<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 {
public:
    bool isMatch(string s, string p) {
        vector<vector<char>> memo(s.size()+1, vector<char>(p.size(), 2));
        return dfsMemo(s, p, 0, 0, memo);
    }
    
    bool dfsMemo(const string& s, const string& p, int i, int j, 
                 vector<vector<char>>& memo) {
        if(i==s.size() && j==p.size()) return true;
        if(j==p.size()) return false;
        
        if(memo[i][j]!=2) return memo[i][j];
        bool res = false;
        if(p.at(j)=='*') {
            if(i<s.size()) {
                // use and skip
                res |= dfsMemo(s, p, i+1, j+1, memo);
                // use and keep    
                res |= dfsMemo(s, p, i+1, j, memo);
            }
            // skip
            res |= dfsMemo(s, p, i, j+1, memo);
        }
        else if(i<s.size() && (s.at(i)==p.at(j) || p.at(j)=='?'))
            res |= dfsMemo(s, p, i+1, j+1, memo);
        return memo[i][j] = res;
    }
};
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