<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>

struct State {
    char edge;
    bool looped;
    State(char e, bool l): edge{e}, looped{l} {}
};

class Solution {
public:
    bool isMatch(string s, string p) {
        std::vector<State> states;

        std::optional<char> last_c = {};
        for (auto& c: p) {
            if (c == '*') {
                states.emplace_back( *last_c, true );
                last_c = {};
            } else {
                if (last_c.has_value())
                    states.emplace_back( *last_c, false );
                last_c = c;
            }
        }
        if (last_c.has_value())
            states.emplace_back( *last_c, false );

        std::unordered_set<size_t> curr_states = { 0 };
        for (auto& c: s) {
            std::unordered_set<size_t> to_walk = curr_states;
            for(auto& state: to_walk) {
                size_t ss = state;
                while(true) {
                    if (ss == states.size() || !states[ss].looped)
                        break;
                    size_t new_state = ss + 1;
                    if (curr_states.contains(new_state))
                        break;
                    curr_states.insert(new_state);
                    ss++;
                }
            }

            std::unordered_set<size_t> new_states = {};
            for(auto& state_idx: curr_states) {
                if (state_idx == states.size())
                    continue;
                auto& state = states[state_idx];
                if (state.edge == '.' || state.edge == c) {
                    new_states.insert( state.looped ? state_idx : state_idx + 1 );
                }
            }
            curr_states = std::move(new_states);
        }
        std::unordered_set<size_t> to_walk = curr_states;
        for(auto& state: to_walk) {
            size_t ss = state;
            while(true) {
                if (ss == states.size() || !states[ss].looped)
                    break;
                size_t new_state = ss + 1;
                if (curr_states.contains(new_state))
                    break;
                curr_states.insert(new_state);
                ss++;
            }
        }

        return curr_states.contains(states.size());
    }
};

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