## Regular Expression Matching

### 描述

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


### 递归版

// Regular Expression Matching
// Time complexity: O(n)
// Space complexity: O(1)
class Solution {
public:
bool isMatch(const string& s, const string& p) {
return isMatch(s.c_str(), p.c_str());
}
private:
bool matchFirst(const char *s, const char *p) {
return *p == *s || (*p == '.' && *s != '\0');
}

bool isMatch(const char *s, const char *p) {
if (*p == '\0') return *s == '\0';    //empty

// next char is not '*', then must match current character
if (*(p + 1) != '*') {
if (matchFirst(s, p)) return isMatch(s + 1, p + 1);
else return false;
} else { // next char is '*'
if (isMatch(s, p + 2)) return true;    // try the length of 0
while ( matchFirst(s, p) )       // try all possible lengths
if (isMatch(++s, p + 2)) return true;
return false;
}
}
};