<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>

#include <map>

struct indices {
    indices(int ii, int jj) : i(ii), j(jj) {}
    int i;
    int j;
};
bool operator<(const indices& l, const indices& r) {
    return (l.i < r.i || (l.i == r.i && l.j < r.j));
}

class Solution {

private:
    string str;
    string pat;

    int sl;
    int pl;

    std::map<indices, bool> memo{};

    bool r(int i, int j) {
        indices ind(i, j);
        if (memo.contains(ind))
            return memo[ind];

        if (i >= sl && j >= pl)
            return true;
        if (j >= pl)
            return false;

        bool match = i < sl && (str[i] == pat[j] || pat[j] == '.');

        if (j + 1 < pl && pat[j + 1] == '*') {
            memo[ind] = r(i, j + 2) || (match && r(i + 1, j));
            return memo[ind];
        } else if (match) {
            memo[ind] = r(i + 1, j + 1);
            return memo[ind];
        } else {
            memo[ind] = false;
            return memo[ind];
        }
    }

public:
    bool isMatch(string s, string p) {
        str = s;
        pat = p;
        sl = str.length();
        pl = pat.length();
        return r(0, 0);
    }
};
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