10. Regular Expression Matching

// Depth-first Search
public boolean isMatch(String s, String p) {
        if (p.length() == 0) return s.length() == 0;

        boolean firstMatch = s.length() > 0 &&
        (s.charAt(0) == p.charAt(0) || p.charAt(0) == '.');

        if (p.length() >= 2 && p.charAt(1) == '*') {
            return isMatch(s, p.substring(2)) ||
             (firstMatch && isMatch(s.substring(1), p));
        } else {
            return firstMatch && isMatch(s.substring(1), p.substring(1));
        }
}

// Dynamic Programming
public boolean isMatch(String s, String p) {
        int m = s.length();
        int n = p.length();
        boolean[][] dp = new boolean[m + 1][n + 1];
        dp[0][0] = true;

        for (int i = 2; i <= n; i++) {
            if (p.charAt(i - 1) == '*') {
                dp[0][i] = dp[0][i - 2];
            }
        }

        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                char sc = s.charAt(i - 1);
                char pc = p.charAt(j - 1);

                if (sc == pc || pc == '.') {
                    dp[i][j] = dp[i - 1][j - 1];
                } else if (pc == '*') {
                    if (dp[i][j - 2]) {
                        dp[i][j] = true;
                    } else if (sc == p.charAt(j - 2) ||
                              p.charAt(j - 2) == '.') {
                        dp[i][j] = dp[i - 1][j];
                    }
                }
            }
        }

        return dp[m][n];
}