<p>A <strong>transformation sequence</strong> from word <code>beginWord</code> to word <code>endWord</code> using a dictionary <code>wordList</code> is a sequence of words <code>beginWord -&gt; s<sub>1</sub> -&gt; s<sub>2</sub> -&gt; ... -&gt; s<sub>k</sub></code> such that:</p>

<ul>
	<li>Every adjacent pair of words differs by a single letter.</li>
	<li>Every <code>s<sub>i</sub></code> for <code>1 &lt;= i &lt;= k</code> is in <code>wordList</code>. Note that <code>beginWord</code> does not need to be in <code>wordList</code>.</li>
	<li><code>s<sub>k</sub> == endWord</code></li>
</ul>

<p>Given two words, <code>beginWord</code> and <code>endWord</code>, and a dictionary <code>wordList</code>, return <em>all the <strong>shortest transformation sequences</strong> from</em> <code>beginWord</code> <em>to</em> <code>endWord</code><em>, or an empty list if no such sequence exists. Each sequence should be returned as a list of the words </em><code>[beginWord, s<sub>1</sub>, s<sub>2</sub>, ..., s<sub>k</sub>]</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> beginWord = &quot;hit&quot;, endWord = &quot;cog&quot;, wordList = [&quot;hot&quot;,&quot;dot&quot;,&quot;dog&quot;,&quot;lot&quot;,&quot;log&quot;,&quot;cog&quot;]
<strong>Output:</strong> [[&quot;hit&quot;,&quot;hot&quot;,&quot;dot&quot;,&quot;dog&quot;,&quot;cog&quot;],[&quot;hit&quot;,&quot;hot&quot;,&quot;lot&quot;,&quot;log&quot;,&quot;cog&quot;]]
<strong>Explanation:</strong>&nbsp;There are 2 shortest transformation sequences:
&quot;hit&quot; -&gt; &quot;hot&quot; -&gt; &quot;dot&quot; -&gt; &quot;dog&quot; -&gt; &quot;cog&quot;
&quot;hit&quot; -&gt; &quot;hot&quot; -&gt; &quot;lot&quot; -&gt; &quot;log&quot; -&gt; &quot;cog&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> beginWord = &quot;hit&quot;, endWord = &quot;cog&quot;, wordList = [&quot;hot&quot;,&quot;dot&quot;,&quot;dog&quot;,&quot;lot&quot;,&quot;log&quot;]
<strong>Output:</strong> []
<strong>Explanation:</strong> The endWord &quot;cog&quot; is not in wordList, therefore there is no valid transformation sequence.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= beginWord.length &lt;= 5</code></li>
	<li><code>endWord.length == beginWord.length</code></li>
	<li><code>1 &lt;= wordList.length &lt;= 500</code></li>
	<li><code>wordList[i].length == beginWord.length</code></li>
	<li><code>beginWord</code>, <code>endWord</code>, and <code>wordList[i]</code> consist of lowercase English letters.</li>
	<li><code>beginWord != endWord</code></li>
	<li>All the words in <code>wordList</code> are <strong>unique</strong>.</li>
	<li>The <strong>sum</strong> of all shortest transformation sequences does not exceed <code>10<sup>5</sup></code>.</li>
</ul>

class Solution {
 public:
  vector<vector<string>> findLadders(string beginWord, string endWord,
                                     vector<string>& wordList) {
    unordered_set<string> wordSet{wordList.begin(), wordList.end()};
    if (!wordSet.contains(endWord))
      return {};

    unordered_map<string, int> distFromBeginWord{{beginWord, 0}};
    if (!bfs(beginWord, endWord, wordSet, distFromBeginWord))
      return {};

    vector<vector<string>> ans;
    wordSet.insert(beginWord);
    dfs(endWord, beginWord, distFromBeginWord, wordSet, {endWord}, ans);
    return ans;
  }

 private:
  // Uses BFS to update the minimum steps to reach `endWord` from `beginWord` by
  // using the words in `wordSet`.
  bool bfs(const string& beginWord, const string& endWord,
           unordered_set<string>& wordSet,
           unordered_map<string, int>& distFromBeginWord) {
    queue<string> q{{beginWord}};
    while (!q.empty()) {
      for (int sz = q.size(); sz > 0; --sz) {
        const string parent = q.front();
        q.pop();
        if (parent == endWord)
          return true;
        for (const string& child : getChildren(parent, wordSet)) {
          if (distFromBeginWord.contains(child))
            continue;
          distFromBeginWord[child] = distFromBeginWord[parent] + 1;
          q.push(child);
        }
      }
    }
    return false;
  }

  void dfs(const string& word, const string& beginWord,
           const unordered_map<string, int>& distFromBeginWord,
           const unordered_set<string>& wordSet, vector<string>&& path,
           vector<vector<string>>& ans) {
    if (word == beginWord) {
      ans.push_back({path.rbegin(), path.rend()});
      return;
    }

    const int currDist = distFromBeginWord.at(word);

    for (const string& child : getChildren(word, wordSet)) {
      if (const auto it = distFromBeginWord.find(child);
          it != distFromBeginWord.cend() && it->second == currDist - 1) {
        path.push_back(child);
        dfs(child, beginWord, distFromBeginWord, wordSet, std::move(path), ans);
        path.pop_back();
      }
    }
  }

  vector<string> getChildren(const string& parent,
                             const unordered_set<string>& wordSet) {
    vector<string> children;
    string child(parent);
    for (int i = 0; i < child.length(); ++i) {
      const char cache = child[i];
      for (char c = 'a'; c <= 'z'; ++c) {
        if (c == cache)
          continue;
        child[i] = c;
        if (wordSet.contains(child))
          children.push_back(child);
      }
      child[i] = cache;
    }
    return children;
  }
};
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