<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 {
private:
    vector<int> cache;

    bool __isMatch(string& s, string& p, string::iterator sidx, string::iterator pidx) {
        for (; pidx != end(p); pidx++) {
            if (*pidx == '*') {
                for (;;) {
                    ++pidx;
                    if (pidx == end(p))
                        return true;
                    if (*pidx != '*')
                        break;
                }
                for (;;) {
                    if (_isMatch(s, p, sidx, pidx))
                        return true;
                    if (sidx == end(s))
                        break;
                    ++sidx;
                }
                return false;
            }
            if (sidx == end(s) || (*pidx != '?' && *sidx != *pidx))
                return false;
            ++sidx;
        }

        return sidx == end(s);
    }

    bool _isMatch(string& s, string& p, string::iterator sidx, string::iterator pidx) {
        bool res;
        int i, j;
        int val;

        i = sidx == end(s) ? s.length() : sidx - begin(s);
        j = pidx == end(p) ? p.length() : pidx - begin(p);

        val = cache[i * p.length() + j];
        if (val != 0)
            return val == 1;

        res = __isMatch(s, p, sidx, pidx);

        cache[i * p.length() + j] = res ? 1 : -1;

        return res;
    }

public:
    bool isMatch(string s, string p) {
        cache = vector<int>((s.length() + 1) * (p.length() + 1));

        return _isMatch(s, p, begin(s), begin(p));
    }
};
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