<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) {

    const int m = s.length();

    const int n = p.length();

    // dp[i][j] := true if s[0..i) matches p[0..j)

    vector<vector<bool>> dp(m + 1, vector<bool>(n + 1));

    dp[0][0] = true;

    auto isMatch = [&](int i, int j) -> bool {

      return j >= 0 && p[j] == '?' || s[i] == p[j];

    };

    for (int j = 0; j < p.length(); ++j)

      if (p[j] == '*')

        dp[0][j + 1] = dp[0][j];

    for (int i = 0; i < m; ++i)

      for (int j = 0; j < n; ++j)

        if (p[j] == '*') {

          const bool matchEmpty = dp[i + 1][j];

          const bool matchSome = dp[i][j + 1];

          dp[i + 1][j + 1] = matchEmpty || matchSome;

        } else if (isMatch(i, j)) {

          dp[i + 1][j + 1] = dp[i][j];

        }

    return dp[m][n];

  }

};

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