<p>Given an input string <code>s</code>&nbsp;and a pattern <code>p</code>, implement regular expression matching with support for <code>&#39;.&#39;</code> and <code>&#39;*&#39;</code> where:</p>

<ul>
	<li><code>&#39;.&#39;</code> Matches any single character.​​​​</li>
	<li><code>&#39;*&#39;</code> Matches zero or more of the preceding element.</li>
</ul>

<p>The matching should cover the <strong>entire</strong> input string (not partial).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aa&quot;, p = &quot;a&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong> &quot;a&quot; does not match the entire string &quot;aa&quot;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aa&quot;, p = &quot;a*&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> &#39;*&#39; means zero or more of the preceding element, &#39;a&#39;. Therefore, by repeating &#39;a&#39; once, it becomes &quot;aa&quot;.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;ab&quot;, p = &quot;.*&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> &quot;.*&quot; means &quot;zero or more (*) of any character (.)&quot;.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length&nbsp;&lt;= 20</code></li>
	<li><code>1 &lt;= p.length&nbsp;&lt;= 20</code></li>
	<li><code>s</code> contains only lowercase English letters.</li>
	<li><code>p</code> contains only lowercase English letters, <code>&#39;.&#39;</code>, and&nbsp;<code>&#39;*&#39;</code>.</li>
	<li>It is guaranteed for each appearance of the character <code>&#39;*&#39;</code>, there will be a previous valid character to match.</li>
</ul>

class Solution {
public:
    bool helper(string s , string p, vector<vector<int>>&dp){
        if (p.length() == 0 && s.length() == 0) {
            return true;
        }
        if (s.length() == 0) {
            if (p.length() >= 2 && p[p.length() - 1] == '*' && helper(s, p.substr(0, p.length() - 2), dp)) {
                return true;
            }
            return false;
        }
        if (p.length() == 0) {
            return false;
        }
        if(dp[s.length()][p.length()]!=-1){
            return dp[s.length()][p.length()];
        }
        bool flag = false;
        if(s[s.length()-1] == p[p.length()-1]){
            flag =  helper(s.substr(0,s.length()-1), p.substr(0,p.length()-1),dp);
        }else{
            if(p[p.length()-1] == '.'){
                flag = helper(s.substr(0,s.length()-1), p.substr(0,p.length()-1),dp);
            }else if(p[p.length()-1] == '*'){
                if(p.length() == 1){
                    flag = flag || helper(s,p.substr(0,p.length()-1),dp);
                }else{
                    if(p[p.length()-2] == s[s.length()-1] || p[p.length()-2] == '.'){
                        flag = flag || helper(s.substr(0,s.length()-1), p,dp);
                        flag = flag || helper(s,p.substr(0,p.length()-2),dp);
                    }else{
                        flag = flag || helper(s,p.substr(0,p.length()-2),dp);
                    }
                }
                
            }
        }
        return dp[s.length()][p.length()] = flag;

    }
    bool isMatch(string s, string p) {
        vector<vector<int>>dp(s.length()+1,vector<int>(p.length()+s.length()+2,-1));
        return helper(s,p,dp);
    }
};
13868