<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 {
    map<pair<string,string>,bool> mem;
public:
    bool isMatch(string s, string p) {;
        if(mem.find({s,p})!=mem.end()) return mem[{s,p}];

        if(s.size()==0 && p.size()==0) return true;
        if(s.size()==0 && p.size()>=2 && p[1]=='*') return mem[{s,p}]=isMatch(s,p.substr(2));
        if(s.size()==0 || p.size()==0) return false;
        bool ans=false;
        if(p.size()>=2 && (s[0]==p[0] || p[0]=='.') && p[1]=='*'){
            if(s.size()==1 && p.size()==2) ans|= true;
            else ans|= (isMatch(s.substr(1),p) || isMatch(s,p.substr(2)));
        }
        else if(p.size()>=2 && (s[0]!=p[0]) && p[1]=='*'){
           ans|= isMatch(s,p.substr(2));
        }
        else if(p.size()>=2 && (s[0]==p[0] || p[0]=='.') && p[1]!='*'){
            ans|= isMatch(s.substr(1),p.substr(1));
        }
        else if(p.size()==1 && (s[0]==p[0] || p[0]=='.')){
            ans|= isMatch(s.substr(1),p.substr(1));
        }
        return mem[{s,p}]=ans;
    }
};
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