<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_map<string,unordered_set<string>> adjList, parents;
        unordered_map<string,int> distance;

        for(auto &s:wordList){
            int count = 0;
            for(int i=0;i<beginWord.size();i++){
                if(s[i]!=beginWord[i])
                    count++;
            }
            if(count==1)
                adjList[beginWord].insert(s);
        }
        for(int i=0;i<wordList.size();i++)
            for(int j=0;j<wordList.size();j++)
                if(i!=j){
                    int count = 0;
                    for(int k=0;k<beginWord.size();k++){
                        if(wordList[i][k]!=wordList[j][k])
                            count++;
                    }
                    if(count==1)
                        adjList[wordList[i]].insert(wordList[j]);
                }

        queue<pair<string,int>> q;
        q.push({beginWord,0});
        distance[beginWord] = 0;
        while(!q.empty()){
            string w = q.front().first;
            int d = q.front().second;
            q.pop();
            for(auto &c:adjList[w]){
                if(distance.find(c)==distance.end()){
                    distance[c] = d + 1;
                    q.push({c,d+1});
                    parents[c].insert(w);
                }else if(d+1==distance[c]){
                    parents[c].insert(w);
                }
            }
        }

        function<void(string,vector<string>&, vector<vector<string>>&)> recursion = 
        [&](string s, vector<string> &curr,vector<vector<string>> &ans)->void{
            curr.push_back(s);
            if(s==beginWord){
                ans.push_back(curr);
                curr.pop_back();
                return;
            }
            for(auto &p: parents[s]){
                recursion(p,curr,ans);
            }
            curr.pop_back();
        };

        vector<string> curr;
        vector<vector<string>> ans;
        recursion(endWord,curr,ans);

        for(int i=0;i<ans.size();i++)
            reverse(ans[i].begin(),ans[i].end());
        return ans;
    }
};
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