<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:
        len_s, len_p = len(s), len(p)
        memo = {}
        
        def _is_match_from(s_idx: int, p_idx: int) -> bool:
            cache_key = (s_idx, p_idx)
            if cache_key in memo:
                return memo[cache_key]
            if s_idx == len_s:
                return p_idx == len_p or set(p[p_idx:]) == set('*')
            if p_idx == len_p:
                return s_idx == len_s

            match = s[s_idx] == p[p_idx] or p[p_idx] == '?'
            memo[cache_key] = False
            if match:
                memo[cache_key] =  _is_match_from(s_idx + 1, p_idx + 1)
            elif p[p_idx] == '*':
                memo[cache_key] = _is_match_from(s_idx + 1, p_idx) or _is_match_from(s_idx + 1, p_idx + 1) or _is_match_from(s_idx, p_idx + 1)
            
            return memo[cache_key]
        
        return _is_match_from(0, 0)

            
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