<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<int>> g;
    vector<int> dis;
    vector<vector<int>> par;
    int dif(string s1,string s2){
        int cnt=0;
        for(int i=0;i<s1.size();i++){
            if(s1[i]!=s2[i]) cnt++;
        }
        return cnt;
    }
    void bfs(){
        queue<int> q; q.push(0);
        dis[0] = 1;
        par[0].push_back(-1);
        while(!q.empty())
        {
            int cur = q.front();
            q.pop();
            for(auto neigh: g[cur])
            {
                if(dis[neigh]>dis[cur]+1){
                    dis[neigh]=dis[cur]+1;
                    par[neigh].push_back(cur);
                    q.push(neigh);
                }
                else if(dis[neigh]==dis[cur]+1){
                    par[neigh].push_back(cur);
                }
            }
        }
    }
    vector<vector<string>> answers(int f,string &be, string &e, vector<string>& words){
        vector<vector<string>> ans;
        if(f==0){
            vector<string> v; v.push_back(be);
            ans.push_back(v);
            return ans;
        }

        for(auto i: par[f]){
            vector<vector<string>> temp = answers(i,be,e,words);
            for(auto j: temp){
                j.push_back(words[f-1]);
                ans.push_back(j);
            } 
        }
        return ans;
    }
    vector<vector<string>> findLadders(string be, string e, vector<string>& words) {
        vector<vector<string>> ans;
        int n = words.size(), f = 0;
        g.resize(n+1); par.resize(n+1);
        for(int i=0;i<n;i++) if(words[i]==e) {f = i+1;}

        if(f==0) return ans;

        for(int i=0;i<n;i++){
            for(int j=i+1;j<n;j++){
                if(dif(words[i],words[j])==1){
                    g[i+1].push_back(j+1);
                    g[j+1].push_back(i+1);
                }
            }
        }
        for(int i=0;i<n;i++){
            if(dif(words[i],be)==1){
                g[0].push_back(i+1);
                g[i+1].push_back(0);
            }
        }
        dis.assign(n+1,1e9);
        bfs();
        
        if(dis[f]==1e9) return ans;
        else{
            return answers(f,be,e,words);
        }
    }
};
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