<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 isMatch(string sequence, string pattern)
    {
        // cout << "isMatch called" << endl;
        int i = 0;
        int j = 0;
        while (1)
        {
            if (i >= sequence.length() && j >= pattern.length())
                return true;
            if (j >= pattern.length())
                return false;

            if (j + 1 < pattern.length() && pattern[j + 1] == '*')
            {
                if (i >= sequence.length())
                    j += 2;
                else if ((j+2 < pattern.length()) && isMatch(sequence.substr(i, sequence.length() - (i - 1)),
                            pattern.substr(j + 2, pattern.length() - j - 1)))
                {
                    return true;
                }
                else if ((sequence[i] == pattern[j]))
                {
                    i++;
                    // cout << "smd" << endl;
                }
                else if (pattern[j] == '.')
                {
                    if (isMatch(
                            sequence.substr(i, sequence.length() - (i - 1)),
                            pattern.substr(j + 2, pattern.length() - j - 1)))
                    {
                        // cout << "smd1" << endl;
                        return true;
                    }
                    else
                    {
                        // cout << "smd2" << endl;
                        i++;
                    }
                }
                else
                {
                    // cout << "smd3" << endl;
                    j += 2;
                }
            }
            else
            {
                if (i >= sequence.length())
                    return false;
                else if ((sequence[i] == pattern[j]) || (pattern[j] == '.'))
                {
                    i++, j++;
                }
                else
                    return false;
            }
        }
    }
};
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