Regular Expression Matching

Hard Subject: 2-D Dynamic Programming

Time Complexity

O(M * N)

Space Complexity

O(M * N)

Problem Description

Problem Statement

Given an input string s and a pattern p, implement regular expression matching with support for '.' and '*' where '.' Matches any single character and '*' Matches zero or more of the preceding element.

Example 1:

Input: s = "aa", p = "a*"
Output: true

Optimal Solution

Python

Approach: 2-D DP

dp[i][j] indicates if s[0...i-1] matches p[0...j-1]. If p[j-1] is *, we can either match zero occurrences (dp[i][j-2]) or one/more occurrences if the preceding char matches (dp[i-1][j]).

class Solution:
    def isMatch(self, s: str, p: str) -> bool:
        m, n = len(s), len(p)
        dp = [[False] * (n + 1) for _ in range(m + 1)]
        dp[0][0] = True

        for j in range(2, n + 1):
            if p[j-1] == '*':
                dp[0][j] = dp[0][j-2]

        for i in range(1, m + 1):
            for j in range(1, n + 1):
                if p[j-1] == s[i-1] or p[j-1] == '.':
                    dp[i][j] = dp[i-1][j-1]
                elif p[j-1] == '*':
                    dp[i][j] = dp[i][j-2]
                    if p[j-2] == s[i-1] or p[j-2] == '.':
                        dp[i][j] = dp[i][j] or dp[i-1][j]
        return dp[m][n]