<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:
        
        # wildcard matching
        # maintain i and j pointers for s and p
        # ? can match with any character
        # * can match with any sequence
        # * can match with empty sequence
        # use * as a skip


        cache = {}

        def dfs(i, j):
            # print(i, j)
            # matched both parts of entire string
            if i == len(s):
                return set(p[j:]) == { "*" } or j == len(p)
            
            # got through 
            if j == len(p):
                return i == len(s)
            
            if (i, j) in cache:
                return cache[(i, j)]
            
            # both chars are equal
            # or p is a ? at this point
            match = s[i] == p[j] or p[j] == "?"

            # advance both pointers at once
            if match:
                cache[(i, j)] = dfs(i + 1, j + 1)
                return cache[(i, j)]
            
            # no match
            else:
                # handle asterisks
                if p[j] == "*":
                    # consider as empty sequence
                    # continue to next char
                    empty = dfs(i, j + 1)

                    # match any sequence of characters
                    # advance i pointer only
                    anySeq = dfs(i + 1, j)

                    cache[(i, j)] = empty or anySeq
                    return cache[(i, j)]
                
                # character mismatch: immediately return False
                else:
                    cache[(i, j)] = False
                    return cache[(i, j)]

        return dfs(0, 0)
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