<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:
        """
        w/o wildcard matching

        '?' matches any single character. Q: can this be matched w/ ""?
        '*' Matches any sequence of characters (including the empty sequence).

        asdfsdaf 
        x 
        *
        b
        ..
        O(nm)
        """
        def _is_match(s, p, s_i, p_i, mem):
            if (s_i, p_i) in mem:
                return False

            mem.add((s_i, p_i))
            if len(p) == p_i:
                if len(s) == s_i:
                    return True  # fully matched
                else:
                    return False # we used all the pattern
            else:
                if p[p_i] == "?":
                    if len(s) == s_i:
                        return False
                    else:
                        return _is_match(s, p, s_i+1, p_i+1, mem)
                elif p[p_i] == "*":
                    if len(s) == s_i:
                        return _is_match(s, p, s_i, p_i+1, mem)  # skip
                    else:
                        return (
                            _is_match(s, p, s_i+1, p_i, mem) or  # use
                            _is_match(s, p, s_i, p_i+1, mem)     # skip
                        )
                else:
                    if len(s) == s_i or s[s_i] != p[p_i]:
                        return False
                    else:
                        return _is_match(s, p, s_i+1, p_i+1, mem) # char matched
        
        return _is_match(s, p, 0, 0, set())

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