Regular expression matching

Problem:

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

Solution:

class Solution {
public:
     bool isMatch(const char *s, const char *p) {
        if (*s == '\0' && *p == '\0') return true;
        if (*s == '\0' && *(p+1) == '*') return isMatch(s, p+2);      
        if (*s == '\0' || *p == '\0') return false;
       
        if (* (p+1) == '*'){
            if (*p != *s && *p != '.') return isMatch(s, p+2);
            return isMatch(s+1, p) || isMatch(s, p+2);          
        }
       
        if (*p == '.')  return isMatch(s+1, p+1);

        if  (*s != *p) return false;      
       
        return isMatch(s+1, p+1);
    }
   
};