<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:
        def rec(index1, index2, s, p, visited, ans):
            if (visited[index1][index2]):
                return ans[index1][index2]

            visited[index1][index2] = True
            if (index1 == len(s)):
                orig_index2 = index2
                while (index2 < len(p) and p[index2] == '*'):
                    index2 += 1
                ans[index1][orig_index2] = index2 == len(p)
                return index2 == len(p)
            if (index2 == len(p)):
                visited[index1][index2] = True
                ans[index1][index2] = False
                return False
            
            if (p[index2] == '?'):
                ans[index1][index2] = rec(index1 + 1, index2 + 1, s, p, visited, ans)
                return ans[index1][index2]
            elif (p[index2] == '*'):
                pos = False
                for i in range(index1, len(s) + 1):
                    pos = pos or rec(i, index2 + 1, s, p, visited, ans)
                ans[index1][index2] = pos
                return pos
            else:
                if (s[index1] == p[index2]):
                    ans[index1][index2] = rec(index1 + 1, index2 + 1, s, p, visited, ans)
                    return ans[index1][index2]
                else:
                    ans[index1][index2] = False
                    return False
        visited = [[False for _ in range(len(p) + 1)] for _ in range(len(s) + 1)]
        ans = [[False for _ in range(len(p) + 1)] for _ in range(len(s) + 1)]
        return rec(0, 0, s, p, visited, ans)
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