<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) {
        vector<vector<string>> ans;
        unordered_set<string> s(wordList.begin(), wordList.end());
        if (s.find(endWord) == s.end()) return ans; // endWord not in wordList
        
        queue<string> q; // BFS queue storing words
        unordered_map<string, vector<string>> bt; // backtracking map (word -> all parents)
        unordered_map<string, int> dist; // map to store the shortest distance to each word
        
        q.push(beginWord);
        dist[beginWord] = 0;
        bool found = false;
        
        while (!q.empty() && !found) {
            int qSize = q.size();
            unordered_set<string> wordsToRemove; // to store words to erase after level is processed
            
            for (int i = 0; i < qSize; ++i) {
                string word = q.front();
                q.pop();
                
                string originalWord = word;
                for (char& ch : word) {
                    char originalChar = ch;
                    for (char c = 'a'; c <= 'z'; ++c) {
                        ch = c;
                        if (s.find(word) != s.end()) { // valid transformation
                            if (dist.find(word) == dist.end()) {
                                dist[word] = dist[originalWord] + 1;
                                q.push(word);
                                wordsToRemove.insert(word);
                            }
                            if (dist[word] == dist[originalWord] + 1) {
                                bt[word].push_back(originalWord); // track parent
                            }
                            if (word == endWord) {
                                found = true; // stop when endWord is found
                            }
                        }
                    }
                    ch = originalChar; // revert change
                }
            }
            for (const string& w : wordsToRemove) {
                s.erase(w); // mark as visited after processing this level
            }
        }
        
        // If endWord is found, backtrack to build all paths
        if (found) {
            vector<string> path = {endWord};
            backtrack(ans, path, bt, beginWord, endWord);
        }
        
        return ans;
    }

    void backtrack(vector<vector<string>>& ans, vector<string>& path, unordered_map<string, vector<string>>& bt, const string& beginWord, const string& curWord) {
        if (curWord == beginWord) {
            vector<string> temp = path;
            reverse(temp.begin(), temp.end());
            ans.push_back(temp);
            return;
        }
        for (const string& parent : bt[curWord]) {
            path.push_back(parent);
            backtrack(ans, path, bt, beginWord, parent);
            path.pop_back();
        }
    }
};

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