<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 solve(vector<vector<int>> &dp,string s,string p,int i,int j){
        if(i==-1 && j==-1){
            return true;
        }
        if(i==-1 && j>=0){
            while(j>=0){
                if(p[j]=='*'){
                    j=j-2;
                }
                else{
                    return false;
                }
            }
            if(j==-1){
                return true;
            }
            return false;
        }
        if(i<0 || j<0){
            return false;
        }
        if(dp[i][j]!=-1){
            return dp[i][j];
        }
        bool o1 = false;
        if(s[i]==p[j] || p[j]=='.' ){
            o1 = o1 || solve(dp,s,p,i-1,j-1);
        }
        else if(p[j]=='*'){
            o1 = o1 || solve(dp,s,p,i,j-2);
            o1 = o1 || ((s[i]==p[j-1] || p[j-1]=='.') && solve(dp,s,p,i-1,j));
        }
        return dp[i][j] = o1;
    }
    bool isMatch(string s, string p) {
        int ns = s.length();
        int np = p.length();
        vector<vector<int>> dp(ns+1,vector<int> (np+1,-1));
        return solve(dp,s,p,ns-1,np-1);
    }
};
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