<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 isFirstMatch(string& s, string& p, int i, int j)
    {
        if (s[i] == p[j] || (p[j] == '.' && i < s.size()))
            return true;
        return false;
    }

    bool isMatch(string s, string p)
    {
        return isMatch(s, p, 0, 0);
    }

    bool isMatch(string& s, string& p, int i, int j) {
        if (j == p.size())
            return i == s.size();
        
        if (st.find({i, j}) == st.end())
            st.insert({i, j});
        else
            return false;

        if ( j==(p.size()-1) || p[j+1] != '*')
        {
            if (isFirstMatch(s, p, i, j))
                return isMatch(s, p, i+1, j+1);
            else
                return false;
        }

        if (isMatch(s, p, i, j+2))
            return true;

        int k=0;
        while (isFirstMatch(s, p, i+k, j))
        {
            if (isMatch(s, p, i+k+1, j+2))
                return true;
            k++;
        }
        return false;
    }

    set<pair<int, int>> st;
};
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