<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:
        n = len(s)
        m = len(p)
       
        cache = {}

        def match(s_idx, p_idx) -> bool:
            if (s_idx, p_idx) in cache:
                return cache[(s_idx, p_idx)]
            # Wait for pattern to be exhausted
            if p_idx == m:
                finalValueToReturn = s_idx == n
                cache[(s_idx, p_idx)] = finalValueToReturn
                return finalValueToReturn # string must be exhausted if it matches the pattern
            
            elif s_idx > n: # if string is exhausted before pattern is exhausted, return False
                cache[(s_idx, p_idx)] = False
                return False
            
            else: # for all other scenarios
                # see if string matches the current pattern
                matched = ((s_idx < n) and (s[s_idx] == p[p_idx])) or (p[p_idx] in ["*", "?"])
                
                # if nothing matches, return false
                if not matched:
                    cache[(s_idx, p_idx)] = False
                
                else: # in case of a match
                    # check if pattern has "*"
                    if p[p_idx] == "*":
                        finalValueToReturn = (match(s_idx+1, p_idx) or # increment string index and stay at same pattern index
                                match(s_idx+1,p_idx+1) or # increment both string and patter index
                                match(s_idx, p_idx+1)) # increment pattern index and stay at the same string index
                    
                    else: # if pattern doesn't have "*", then it either have "?" or same char as string
                        finalValueToReturn = match(s_idx+1, p_idx+1) # increment both string and pattern index
                    
                    cache[(s_idx, p_idx)] = finalValueToReturn
                    return finalValueToReturn
        
        return match(0,0)
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