<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 {

    // bfs for minLevel
    // parent map

    // retrace path using parent map

    void dfs(string beginWord, string endWord, map<string, set<string>> &parent, map<string, int> &visited, vector<string> &bucket, vector<vector<string>> &res, int level, int currLevel) {
        if(visited[endWord] == 3) {
            return;
        }

        if(currLevel > level) {
            return;
        }

        if(endWord == beginWord && bucket.size() == level-1) {
            bucket.push_back(beginWord);
            res.push_back(bucket);
            bucket.pop_back();
            return;
        }

        bucket.push_back(endWord);
        visited[endWord] = 3;

        for(auto par:parent[endWord]) {
            if(visited[par] != 3) {
                dfs(beginWord, par, parent, visited, bucket, res, level, currLevel+1);
            }
        }

        bucket.pop_back();
        visited[endWord] = 2;

    }


public:
    vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
        map<string, int> mp;
        map<string, set<string>> parent;

        for(auto ele:wordList) {
            mp[ele]++;
        }
        
        queue<string> q;

        q.push(beginWord);
        mp[beginWord] = 2;
        int level = 0;
        int found = 0;

        while(!q.empty()) {
            int sz = q.size();
            level++;
            while(sz--) {
                auto currWord = q.front();
                q.pop();
                // cout<<currWord<<" "<<level<<endl;
                if(currWord == endWord) {
                    found = 1;
                }

                for(int i=0; i<currWord.size(); i++) {
                    for(int j=0; j<26; j++) {
                        auto nextWord = currWord;
                        nextWord[i] = 'a' + j;
                        // if(currWord == "mist" && nextWord == "miss") {
                        //     cout<<"hi";
                        // }

                        if(nextWord != currWord && mp.find(nextWord) != mp.end()) {
                            if(mp[nextWord] == 1) {
                                q.push(nextWord);
                                mp[nextWord] = 2;
                            }
                            if(parent[currWord].find(nextWord) == parent[currWord].end()) {
                                parent[nextWord].insert(currWord);
                            }
                        }
                    }
                }
            }
            if(found ==  1) {
                break;
            }
        }
        if(found == 0) {
            return {};
        }

        // cout<<level<<endl;

        // for(auto ele:parent) {
        //     cout<<ele.first<<" -> ";
        //     for(auto e:ele.second) {
        //         cout<<e<<" ";
        //     }
        //     cout<<endl;
        // }



        vector<string> bucket;
        vector<vector<string>> res;

        dfs(beginWord, endWord, parent, mp, bucket, res, level, 0);

        for(int i=0; i<res.size(); i++) {
            reverse(res[i].begin(), res[i].end());
        }

        return res;
    }
};

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