<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 help(string& s,string& p,int i,int j,vector<unordered_map<int,bool>>& hash)
    {
        
        if((i==s.length())&&(j==p.length()))
        {
            return true;
        }
        else if(j==p.length())
        {
            return false;
        }
        else if(i==s.length())
        {
            for(;j<p.length();j=j+2)
            {
                if(!((j+1<p.length())&&(p[j+1]=='*')))
                {
                    return false;
                }
            }
            return true;
        }
        if(hash[i].count(j))
        {
            return hash[i][j];
        }
        if((j+1<p.length())&&(p[j+1]=='*'))
        {
            bool dis=help(s,p,i,j+2,hash);
            bool con=false;
            if((s[i]==p[j])||(p[j]=='.'))
            {
                con=help(s,p,i+1,j,hash);
            }
            hash[i][j]=dis||con;
            return dis||con;
        }
        else
        {
            bool result=false;
            if((s[i]==p[j])||(p[j]=='.'))
            {
                result=help(s,p,i+1,j+1,hash);
            }
            hash[i][j]=result;
            return result;
        }
    }
    bool isMatch(string s, string p) 
    {
        int m=s.length(),n=p.length();
        vector<unordered_map<int,bool>> hash(m);
        return help(s,p,0,0,hash);
    }
};
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