<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>

from functools import cache

class Solution:
    def isMatch(self, s: str, p: str) -> bool:
        # s = aaeabelb
        # p = **e*b
        # a*
        # a*b*
        idx = defaultdict(list)
        for i, c in enumerate(s):
            idx[c].append(i)

        @cache
        def is_match(i, j):
            if i > len(s):
                return False
            if j == len(p):
                return i == len(s)
            if p[j] == '?' or i < len(s) and s[i] == p[j]:
                return is_match(i + 1, j + 1)
            if p[j] == '*':
                while p[j] == '*':
                    j += 1
                    if j == len(p): 
                        return True
                if p[j] != '?':
                    idxs = idx[p[j]]
                    x = bisect_left(idxs, i)
                    for xx in range(x, len(idxs)):
                        if is_match(idxs[xx], j):
                            return True
                else:
                    for ii in range(i, len(s)):
                        if ii >= i and is_match(ii, j):
                            return True
            return False

        return is_match(0, 0)





        
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