<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:
        self.memo = {}
        self.s = s
        self.p = p
        return self.iterate(0,0)
    
    def iterate(self, s_idx: int, p_idx: int) -> bool:
        if s_idx == len(self.s) and p_idx == len(self.p):
            return True
        elif s_idx == len(self.s) and p_idx != len(self.p) and self.p[p_idx] != "*":
            return False
        elif s_idx == len(self.s) and p_idx != len(self.p) and self.p[p_idx] == "*":
            return self.iterate(s_idx, p_idx+1)
        elif s_idx != len(self.s) and p_idx == len(self.p):
            return False
        
        key = f"{s_idx}-{p_idx}"
        if key in self.memo:
            return self.memo[key]
        
        if self.p[p_idx] not in "*?":
            if self.p[p_idx] != self.s[s_idx]:
                result = False
            else:
                result = self.iterate(s_idx+1, p_idx+1)
        elif self.p[p_idx] == "?":
            result = self.iterate(s_idx+1, p_idx+1)
        elif self.p[p_idx] == "*":
            result = self.iterate(s_idx, p_idx+1) or self.iterate(s_idx+1, p_idx)
        else:
            raise f"Implementation error"
        
        self.memo[key] = result
        # print(f"iterating {self.s[s_idx:]} | {self.p[p_idx:]} => {result}")
        return result

60291