<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:
    unordered_map<string, int> step;
    vector<string> allPossible(string &s,  unordered_set<string> &bank){
        vector<string> res;
        string temp = s;
        for(int i = 0; i < s.length(); i++){
            for(int j = 0; j < 26; j++){
                temp[i] = 'a' + j;
                if(bank.count(temp)) res.push_back(temp);
            }
            temp = s;
        }
        return res;
    }

    void solve(string s, string e, unordered_set<string> bank){
        queue<string> q;
        q.push(s);
        bank.erase(s);
        int cnt = 0;
        step[s] = 0;
        while(!q.empty()){
            cnt++;
            int n = q.size();
            for(int i = 0; i < n; i++){
                string curr = q.front(); q.pop();
                if(curr == e){
                    return;
                }
                for(auto it:allPossible(curr, bank)){
                    q.push(it);
                    step[it] = cnt;
                    bank.erase(it);
                }
            }
        }
    }

    vector<vector<string>> findLadders(string s, string e, vector<string>& wordList) {
        unordered_set<string> bank;
        for(auto it:wordList) bank.insert(it);
        if(!bank.count(e)) return {};
        solve(s, e, bank);
        if(!step.count(e)) return {};
        vector<vector<string>> res;
        queue<pair<string, vector<string>>> q;
        q.push({e, {e}});
        bank.insert(s);
        // for(auto it:step) cout << it.first << " " << it.second << endl;
        while(!q.empty()){
            int n = q.size();
            // cout << n << endl;
            for(int i = 0; i < n; i++){
                string curr = q.front().first;
                // cout << curr << endl;
                vector<string> list = q.front().second;
                q.pop();
                if(curr == s){
                    res.push_back(list);
                    continue;
                }
                for(auto it:allPossible(curr, bank)){
                    if(step[it] == step[curr] - 1){
                        list.push_back(it);
                        q.push({it, list});
                        list.pop_back();
                    }
                }
                // cout << q.size() << endl;
            }
            if(res.size()) break;
        }
        for(auto &it:res){
            reverse(it.begin(), it.end());
        }
        return res;
    }
};
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