<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:
        cache = {}
        def dfs(indexS, indexP):
            if (indexS, indexP) in cache.keys():
                return cache[(indexS, indexP)]
            if indexS >= len(s) and indexP >= len(p):
                return True
            elif indexP >= len(p):
                return False
            elif indexS >= len(s):
                return p[indexP:] == "*" * len(p[indexP:])
            else:
                if indexS < len(s) and indexP < len(p):
                    if s[indexS] == p[indexP] or p[indexP] == "?":
                        cache[(indexS + 1, indexP + 1)] = dfs(indexS + 1, indexP + 1)
                        return cache[(indexS + 1, indexP + 1)]
                    elif p[indexP] == "*":
                        cache[(indexS + 1, indexP)] = dfs(indexS + 1, indexP)
                        cache[(indexS, indexP + 1)] = dfs(indexS, indexP + 1)
                        return cache[(indexS + 1, indexP)] or cache[(indexS, indexP + 1)]
                    return False
        return dfs(0, 0)



        
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