<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.find(endWord) == wordSet.end()) return {};

        unordered_map<string, vector<string>> adj;
        unordered_set<string> visited;
        queue<string> q;
        q.push(beginWord);
        visited.insert(beginWord);
        bool found = false;

        while (!q.empty() && !found) {
            int levelSize = q.size();
            unordered_set<string> currentLevelVisited;
            for (int i = 0; i < levelSize; ++i) {
                string currentWord = q.front();
                q.pop();
                string tempWord = currentWord;

                for (int j = 0; j < currentWord.size(); ++j) {
                    char originalChar = currentWord[j];
                    for (char c = 'a'; c <= 'z'; ++c) {
                        if (c == originalChar) continue; // Skip if character is same as original
                        currentWord[j] = c;
                        if (wordSet.find(currentWord) != wordSet.end()) {
                            if (currentWord == endWord) found = true;
                            if (visited.find(currentWord) == visited.end()) {
                                if (currentLevelVisited.find(currentWord) == currentLevelVisited.end()) {
                                    q.push(currentWord);
                                    currentLevelVisited.insert(currentWord);
                                }
                                adj[currentWord].push_back(tempWord);
                            }
                        }
                    }
                    currentWord[j] = originalChar;
                }
            }
            visited.insert(currentLevelVisited.begin(), currentLevelVisited.end());
        }

        vector<vector<string>> res;
        if (found) {
            vector<string> path = {endWord};
            backtrack(endWord, beginWord, adj, path, res);
        }
        return res;
    }
    void backtrack(const string& currentWord, const string& beginWord, unordered_map<string, vector<string>>& adj, vector<string>& path, vector<vector<string>>& res) {
        if (currentWord == beginWord) {
            vector<string> result = path;
            reverse(result.begin(), result.end());
            res.push_back(result);
            return;
        }
        for (const string& nextWord : adj[currentWord]) {
            path.push_back(nextWord);
            backtrack(nextWord, beginWord, adj, path, res);
            path.pop_back();
        }
    }
            
};
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