<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:
    unordered_map<string, bool> memo;
    bool isMatch(string s, string p) {
        string key = s + "____" + p;
        if (memo.find(key) != memo.end()) {
            return memo[key];
        }

        auto isCharOrDot = [](const char &s) -> bool {
            return (s == '.') || isalpha(s);
        };

        auto matchChar = [](const char &c1, const char &c2) -> bool {
            return c1 == '.' || c2 == c1;
        };
        
        bool ret = false;

        if ((p.size() >= 2) && isCharOrDot(p.at(0)) && (p.at(1) == '*')) {
                char toMatch = p.at(0);
                int spos = 0;
                string newP = p.substr(2);
                while (((spos < s.size()) && matchChar(toMatch, s.at(spos))) || spos == s.size()) {
                    string newS = s.substr(spos);
                    if (this->isMatch(newS, newP)) { ret = true; break; }
                    spos++;
                }
                ret = ret || (this->isMatch(s, newP)) || (spos < s.size() ? this->isMatch(s.substr(spos), newP) : false);
            } else if ((0 < s.size()) && (0 < p.size()) && matchChar(p.at(0), s.at(0))) {
                ret = (this->isMatch(s.substr(1), p.substr(1)));
            } else if (s == "" && p == "") {
                ret = true;
            } else {
                ret = false;
            }
        memo[key] = ret;
        return ret;
    }
};
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