<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>

import numpy as np

class Solution:
    
    def isMatch(self, s: str, p: str) -> bool:
        """
        dp[i, j] = True if the prefix 0..i in patt matches the prefix of 0..j in input s
        dp[i, j] = dp[i-1, j-1] & ((s[j]==p[i]) or (p[i]=='?') or (p[i]=='*')) OR
                    dp[i,j-1] if p[i] == '*' OR
                    dp[i-1, j]
        """
        n = len(s)
        m = len(p)
        dp = np.zeros((m+1, n+1), dtype=bool)
        dp[0, 0] = True
        for i in range(m):
            if p[i] == '*':
                dp[i+1, 0] |= dp[i, 0]
        for i in range(m):
            for j in range(n+1):
                if (j < n) and ((s[j] == p[i]) or (p[i] == '?') or (p[i] == '*')):
                    dp[i+1, j+1] |= dp[i, j]
                if p[i] == '*':
                    if i < m:
                        dp[i+1, j] |= dp[i, j]
                    if j < n:
                        dp[i, j+1] |= dp[i, j]
        return dp[m, n]
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