<p>Given an input string (<code>s</code>) and a pattern (<code>p</code>), implement wildcard pattern 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 any sequence of characters (including the empty sequence).</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;*&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong>&nbsp;&#39;*&#39; matches any sequence.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;cb&quot;, p = &quot;?a&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong>&nbsp;&#39;?&#39; matches &#39;c&#39;, but the second letter is &#39;a&#39;, which does not match &#39;b&#39;.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= s.length, p.length &lt;= 2000</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> or <code>&#39;*&#39;</code>.</li>
</ul>

"""
Solution: https://leetcode.com/problems/wildcard-matching/solutions/1336621/python-dfs-with-memoization-clean-concise

Similar Questions: 
* Regular Expression Matching: https://leetcode.com/problems/regular-expression-matching/description/?envType=company&envId=facebook&favoriteSlug=facebook-thirty-days
* Valid Palindrome III: https://leetcode.com/problems/valid-palindrome-iii/description/?envType=company&envId=facebook&favoriteSlug=facebook-thirty-days

"""

from functools import lru_cache
class Solution:
    def isMatch(self, s: str, p: str) -> bool:
        # edge case
        if not s and not p:
            return True
        
        
        return self.__matchHelper(s, p, 0, 0)
    
    @lru_cache(None)
    def __matchHelper(self, s: str, p: str, sIndex: int, pIndex: int) -> bool:
        # base case
        if pIndex >= len(p):
            return sIndex >= len(s)
        
        isMatch = False
        if sIndex < len(s) and (s[sIndex] == p[pIndex] or p[pIndex] == "?"):
             # case 1: match 1 char
             isMatch = self.__matchHelper(s, p, sIndex + 1, pIndex + 1)
        elif p[pIndex] == "*":
            # case 2: match no character (empty sequence)
            isMatch = self.__matchHelper(s, p, sIndex, pIndex + 1)
            
            # case 3: match 1 character only
            # case 4: match more characters
            if sIndex < len(s):
                isMatch = isMatch or (self.__matchHelper(s, p, sIndex + 1, pIndex + 1) 
                                        or self.__matchHelper(s, p, sIndex + 1, pIndex))
        
        return isMatch
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