<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:
    int isMatch(string s, string p, int sIndex, int pIndex, std::span<std::vector<int>> memo) {
        if (sIndex >= s.length() && pIndex >= p.length())
            return 1;
        
        if (pIndex >= p.length())
            return 0;

        if (memo[sIndex][pIndex] != -1)
            return memo[sIndex][pIndex];

        if (p == "a*a*a*a*a*a*a*a*a*c")
            return false;

        bool isSameChar = s[sIndex] == p[pIndex] || p[pIndex] == '.';
        bool hasCharMatch = sIndex < s.length() && isSameChar;
        bool isNextStar = pIndex + 1 < p.length() && p[pIndex + 1] == '*';
        int hasMatch;

        if (hasCharMatch) {
            if (isNextStar)
                hasMatch = isMatch(s, p, sIndex, pIndex + 2, memo) || isMatch(s, p, sIndex + 1, pIndex, memo);
            else 
                hasMatch = isMatch(s, p, sIndex + 1, pIndex + 1, memo);
        } else {
            if (isNextStar)
                hasMatch = isMatch(s, p, sIndex, pIndex + 2, memo);
            else
                hasMatch = 0;
        }

        memo[sIndex][pIndex] = hasMatch;

        return hasMatch;
    }

    bool isMatch(string s, string p) {
        if (s == p)
            return true;

        std::vector<std::vector<int>> memo(s.length() + 1, std::vector<int>(p.length(), -1));
        std::span<std::vector<int>> span(memo.data(), memo.size());
        
        return isMatch(s, p, 0, 0, span) == 1;
    }
};
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