<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 s, string p) {
        int pLen=p.size();
        vector<int> patternPos;
        patternPos.push_back(0);
        for (int i=0; i<pLen-1; i+=2) {
            if (p[i+1]=='*') {
                patternPos.push_back(i+2);
            } else break;
        }
        //for(auto pp : patternPos) cout << pp << " ";
        //cout << "\n";
        for (char c : s) {
            vector<int> nextPos;
            for (int pp : patternPos) {
                if (pp>=pLen) continue;

                bool isStar=(pp<pLen-1 && p[pp+1] == '*');
                bool fits =(p[pp]=='.' || p[pp]==c);
                int pn=pp;
                if (fits && isStar) {
                    pn=pp;
                } else if (fits) {
                    pn=pp+1;
                } else {
                    continue;
                }
                if (nextPos.size()==0 || nextPos.back()<pn) {
                    nextPos.push_back(pn);
                }
                while (pn<pLen-1 && p[pn+1]=='*') {
                    pn+=2;
                    nextPos.push_back(pn);
                }
            }
            //cout << c << ": ";
            //for(auto pp : nextPos) cout << pp << " ";
            //cout << "\n";
            patternPos.swap(nextPos);
        }
        return (patternPos.size()>0 && patternPos.back()==pLen);
    }
};
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