<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>> ans;

    void backtrack(unordered_map<string, unordered_set<string>> & adj, unordered_map<string, int> & dist, unordered_set<string> & vis, string node, vector<string> & path) {
        if (dist[node] == 1) {
            vector<string> res = path;
            reverse(res.begin(), res.end());
            ans.push_back(res);
            return;
        }
        for (auto & v : adj[node]) {
            if (vis.count(v) or dist[v] + 1 != dist[node]) continue;
            vis.insert(v);
            path.push_back(v);
            backtrack(adj, dist, vis, v, path);
            vis.erase(v);
            path.pop_back();
        }
    }

    vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
        wordList.emplace_back(beginWord);
        unordered_set<string> words;
        for (auto & word : wordList) {
            words.insert(word);
        }
        unordered_map<string, unordered_set<string>> adj;
        for (auto & word : wordList) {
            string temp_word = word;
            for (int i = 0; i < temp_word.size(); ++i) {
                // modify character, check if it's in set -- create edge
                for (int a = 'a'; a <= 'z'; ++a) {
                    if (word[i] == a) continue;
                    temp_word[i] = a;
                    if (words.count(temp_word)) {
                        adj[word].insert(temp_word);
                        adj[temp_word].insert(word);
                    }
                }
                // reset
                temp_word[i] = word[i];
            }
        }
        // for (auto & [src, v] : adj) {
        //     cout << src << ": ";
        //     for (auto & x : v) cout << x << " ";
        //     cout << endl;
        // }
        queue<string> q;
        unordered_map<string, int> dist;
        q.push(beginWord);
        dist[beginWord] = 1;
        while (!q.empty()) {
            auto cur = q.front(); q.pop();
            for (auto & v : adj[cur]) {
                if (dist.count(v)) continue;
                dist[v] = dist[cur] + 1;
                q.push(v);
            }
        }
        unordered_set<string> vis;
        vector<string> path;
        vis.insert(endWord);
        path.push_back(endWord);
        backtrack(adj, dist, vis, endWord, path);
        return ans;
    }
};
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