<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:
    unordered_map<string, unordered_map<string, bool>> map;

    bool isMatch(string s, string p) {
        if (s.size() == 0 && p.size() == 0)
            return true;
        if (s.size() > 0 && p.size() == 0)
            return false;
        if (map[s].find(p) != map[s].end())
            return map[s][p];

        // cout << "s = \"" << s << "\", p = \"" << p << "\"" << endl;

        // next char is not '*'
        if (p.size() < 2 || p[1] != '*') {
            if (s.size() == 0 || (p[0] != '.' && p[0] != s[0])) {
                map[s][p] = false;
                return false;
            }

            map[s][p] = isMatch(s.substr(1), p.substr(1));
            return map[s][p];
        }

        // next char is '*' and current char is '.'
        if (p[0] == '.') {
            map[s][p] = false;
            for (int i = 0; !map[s][p] && i <= s.size(); ++i)
                map[s][p] |= isMatch(s.substr(i), p.substr(2));
            return map[s][p];
        }
        
        // next char is '*' and current char is not '.'
        map[s][p] = isMatch(s, p.substr(2));
        for (int i = 0; !map[s][p] && s[i] == p[0]; ++i)
            map[s][p] |= isMatch(s.substr(i + 1), p.substr(2));
        return map[s][p];
    }
};
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