<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 isMatch(string s, string p) {
        /* top down DP-approach */
        int s_len = s.length();
        int p_len = p.length();
        if (p_len == 0){
            return !s_len;
        }
        if (p[p_len-1] == '*'){
            if (s_len == 0){
                return isMatch(s,p.substr(0,p_len-2));
            }
            else if (s[s_len-1] == p[p_len-2] || p[p_len-2] == '.'){
                return isMatch(s.substr(0,s_len-1),p.substr(0,p_len-2)) || isMatch(s.substr(0,s_len-1), p.substr(0,p_len)) || isMatch(s, p.substr(0,p_len-2));
            }
            else{
                return isMatch(s, p.substr(0,p_len-2));
            }
        }
        else{
            if (s_len == 0){
                return false;
            }
            else if (s[s_len-1] == p[p_len-1] || p[p_len-1] == '.') {
                return isMatch(s.substr(0,s_len-1),p.substr(0,p_len-1));
            }
            else{
                return false;
            }
        }
    }
};
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