[LeetCode #10] Regular Expression Matching

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

class Solution {
public:
    bool isMatch(string s, string p) {
        int m = s.size(), n = p.size();
        
        vector<vector<bool>> dp (m+1, vector<bool> (n+1, false));
        
        dp[0][0] = true;
        
        for (int i = 0; i < m; i++){
            dp[i+1][0] = false;
        }
        
        for (int j = 0; j < n; j++){
            dp[0][j+1] = j > 0 && p[j] == '*' && dp[0][j-1];
        }
        
        for (int i = 0; i < m; i++){
            for (int j = 0; j < n; j++){
                if (p[j] != '*'){
                    dp[i+1][j+1] = dp[i][j] && (s[i] == p[j] || p[j] == '.');
                }else{
                    dp[i+1][j+1] = dp[i+1][j-1] || ((dp[i][j+1]) && (s[i] == p[j-1] || p[j-1] == '.'));
                }
            }
        }
        
        return dp[m][n];
    }
};