<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>

template<typename T>
void
hash_combine(std::size_t &seed, T const &key) {
  std::hash<T> hasher;
  seed ^= hasher(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
}

namespace std {
  template<typename T1, typename T2>
  struct hash<std::pair<T1, T2>> {
    std::size_t operator()(std::pair<T1, T2> const &p) const {
      std::size_t seed1(0);
      ::hash_combine(seed1, p.first);
      ::hash_combine(seed1, p.second);

      std::size_t seed2(0);
      ::hash_combine(seed2, p.second);
      ::hash_combine(seed2, p.first);

      return std::min(seed1, seed2);
    }
  };
}


class Solution {
    // Means that s[0..strIdx-1] is matched with p[0..patIdx-1]
    struct MatchState {
        int strIdx;
        int patIdx;
    };

    struct PatternMatch {
        char c;
        bool repeat;
    };

public:
    bool isMatch(string s, string p) {
        std::unordered_set<std::pair<int, int>> states;
        states.emplace(0, 0);

        std::vector<PatternMatch> pattern;
        for (int i = 0; i < p.size(); i++) {
            if (p[i] == '*') continue; // handled in prev iteration of loop

            if (i + 1 < p.size() && p[i + 1] == '*') {
                pattern.emplace_back(p[i], true);
            } else {
                pattern.emplace_back(p[i], false);
            }
        }

        while (states.size() != 0) {
            decltype(states) newStates;

            for (const auto [strIdx, patIdx]: states) {
                if (patIdx == pattern.size()) {
                    if (strIdx == s.size()) {
                        return true;
                    }
                    continue;
                }

                // ASSERT : patIdx < pattern.size()
                if (pattern[patIdx].repeat) {
                    newStates.emplace(strIdx, patIdx + 1);
                }

                if (strIdx == s.size()) {
                    continue;
                }
                // ASSERT: strIdx < s.size() && patIdx < pattern.size()

                if (s[strIdx] == pattern[patIdx].c || pattern[patIdx].c == '.') {
                    newStates.emplace(strIdx + 1, patIdx + 1);
                    if (pattern[patIdx].repeat) {
                        newStates.emplace(strIdx + 1, patIdx);
                    }
                }
            }

            states = newStates;
        }

        return false;
    }
};
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