<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: 
    bool check(string p,int i)
    {
        for(int j=0;j<=i;j++)
        {
            if(p[j]!='.')
            {
                return false;
            }
        }
        return true;
    }
    bool solve(int i,int j,string s,string p,vector<vector<int>>&dp)
    {
        if(i<0 and j<0)
        {
            return true;
        }
        if(i<0 and j>=0)
        {
            return false;
        }
        if(i>=0 and j<0)
        {
            while(i >= 0 && p[i] == '*')
            {
                i -= 2;
            }
            return i < 0;
        }
        if(dp[i][j]!=-1){
            return dp[i][j];
        }
        if(p[i]==s[j] or p[i]=='.')
        {
            return dp[i][j] = solve(i-1,j-1,s,p,dp);
        }
        else 
        {
            if(p[i]=='*')
            {
                bool matchZero = solve(i-2, j, s, p, dp);
                bool matchOneOrMore = (p[i-1]==s[j] || p[i-1]=='.') && solve(i, j-1, s, p, dp);
                return dp[i][j] = matchZero || matchOneOrMore;
            }
            else
            {
                return false;
            }
        }
    }
    bool isMatch(string s, string p) {
        int i = p.length()-1;
        int j=  s.length()-1;
        vector<vector<int>>dp(i+1,vector<int>(j+1,-1));
        bool answer = solve(i,j,s,p,dp);
        return answer;
    }
};

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