<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>

# include <bits/stdc++.h>
using namespace std;

class Solution {
public:
    bool isMatch(string s, string p) {
        vector<vector<bool>> matriz;
    string s_vazio = " ";
    s_vazio.append(s);
    string p_vazio = " ";
    p_vazio.append(p);
    for (int y=0 ; y<p.size()+1;y++){
        vector<bool> linha;
        for (int x=0; x<s.size()+1;x++){
            if (y==0 || x==0){
                if (s_vazio[x] == p_vazio[y]){
                    linha.push_back(1);
                }else if (p_vazio[y] == '*'){
                    linha.push_back((matriz[y-1][x] || matriz[y-2][x]));
                }else{
                    linha.push_back(0);
                }
            }else {
                if (s_vazio[x] == p_vazio[y] || p_vazio[y] == '.'){
                    linha.push_back(matriz[y-1][x-1]);
                } else if (p_vazio[y] == '*'){
                    if (s_vazio[x] == p_vazio[y-1] || p_vazio[y-1] == '.'){
                        linha.push_back((matriz[y-1][x] || matriz[y-2][x] || linha[x-1]));
                    } else{
                        linha.push_back((matriz[y-1][x] || matriz[y-2][x]));
                    }
                    
                }else{
                    linha.push_back(0);
                }
            }
        }
        matriz.push_back(linha);
    }
    return matriz[p.size()][s.size()];
    }
};
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