<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:
        # some kind of 2D DP
        #    '', a, a
        # ''  T, F, F
        #  a  F, T, [F]

        #    '', m, i, s, s
        # ''  T, F, F, F, F
        #  m  F, T, F, F, F
        #  ?  F, F, T, F, F
        #  ?  F, F, T, F, F
        #  *  F, T, T, F, F
        #  s  F, T, T, F, F

        #    '', c, b
        # ''  T, F, F
        #  ?  F, T, F
        #  b  F, F, T

        # for ? or s[x] == s[y] -> dp[x-1][y-1] 
        # for * -> dp[x-1][y] or dp[x][y-1] (* means empty or * covers curr char)

        dp = [[False for _ in range(len(s)+1)] for _ in range(len(p)+1)]
        dp[0][0] = True # '' to ''
        for x in range(1, len(dp)):
            for y in range(len(dp[0])):
                if p[x-1] == '*':
                    dp[x][y] = dp[x-1][y] or (y > 0 and dp[x][y-1])
                elif y > 0 and (p[x-1] == s[y-1] or p[x-1] == '?'):
                    dp[x][y] = dp[x-1][y-1]

        return dp[-1][-1]
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