<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:

    vector<vector<int>> dp;
    bool rec(string s, string p,int n,int m,int i,int j) {
        if (i < 0 && j < 0) return true;
        if (j < 0) {
            return false;
        }
        if (i < 0) {
            return p[j] == '*' ? rec(s,p,n,m,i,j-2): false;
        }

        if (dp[i][j] != -1) return dp[i][j];

        if (s[i] == p[j] || p[j] == '.') {
            return dp[i][j] = rec(s,p,n,m,i-1,j-1);
        }
        if (p[j] == '*') {
            if (s[i] == p[j-1] || p[j-1] == '.') {
                return dp[i][j] = rec(s,p,n,m,i-1,j) || rec(s,p,n,m,i,j-2);
            }
            return dp[i][j] = rec(s,p,n,m,i,j-2);
        }
        return dp[i][j] = false;
    }

    bool isMatch(string s, string p) {
        int n = s.size();
        int m = p.size();
        dp.clear();
        dp.assign(n+1,vector<int>(m+1,-1));
        return rec(s,p,n,m,n-1,m-1);
    }
};
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