<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 = {}
        old_p = p
        p = list()
        for c in old_p:
            if p and p[-1] == '*':
                if c == '*':
                    continue
            p.append(c)
            
        def helper(i, j):
            if (i,j) in dp:
                return dp[(i,j)]
            # print(f"s: {s}, p: {p}")
            if i == len(s) and j == len(p): # no more of each
                return True

            if i == len(s) and (len(p) - j == 1) and p[j] == '*': # 
                return True

            if i == len(s) or j == len(p): # no more of one but not the other
                return False

            ret = False
            if p[j] == '?':
                ret = helper(i+1, j+1)
            elif p[j] == '*':
                # two choices here, match the next char or not
                ret = helper(i+1, j) or helper(i, j+1)
            elif p[j] == s[i]:
                ret = helper(i+1, j+1)

            dp[(i,j)] = ret  

            return ret
        # first we collapse all * in p
  
        ret =  helper(0,0)
        return ret

        
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