<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:
    bool check(string s1, string s2){
        int count = 0;
        for(int i=0;i<min(s1.size(),s2.size());i++){
            if(s1[i]!=s2[i])count++;
        }
        return count == 1;
    }
    void dfs(vector<vector<int>> &par, int node, vector<int> &path, vector<vector<int>> &paths, int &st){
            if(node==st){
                paths.push_back(path);
                reverse(paths.back().begin(), paths.back().end());
                return;
            }
            for(auto child:par[node]){
                path.push_back(child);
                dfs(par,child,path,paths,st);
                path.pop_back();
            }
    }
    vector<vector<string>> findLadders(string start, string end, vector<string>& dict) {
        queue<int>q;
        int n = dict.size();
        dict.push_back(start);
        vector<int>v(n,1e9);
        q.push(n);
        v.push_back(1);
        vector<vector<int>> par(n+1);
        par[n] = {n};
        while(!q.empty()){
            int node= q.front();
            q.pop();
            for(int i=0;i<n;i++){
                if((v[node]+1<=v[i]) && check(dict[node],dict[i])){
                    if(v[i]>=(1e9)) q.push(i);
                    v[i]= v[node]+1;
                    par[i].push_back(node);
                }
            }
        }
        vector<vector<string>> ans;
        int ed = -1;
        for(int i=0; i<n; i++){
            if(dict[i]==end && v[i]>=(1e9)) return ans;
            else if (dict[i]==end) ed=i;
        }
        if(ed==-1) return ans;
        vector<vector<int>> paths;
        vector<int> path;
        path.push_back(ed);
        dfs(par,ed,path, paths,n);
        for(auto path:paths){
            vector<string> aa;
            for(auto ind:path) aa.push_back(dict[ind]);
            ans.push_back(aa);
        }
        return ans;
    }
};
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