<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:

    void backtrack(int curnode, vector<int>& path, vector<vector<int>>& sols,
                    int& sourcenode, vector<set<int>>& parent) {
        if(curnode == sourcenode) {
            sols.push_back(path);
            return;
        }
        for(auto &p : parent[curnode]) {
            path.push_back(p);
            backtrack(p, path, sols, sourcenode, parent);
            path.pop_back();
        }
    }

    vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
        map<string, int> mp;
        map<int, string> rmp;
        int cnt = 0;
        vector<vector<string>> ans;
        if(find(wordList.begin(), wordList.end(), endWord) == wordList.end()) return ans;
        wordList.push_back(beginWord);
        wordList.push_back(endWord);
        for(auto& word : wordList) {
            if(mp.find(word) == mp.end()) {
                mp[word] = cnt++;
                rmp[mp[word]] = word;
            }
        }
        vector<vector<pair<int, int>>> g(cnt * 6);
        for(auto& word : wordList) {
            for(int i = 0; i < word.size(); i += 1) {
                string superword = word;
                superword[i] = '$';
                if(mp.find(superword) == mp.end()) {
                    mp[superword] = cnt++;
                    // rmp[mp[superword]] = superword;
                }
                g[mp[word]].push_back({mp[superword], 0});
                g[mp[superword]].push_back({mp[word], 1});
            }
        }
        vector<int> dist(cnt, 1e9);
        vector<set<int>> parent(cnt);
        deque<int> dq;
        dist[mp[beginWord]] = 0;
        dq.push_back(mp[beginWord]);
        while(!dq.empty()) {
            int cur = dq.front();
            dq.pop_front();
            for(auto &[neigh, weight] : g[cur]) {
                if(dist[neigh] > dist[cur] + weight) {
                    dist[neigh] = dist[cur] + weight;
                    if(weight) dq.push_back(neigh);
                    else dq.push_front(neigh);
                    parent[neigh].insert(cur);
                }
                else if(dist[neigh] == dist[cur] + weight) {
                    parent[neigh].insert(cur);
                }
            }
        }
        // for(int i = 0; i < parent.size(); i += 1) {
        //     cout << rmp[i] << " -> ";
        //     for(auto& p : parent[i]) {
        //         cout << rmp[p] << " ";
        //     }
        //     cout << '\n';
        // }
        vector<vector<int>> sols;
        vector<int> path;
        path.push_back(mp[endWord]);
        backtrack(mp[endWord], path, sols, mp[beginWord], parent);

        for(auto& sol : sols) {
            vector<string> seq;
            for(auto& x : sol) {
                if(rmp.find(x) != rmp.end()) seq.push_back(rmp[x]);
            }
            reverse(seq.begin(), seq.end());
            ans.push_back(seq);
        }
        return ans;
    }
};
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