<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:
    map<pair<int,int>, long long> dp;
    bool isMatchUtil(string &s, string &p , int n, int m){
        if(n == -1 && m == -1)
            return true;
        if(dp.find({n, m}) != dp.end())
            return dp[{n, m}];
        if(m == -1)
            return false;
        if(n == -1){
            if(p[m] != '*')
                return false;
            return dp[{n, m}]=isMatchUtil(s, p, n, m-2);
        }

        bool res = false;
        if(p[m] == '.'){
            res = isMatchUtil(s, p, n-1, m-1);
        }
        else if(p[m] == '*'){
            res = isMatchUtil(s, p, n, m-2);
            if(p[m-1] == '.' || s[n] == p[m-1])
                res = res || isMatchUtil(s, p, n-1, m);
        }
        else
            res = (s[n] == p[m]) && isMatchUtil(s, p, n-1, m-1);
        return dp[{n, m}] = res;
    }
    bool isMatch(string s, string p) {
        dp.clear();
        string regex = "";
        char l = '0';
        for(auto c: p){
            if(c!=l || c != '*'){
                l = c;
                regex += c;
            }
        }
        return isMatchUtil(s, regex, s.size() - 1, regex.size() - 1);
    }
};
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