Regular Expression Matching
<p>Given an input string <code>s</code>&nbsp;and a pattern <code>p</code>, implement regular expression 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 zero or more of the preceding element.</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;a*&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> &#39;*&#39; means zero or more of the preceding element, &#39;a&#39;. Therefore, by repeating &#39;a&#39; once, it becomes &quot;aa&quot;.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;ab&quot;, p = &quot;.*&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> &quot;.*&quot; means &quot;zero or more (*) of any character (.)&quot;.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length&nbsp;&lt;= 20</code></li>
	<li><code>1 &lt;= p.length&nbsp;&lt;= 20</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>, and&nbsp;<code>&#39;*&#39;</code>.</li>
	<li>It is guaranteed for each appearance of the character <code>&#39;*&#39;</code>, there will be a previous valid character to match.</li>
</ul>
Recursion; String; Dynamic Programming
class Solution {
    /**
     * @param String $s
     * @param String $p
     * @return Boolean
     */
    function isMatch($s, $p) {
        $m = strlen($s);
        $n = strlen($p);
        $f = array_fill(0, $m + 1, array_fill(0, $n + 1, 0));

        $dfs = function ($i, $j) use (&$s, &$p, $m, $n, &$f, &$dfs) {
            if ($j >= $n) {
                return $i == $m;
            }
            if ($f[$i][$j] != 0) {
                return $f[$i][$j] == 1;
            }
            $res = -1;
            if ($j + 1 < $n && $p[$j + 1] == '*') {
                if (
                    $dfs($i, $j + 2) ||
                    ($i < $m && ($s[$i] == $p[$j] || $p[$j] == '.') && $dfs($i + 1, $j))
                ) {
                    $res = 1;
                }
            } elseif ($i < $m && ($s[$i] == $p[$j] || $p[$j] == '.') && $dfs($i + 1, $j + 1)) {
                $res = 1;
            }
            $f[$i][$j] = $res;
            return $res == 1;
        };

        return $dfs(0, 0);
    }
}