<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 checkForStar(string p, int x) {
        for (int i=x+1; i < p.size(); i+=2) {
            if (p[i] != '*') return false;
        }
        if (p[p.size()-1] != '*') return false;

        return true;
    }
    bool fn(string s, string p, int x, int y, vector<vector<int>>& dp) {
         cout << x << " " << y <<endl;
       if (x == s.size()) {
        if (y!= p.size()) {
            return checkForStar(p, y);
        }
        return true;
       }
       if (y== p.size()) {
        return false;
       }
       if (dp[x][y] != -1) return dp[x][y];

       if (y+1 < p.size() && p[y+1] == '*') {
        if (p[y] == '.') {
            for (int i=x; i<=s.size(); i++) {
                int resp = fn(s,p,i, y+2, dp);
                if (resp) {
                    dp[x][y] = 1;
                    break;
                }
            }  
            if (dp[x][y] == -1) dp[x][y] = 0; 
        } else {
            for (int i=x; i<=s.size(); i++) {
                
                int resp = fn(s,p,i, y+2, dp);
                
                if (resp) {
                    dp[x][y] = 1;
                    break;
                }
                if ( i< s.size() && s[i] != p[y]) {
                    dp[x][y] = resp;
                    break;
                }
            }   
            if (dp[x][y] == -1) dp[x][y] = 0; 
        }
       } else {
        if (p[y] == '.') {
            dp[x][y] = fn(s, p, x+1, y+1, dp);
        } else {
            if (p[y] == s[x]) {
                dp[x][y] = fn(s, p, x+1, y+1, dp);
            } else {
                dp[x][y] = 0;
            }
        }
       }
        cout << x << " " <<  y << " " << dp[x][y] << endl;
       return dp[x][y];
    }

    bool isMatch(string s, string p) {
        vector<vector<int>> dp(s.size(), vector<int>(p.size(), -1));
        return fn(s, p, 0, 0, dp);
    }
};
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