<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>

class Solution {
public:
    bool isMatch(string s, string p) {
        vector memo(s.size()+1, vector<bool>(p.size()+1));
        memo[s.size()][p.size()] = true;
        function<bool(int,int)> canMatch = [&] (int sstart, int pstart) {
            bool firstMatch = sstart < s.size() &&
                              (s[sstart] == p[pstart] || p[pstart] == '.');
            if (pstart+1 < p.size() && p[pstart+1] == '*') {
                memo[sstart][pstart] = memo[sstart][pstart+2] ||
                                       (firstMatch && memo[sstart+1][pstart]);
            } else {
                memo[sstart][pstart] = firstMatch && memo[sstart+1][pstart+1];
            }
            return memo[sstart][pstart];
        };
        for (int i=s.size();i>=0;i--) {
            for (int j=p.size()-1;j>=0;j--) {
                canMatch(i, j);
            }
        }
        // for (auto vec: memo) {
        //     for (auto e: vec) cout << e << " ";
        //     cout << endl;
        // }
        return memo[0][0];
    }
};
10493