
  
  • 1 ≤ p.length ≤ 30
    • 
  
  • s contains only lowercase English letters
    • 
  
  • p contains only lowercase English letters, '.', and '*'
    • 
  
  • Time Complexity: O(m*n) where m and n are lengths of string and pattern
    • 
  
  • Space Complexity: O(m*n)
    •
ArraysDynamic Programming PwCD. E. Shaw
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Hint
Solution

Solution Hints

    
  
  • Use dynamic programming to solve this problem
    • 
  
  • Create a 2D DP table where dp[i][j] represents if s[0...i-1] matches p[0...j-1]
    • 
  
  • Handle the special case of '*' which can match zero or more of the preceding character
    • 
  
  • Initialize the base cases carefully, especially for empty strings
    • 
  
  • Consider all possible pattern combinations when '*' is involved
    •

Steps to solve by this approach:

 Step 1: Create a 2D DP table where dp[i][j] represents if the first i characters of s match the first j characters of p.
 Step 2: Initialize dp[0][0] = true since empty pattern matches empty string.
 Step 3: Handle the case where pattern might match empty string (like a*, a*b*, etc.).
 Step 4: For each character in the string and pattern, analyze different matching scenarios.
 Step 5: If the current pattern character is '*', it can either match zero of the preceding element (dp[i][j-2]) or match one or more of the preceding element if it matches the current string character.
 Step 6: If the current pattern character is '.' or matches the current string character, the result depends on the match status of the previous characters.
 Step 7: Return dp[m][n] which represents if the entire string matches the pattern.

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