<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:

    def matchesEmpty(self, tokens):
        for x in tokens:
            if len(x) != 2:
                return False
        return True

    def generateTokens(self, p):
        prev = None
        result = []
        for x in p:
            if x == "*":
                e = result.pop()
                result.append(e + "*")
            else:
                result.append(x)
        return result

    def isMatchHelper(self, s, startS, tokens, startToken):
        if len(s) == startS and len(tokens) == startToken:
            return True
        elif len(tokens) == startToken:
            return False
        elif startS == len(s):
            # make sure all other patterns can match to nothing
            return self.matchesEmpty(tokens[startToken:])
        else:
            currentToken = tokens[startToken]
            if len(currentToken) == 2:
                # ends with *
                result = self.isMatchHelper(s, startS, tokens, startToken + 1)
                if result:
                    return True
                firstChar = currentToken[0]
                for x in range(startS, len(s)):
                    if firstChar == '.' or s[x] == firstChar:
                        result = self.isMatchHelper(s, x + 1, tokens, startToken + 1)
                        if result:
                            return True
                    else:
                        break
            else:
                if currentToken == '.' or currentToken == s[startS]:
                    return self.isMatchHelper(s, startS + 1, tokens, startToken + 1)
            return False

    def isMatch(self, s: str, p: str) -> bool:
        tokens = self.generateTokens(p)
        return self.isMatchHelper(s, 0, tokens, 0)
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