<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>

namespace {

int dp[2000][2000];

int is_match_recursive(const string &s, const string &p, int i, int j) {
  if (dp[i][j] != -1) {
    return dp[i][j];
  }
  if (i == s.size() && j == p.size()) {
    return 1;
  } else if (p[j] == '*') {
    for (int k = i; k <= s.size(); ++k) {
      if (is_match_recursive(s, p, k, j + 1)) {
        dp[i][j] = 1;
        return dp[i][j];
      }
    }
    dp[i][j] = 0;
    return dp[i][j];
  } else if (i == s.size() || j == p.size()) {
    return 0;
  } else if (p[j] == '?' || s[i] == p[j]) {
    dp[i][j] = is_match_recursive(s, p, i + 1, j + 1);
    return dp[i][j];
  } else {
    dp[i][j] = 0;
    return dp[i][j];
  }
}

} // namespace

class Solution {
public:
  bool isMatch(string s, string p) {
    fill(&dp[0][0], &dp[0][0] + sizeof(dp) / sizeof(dp[0][0]), -1);
    return static_cast<bool>(is_match_recursive(s, p, 0, 0));
  }
};

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