<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 {
    int n;
    map<string,vector<string>> g;
    map<string,vector<string>> par;
    map<string,int> dist;
    bool check(string& s,string& s1){
        int n1 = s.size();
        if(s1.size()!=n1) return false;
        bool f= false;
        for(int i=0;i<n1;i++){
            if(s[i]!=s1[i]){
                if(f) return false;
                f=true;
            }
        }
        return f;
    }

    int bfs(string beginWord, string endWord, vector<string>& wordList){
        for(string& str:wordList) dist[str]=1e9;
        queue<string> q;
        dist[beginWord]=1;
        q.push(beginWord);
        while(!q.empty()){
            auto k = q.front(); q.pop();
            // cout<<k<<endl;
            for(string str:g[k]){
                // cout<<str<<dist[str]<<" "<<dist[k]<<endl;
                if(dist[str]>dist[k]+1){
                    dist[str]=dist[k]+1;
                    q.push(str);
                    par[str].clear();
                    par[str].push_back(k);
                }else if(dist[str]==dist[k]+1){
                    par[str].push_back(k);
                }
            }
        }
        return dist[endWord];
    }

    void rec(string& beginWord, string& endWord,int k,string& s,vector<string>& ref,vector<vector<string>>& ans){
        if(!k){
            ans.push_back(ref);
            return;
        }
        for(auto str:par[s]){
            ref.push_back(str);
            rec(beginWord,endWord,k-1,str,ref,ans);
            ref.pop_back();
        }
    }

public:
    vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
        for(string str:wordList) g[str];
        if(g.find(beginWord)==g.end()) {
            // cout<<"nsnjvr kjn \n";
            wordList.push_back(beginWord);
            g[beginWord];
        }
        n = wordList.size();
        for(int i=0;i+1<n;i++){
            for(int j=i+1;j<n;j++){
                if(check(wordList[i],wordList[j])){
                    g[wordList[i]].push_back(wordList[j]);
                    g[wordList[j]].push_back(wordList[i]);
                }
            }
        }
        // for(int i=0;i<n;i++){
        //     cout<<"p "<<wordList[i]<<endl;
        //     for(string str:g[wordList[i]]) cout<<str<<" ";
        //     cout<<endl;
        // }
        int k = bfs(beginWord,endWord,wordList);
        vector<string> ref;
        vector<vector<string>> ans;
        if(k==0) return ans;
        ref.push_back(endWord);
        rec(beginWord,endWord,k-1,endWord,ref,ans);
        for(auto& r:ans){
            reverse(r.begin(),r.end());
        }
        return ans;
    }
};
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