<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>

#include <bits/stdc++.h>
using namespace std;

// Helper function to generate all possible one-letter transformations
vector<string> generateNextWords(const string& word, const unordered_set<string>& wordSet) {
    vector<string> nextWords;
    string currentWord = word;
    for (int i = 0; i < currentWord.size(); ++i) {
        char originalChar = currentWord[i];
        for (char c = 'a'; c <= 'z'; ++c) {
            if (c == originalChar) continue;
            currentWord[i] = c;
            if (wordSet.find(currentWord) != wordSet.end()) {
                nextWords.push_back(currentWord);
            }
        }
        currentWord[i] = originalChar;
    }
    return nextWords;
}

// Helper function for DFS to find all paths from endWord to beginWord
void dfs(const string& word, const string& beginWord, 
         const unordered_map<string, vector<string>>& graph, 
         vector<string>& path, vector<vector<string>>& result) {
    if (word == beginWord) {
        result.push_back(vector<string>(path.rbegin(), path.rend()));
        return;
    }
    auto it = graph.find(word);
    if (it != graph.end()) {
        for (const string& pred : it->second) {
            path.push_back(pred);
            dfs(pred, beginWord, graph, path, result);
            path.pop_back();
        }
    }
}

class Solution {
public:
    vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
        unordered_set<string> wordSet(wordList.begin(), wordList.end());
        vector<vector<string>> result;

        if (wordSet.find(endWord) == wordSet.end()) return result;

        unordered_map<string, vector<string>> graph;
        unordered_map<string, int> distance;

        queue<string> q;
        q.push(beginWord);
        distance[beginWord] = 0;

        while (!q.empty()) {
            int size = q.size();
            bool found = false;
            unordered_set<string> visited;

            for (int i = 0; i < size; ++i) {
                string word = q.front();
                q.pop();

                for (const string& nextWord : generateNextWords(word, wordSet)) {
                    if (distance.find(nextWord) == distance.end()) {
                        distance[nextWord] = distance[word] + 1;
                        if (nextWord == endWord) {
                            found = true;
                        }
                        q.push(nextWord);
                    }
                    if (distance[nextWord] == distance[word] + 1) {
                        graph[nextWord].push_back(word);
                    }
                }
                visited.insert(word);
            }
            if (found) break;
            for (const string& word : visited) {
                wordSet.erase(word);
            }
        }

        vector<string> path;
        path.push_back(endWord);
        dfs(endWord, beginWord, graph, path, result);

        return result;
    }
};

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