10. Regular Expression Matching¶

Difficulty: Hard

10. Regular Expression Matching

Hard

Given an input string s and a pattern p, 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: false
Explanation: "a" does not match the entire string "aa".

Example 2:

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 3:

Input: s = "ab", p = ".*"
Output: true
Explanation: ".*" means "zero or more (*) of any character (.)".

Constraints:

1 <= s.length <= 20
1 <= p.length <= 20
s contains only lowercase English letters.
p contains only lowercase English letters, '.', and '*'.
It is guaranteed for each appearance of the character '*', there will be a previous valid character to match.

Solution¶

class Solution {
    public boolean isMatch(final String s, final String p) {
        return solve(s, p, 0, 0, new Boolean[s.length()][p.length()]);
    }
    private boolean solve(String s, String p, final int i, final int j, final Boolean[][] dp) {
        if(i >= s.length() && j >= p.length()) return true;
        if(j >= p.length()) return false;
        if(i < s.length() && dp[i][j] != null) return dp[i][j];
        final boolean op1 = i < s.length() && (s.charAt(i) == p.charAt(j) || p.charAt(j) == '.');
        if(j + 1 < p.length() && p.charAt(j + 1) == '*') {
            final boolean op2 = solve(s, p, i, j + 2, dp) || (op1 && solve(s, p, i + 1, j, dp));
            if(i < s.length()) dp[i][j] = op2;
            return op2;
        }
        if(op1) return dp[i][j] = solve(s, p , i + 1, j + 1, dp);
        if(i < s.length()) dp[i][j] = false;
        return false;
    }    
}

Complexity Analysis¶

Time Complexity: O(?)
Space Complexity: O(?)

Approach¶

Detailed explanation of the approach will be added here