<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 main1(s, p)


def main1(s: str, p: str) -> bool:

    memoized = {}

    def recurse(s, s_idx, p, p_idx) -> bool:
        # print(f'recurse')
        if s_idx == len(s) and p_idx < len(p) and p[p_idx] != '*':
            return False

        while p_idx < len(p) and s_idx <= len(s):
            # print(f' - while')
            if p[p_idx] == '*':
                # print(f'  - * match')
                if p_idx == len(p) - 1:
                    # print(f'   - return True')
                    return True
                i = s_idx
                while i <= len(s):
                    key = f'{i}-{p_idx+1}'
                    if key not in memoized:
                        if recurse(s, i, p, p_idx + 1):
                            return True
                        memoized[key] = False
                    i += 1
                return False
            elif s_idx >= len(s) or p[p_idx] != '?' and p[p_idx] != s[s_idx]:
                return False

            # letters match so progress pattern
            p_idx += 1
            s_idx += 1

        if p_idx >= len(p) and s_idx >= len(s):
            return True
        return False

    return recurse(s, 0, p, 0)
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