<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:
    // map<pair<int,int>,bool> mem;
    int dp[21][21];
    bool check(string s,string p, vector<bool>& isst,int i,int j){
        // if(mem.find({i,j})!=mem.end()) return mem[{i,j}];
        if(dp[i][j]!=-1) return dp[i][j];
        if(i==s.length()){
            if(j==p.length()) return dp[i][j]=1;
            if(isst[j]==1){
                return dp[i][j]=check(s,p,isst,i,j+1);
            }
            return dp[i][j]=0;
        }
        if(j==p.length()) return dp[i][j]=0;
        if(s[i]!=p[j] and p[j]!='.'){
            if(isst[j]) return dp[i][j]=check(s,p,isst,i,j+1);
            return dp[i][j]=0;
        }
        if(isst[j]){
            return dp[i][j]=check(s,p,isst,i+1,j+1) or check(s,p,isst,i+1,j) or check(s,p,isst,i,j+1);
        }
        else{
            return dp[i][j]=check(s,p,isst,i+1,j+1);
        }
        return dp[i][j]=0;
    }
    bool isMatch(string s, string p) {
        for(int i=0;i<21;i++){
        for(int j=0;j<21;j++){
            dp[i][j]=-1;
        }
    }
        string p1="";
        vector<bool> isst;
        for(int i=0;i<p.length();i++){
            if(p[i]=='*'){
                isst[isst.size()-1]=1;
            }
            else{
                p1+=p[i];
                isst.push_back(0);
            }
        }
        cout<<p1<<endl;
        for(int i=0;i<isst.size();i++){
            cout<<isst[i]<<" ";
        }
        return check(s,p1,isst,0,0);
    }
};
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