<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 {

    bool chk( vector<vector<int>> & dp, string s, string p, int index1, int index2){
     if(index2 < 0){
        return index1<0;
     }

if(dp[index1+1][index2+1]!=-1){
    return dp[index1+1][index2+1];
}
       if(index2 >0 && p[index2]=='*'){
        return dp[index1+1][index2+1] =  chk(dp,s,p,index1,index2-2) || ((index1 >=0 && (p[index2-1] == s[index1] || p[index2-1]=='.')) &&chk(dp,s,p,index1-1,index2));
       }


       if((index1>=0) && (p[index2]==s[index1] || p[index2]=='.')){
        return dp[index1+1][index2+1]= chk(dp, s,p,index1-1, index2-1);
       }
return dp[index1+1][index2+1]= false;

    }
public:
    bool isMatch(string s, string p) {

        vector<vector<int>>dp(s.size()+1, vector<int> (p.size()+1,-1));
        return chk(dp,s,p,s.size()-1, p.size()-1);
    }
};
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