<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:
        return self._search(s,p,0,0,set())

    def _search(self, s:str, p:str, i:int, j:int,mem:set()) -> bool:
        if i == len(s):
            return self._is_nullified(p, j)
        if j == len(p):
            return i == len(s)
        key = j * len(s) + i
        if key in mem:
            return False
        if p[j] == '*':
            k = j
            while k+1 < len(p) and p[k+1] == '*':
                k += 1
            l = 0
            while i+l <= len(s):
                if self._search(s,p,i+l,k+1,mem):
                    return True
                l += 1
        elif p[j] == '?' or p[j] == s[i]:
            res = self._search(s,p,i+1,j+1,mem)
            if not res:
                mem.add(key)
            return res
        mem.add(key)
        return False

    def _is_nullified(self, p:str, j:int) -> bool:
        for i in range(j, len(p)):
            if p[i] != '*':
                return False
        return True
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