<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:
    int fun(int i,int j,string pattern,string str,vector<vector<int>>& dp){
        if(i==0 and j==0)
            return true;
        else if(i==0 and j>0)
            return false;
        else if(i>0 and j==0)
        {
            if(pattern[i-1]=='*')
                return dp[i][j]=fun(i-2,j,pattern,str,dp);
            else
                return 0;
        }
        if(dp[i][j]!=-1)
            return dp[i][j];
        if(pattern[i-1]==str[j-1] or pattern[i-1]=='.')
            return dp[i][j]=fun(i-1,j-1,pattern,str,dp);
        else if(pattern[i-1]=='*')
        {
            if(fun(i-2,j,pattern,str,dp))
                return dp[i][j]=true;
            if(pattern[i-2]==str[j-1] or pattern[i-2]=='.')
                return dp[i][j]=fun(i,j-1,pattern,str,dp);
            return dp[i][j]=false;
        }
        return dp[i][j]=false;
    }
    bool isMatch(string s, string p) {
        vector<vector<int>> dp(p.size()+1,vector<int>(s.size()+1,-1));
        return fun(p.size(),s.size(),p,s,dp);
    }
};
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