<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:
        dp = {}
        
        def remove_duplicate_start(p):
            res = []
            for i in range(len(p)):
                if i > 0 and p[i] == p[i-1] == "*":
                    continue
                res.append(p[i])
            return "".join(res)


        # check if s[i:] and p[j:] matches
        def check(i, j):
            if (i, j) in dp:
                return dp[(i, j)]
            
            res = False
            if i == len(s):
                res = p[j:] in {"", "*"}
            elif j == len(p):
                res = j-1 >= 0 and p[j-1] == "*"
            elif i > len(s):
                res = False
            else:
                if p[j] in {s[i], "?"}:
                    res = check(i+1, j+1)
                elif p[j] == "*":
                    res = check(i, j+1) or check(i+1, j)
                    # res = any([
                    #     check(i, j+1), # treat * as empty char
                    #     # check(i+1, j+1), # use * to cover current char only
                    #     check(i+1, j) # use * to cover current and the next char
                    # ])
                else:
                    # p[j] and s[i] don't match
                    res = False
            
            dp[(i, j)] = res
            return res

        p = remove_duplicate_start(p)
        # if not s:
        #     return not p or p == "*"

        return check(0, 0)
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