<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 Node{
public:
    string word;
    list<string> nbrs;

    Node(string word){
        this->word = word;
    }
};
class Graph{
private:
    unordered_map<string,Node*> m;
public:
    Graph(vector<string> words){
        for(int i=0;i<words.size();i++){
            m[words[i]] = new Node(words[i]);
        }
    }
    void addEdge(string i,string j){
        m[i]->nbrs.push_back(j);
        m[j]->nbrs.push_back(i);
    }
    unordered_map<string,int> bfs(string start){
        queue<string> q;
        unordered_map<string,int> visited;
        unordered_map<string,int> dist;
        visited[start]=1;
        dist[start]=0;
        q.push(start);
        while(!q.empty()){
            string f = q.front();
            q.pop();
            for(auto nbr: m[f]->nbrs){
                if(visited[nbr]==1) continue;
                else{
                    visited[nbr]=1;
                    dist[nbr]=dist[f]+1;
                    q.push(nbr);
                }
            }
        }
        return dist;
    }
    void allShortPaths(string node,string endWord,vector<vector<string>>& vec,vector<string>currPath,int dist,int minDist,unordered_map<string,int>& distance){
        if(node==endWord){
            currPath.push_back(node);
            vec.push_back(currPath);
            return;
        }
        if(dist+distance[node] > minDist) return;
        currPath.push_back(node);
        for(auto nbr: m[node]->nbrs){
            allShortPaths(nbr,endWord,vec,currPath,dist+1,minDist,distance);
        }
    }
};
class Solution {
public:
    bool contains(string beginWord,vector<string> wordList){
        for(auto word: wordList){
            if(beginWord==word) return true;
        }
        return false;
    }
    bool containsEnd(string endWord,vector<string> wordList){
        for(auto word: wordList){
            if(endWord==word) return true;
        }
        return false;
    }
    bool differByOne(string w1,string w2){
        int count=0;
        for(int i=0;i<w1.length();i++){
            if(w1[i]!=w2[i]) count++;
        }
        if(count==1) return true;
        return false;
    }
    vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
        if(!contains(beginWord,wordList)) wordList.push_back(beginWord);
        if(!contains(endWord,wordList)) return vector<vector<string>>();
        Graph g(wordList);
        for(int i=0;i<wordList.size();i++){
            for(int j=i+1;j<wordList.size();j++){
                if(differByOne(wordList[i],wordList[j])) g.addEdge(wordList[i],wordList[j]);
            }
        }
        unordered_map<string,int> distance = g.bfs(endWord);
        vector<vector<string>> vec;
        vector<string> currPath;
        int dist=0;
        int minDist = distance[beginWord];
        if(minDist==0) return vector<vector<string>>();
        g.allShortPaths(beginWord,endWord,vec,currPath,0,minDist,distance);
        return vec;
    }
};
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