<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>

class Solution:
    def isMatch(self, s: str, p: str) -> bool:

        @cache
        def match(source_idx, pattern_idx, source, pattern):
            if source_idx == len(source) and pattern_idx == len(pattern):
                return True
            
            if source_idx == len(source):
                # if pattern is "*" return True
                return all(p == "*" for p in pattern[pattern_idx:])
            
            if pattern_idx == len(pattern):
                return False

            # abc, a/b
            # abc, ?
            # abc, *
            if source[source_idx] == pattern[pattern_idx]:
                return match(source_idx + 1, pattern_idx + 1, source, pattern)
            
            if pattern[pattern_idx] == "?":
                # match one character
                return match(source_idx + 1, pattern_idx + 1, source, pattern)
            
            if pattern[pattern_idx] == "*":
                # 2 cases
                # case 1: match one character
                return match(source_idx + 1, pattern_idx, source, pattern) or \
                match(source_idx + 1, pattern_idx + 1, source, pattern) or \
                match(source_idx, pattern_idx + 1, source, pattern)
            
            return False

        return match(0, 0, s, p)
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