<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:
        #index i is index of p and j is index of s 
        cache = {}
        def dfs(i, j):
            if i == len(p) and j == len(s): 
                return True 
            if i == len(p): 
                return False 
            if j == len(s): 
                if p[i] != '*': 
                    return False 
            if (i, j) in cache: 
                return cache[(i, j)]

            reg_char = p[i]
            if p[i] == '?': 
                cache[(i, j)] = dfs(i+1, j+1)
            elif p[i] == '*': 
                possible = False
                for index in range(j, len(s)+1): 
                    possible = possible or dfs(i+1, index)
                cache[(i, j)] = possible 
            else: 
                if p[i] == s[j]: 
                    cache[(i, j)] = dfs(i+1, j+1)
                else: 
                    cache[(i, j)] = False
                    return False 
            
            return cache[(i, j)]
        return dfs(0, 0)


        
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