Regular Expression

RegularExpression.java

/**
 * Implement regular expression matching with support for '.' and '*'.
 * '.' Matches any single character.
 * '*' Matches zero or more of the preceding element.
 * The matching should cover the entire input string (not partial).
 * The function prototype should be:
 * bool isMatch(const char *s, const char *p)
 * Some examples:
 * isMatch("aa","a") → false
 * isMatch("aa","aa") → true
 * isMatch("aaa","aa") → false
 * isMatch("aa", "a*") → true
 * isMatch("aa", ".*") → true
 * isMatch("ab", ".*") → true
 * isMatch("aab", "c*a*b") → true
 */
public class Solution {
    public boolean isMatch(String s, String p) {
        if (p.length() == 0)
            return s.length() == 0;
        if (p.length() == 1 || p.charAt(1) != '*') {
            if(s.length() < 1 || (p.charAt(0) != '.' && p.charAt(0) != s.charAt(0))) 
                return false;
            return isMatch(s.substring(1), p.substring(1));
        } else {
            int i = -1;
            while (i < s.length() && (i < 0 || p.charAt(0) == '.' || p.charAt(0) == s.charAt(i))) {
                if (isMatch(s.substring(i + 1), p.substring(2)))
                    return true;
                i++;
            }
            return false;
        }
    }
}

regularExpressionDP.java

public class Solution {
    public boolean isMatch(String s, String p) {
        // Condition 1: if(p.charAt(j) == s.charAt(i)) --> dp[i][j] = d[i - 1][j - 1];
        // Condition 2: if(p.charAt(j) == '.') --> dp[i][j] = d[i - 1][j - 1];
        // Condition 3: if(p.charAt(j) == '*') --> two sub conditions:
        // 				1). if(p.charAt(j - 1) != s.charAt(i)) --> dp[i][j] = dp[i][j - 2]  //in this case, a* only counts as empty
        //				2). if p.charAt(i-1) == s.charAt(i) or p.charAt(i-1) == '.' --> 
        //						dp[i][j] = dp[i-1][j]    //in this case, a* counts as multiple a 
        //                   or dp[i][j] = dp[i][j-1]   // in this case, a* counts as single a
        //                   or dp[i][j] = dp[i][j-2]   // in this case, a* counts as empty
        
    	if (s == null || p == null) {
        	return false;
	    }
	    boolean[][] dp = new boolean[s.length()+1][p.length()+1];
	    dp[0][0] = true;
	    for (int i = 0; i < p.length(); i++) {
	        if (p.charAt(i) == '*' && dp[0][i-1]) {
	            dp[0][i+1] = true;
	        }
	    }
	    for (int i = 0 ; i < s.length(); i++) {
	        for (int j = 0; j < p.length(); j++) {
	            if (p.charAt(j) == '.') {
	                dp[i+1][j+1] = dp[i][j];
	            }
	            if (p.charAt(j) == s.charAt(i)) {
	                dp[i+1][j+1] = dp[i][j];
	            }
	            if (p.charAt(j) == '*') {
	                if (p.charAt(j-1) != s.charAt(i) && p.charAt(j-1) != '.') {
	                    dp[i+1][j+1] = dp[i+1][j-1];
	                } else {
	                    dp[i+1][j+1] = (dp[i+1][j] || dp[i][j+1] || dp[i+1][j-1]);
	                }
	            }
	        }
	    }
	    return dp[s.length()][p.length()];
    }
}