<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:
void findAllPath(vector<vector<string>> &res, string currentWord, string beginWord, unordered_map<string, vector<string>> &parents, vector <string>path) {
if(currentWord == beginWord) {
path.push_back(beginWord);
reverse(path.begin(), path.end());
res.push_back(path);
return;
}
for(auto word: parents[currentWord]) {
path.push_back(currentWord);
findAllPath(res, word, beginWord, parents, path);
path.pop_back();
}
}

vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
    unordered_map<string, bool> wordMap;
    unordered_map<string, vector<string>> parents;
    unordered_map<string, int> levels;
    for(auto word: wordList) {
        wordMap[word] = true;
    }
    queue<string> q;
    q.push(beginWord);
    int level = 0;
    levels[beginWord] = 0;
    while(!q.empty()) {
        string s = q.front();
        q.pop();
        for(int i=0; i<s.size(); i++) {
            string temp = s;
            for(char c='a'; c<='z'; c++) {
                if(s[i] != c) {
                    temp[i] = c;
                    if(wordMap.count(temp) && (levels[temp] == 0 || levels[temp] > levels[s] + 1)) {
                        q.push(temp);
                        parents[temp].clear();
                        parents[temp].push_back(s);
                        levels[temp] = levels[s] + 1;
                    } else if(wordMap.count(temp) && levels[temp] == levels[s] + 1) {
                        parents[temp].push_back(s);
                    }
                }
            }
        }
        level++;
    }
    vector<vector<string>> res;
    vector<string> path;
    findAllPath(res, endWord, beginWord, parents, path);
    return res;
}
};
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