<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 dp[25][25] = {};
    bool init_val=false;
    void init(){
    if(init_val)
    return;
    for(int i=0; i <=20;i++)
        for(int j=0; j <=20;j++)
            dp[i][j]=-1;
    dp[0][0]=1;
    for(int i=1; i <=20;i++)
    dp[i][0]=0;
    init_val = true;
    }
    bool isMatch(string s, string p) {
        init();
        if(s=="" && p[1]=='*'){
            if(dp[0][p.length()-2]!=-1)
                return dp[0][p.length()]=dp[0][p.length()-2];
            else return dp[0][p.length()]=isMatch(s,p.substr(2));}
        if(s=="")
            return dp[0][p.length()]=0;

        int flag = 0;

        if(p[1]=='*'){

            int i=-1;

            do{
                if(dp[s.length()-i-1][p.length()-2]!=-1)
                flag = dp[s.length()-i-1][p.length()-2];
                else
                flag = isMatch(s.substr(i+1),p.substr(2));
                i++;
            }while(flag!=1 && (s[i]==p[0] || p[0]=='.') && i < s.length());

            return dp[s.length()][p.length()]= flag;

        }
        else if(s[0]==p[0] || p[0]=='.'){
            if(dp[s.length()-1][p.length()-1]!=-1)
                return dp[s.length()][p.length()]=dp[s.length()-1][p.length()-1];
            else
                return dp[s.length()][p.length()]=isMatch(s.substr(1),p.substr(1));
        }
        else return dp[s.length()][p.length()]=0;


    }
};
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