<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) {
        int n=wordList.size();

        unordered_set<string> uset;
        for(auto const &it:wordList){
            if(it!=beginWord) uset.insert(it);
        }

        queue<string> q;
        q.push(beginWord);

        vector<pair<string,int>> levels;
        int cnt=0;
        bool flag=false;

        while(!q.empty()){
            int sz=q.size();
        
            for(int i=0;i<sz;i++){
                string node=q.front();
                q.pop();

                levels.push_back({node,cnt});
                
                if(node==endWord){
                    flag=true;
                    break;
                }

                for(int i=0;i<node.length();i++){
                    char original=node[i];
                    for(char j='a';j<='z';j++){
                        if(original==j) continue;
                        
                        node[i]=j;
                        if(uset.find(node)!=uset.end()){
                            q.push(node);
                            uset.erase(node);
                        }
                    }
                    node[i]=original;
                }
            }
            if(flag) break;
            cnt++;
        }
        
        vector<vector<string>> ans;

        if(!flag){
            return ans;
        }

        vector<pair<string,int>>::reverse_iterator it=levels.rbegin();

        vector<string> vec;
        dfs(endWord,levels,ans,vec,it,cnt,beginWord);

        return ans;
    }

private:

    void dfs(string str,vector<pair<string,int>> &levels,vector<vector<string>> &ans,vector<string> &vec,vector<pair<string,int>>::reverse_iterator it,int cnt,string &beginWord){
        if(str==beginWord){
            vec.push_back(str);
            reverse(vec.begin(),vec.end());
            ans.push_back(vec);
            reverse(vec.begin(),vec.end());
            vec.pop_back();

            return;
        }
        
        while(it!=levels.rend() && it->second==cnt){
            it++;
        }

        while(it!=levels.rend() && it->second==cnt-1){
            if(isPossible(str,it->first)){
                vec.push_back(str);
                dfs(it->first,levels,ans,vec,it,cnt-1,beginWord);
                vec.pop_back();
            }
            it++;
        }
    }

    bool isPossible(string str1,string str2){
        int n=str1.length();

        int diff=0;
        for(int i=0;i<n;i++){
            if(str1[i]!=str2[i]){
                diff++;
            }

            if(diff>1) return false;
        }

        return true;
    }
};

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