<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:
    def __init__(self):
        self.mpp = {}
        self.ans = []
        self.b = ""

    def dfs(self, word, seq):
        if(word == self.b):
            dup = seq[::-1]
            self.ans.append(dup)
            return
        
        wordSize = len(word)
        steps = self.mpp[word]

        for i in range(wordSize):
            wordArr = list(word)
            origChar = wordArr[i]
            for ch in range(ord('a'), ord('z')+1):
                wordArr[i] = chr(ch)
                newWord = ''.join(wordArr)
                if(newWord in self.mpp.keys() and self.mpp[newWord]+1 == steps):
                    seq.append(newWord)
                    self.dfs(newWord,seq)
                    seq.pop()
            wordArr[i] = origChar

    def findLadders(self, beginWord: str, endWord: str, wordList: List[str]) -> List[List[str]]:
        self.ans = []
        wordSet = set(wordList)
        # if(endWord in wordSet):
        #     return self.ans
        
        q = deque([beginWord])
        wordSet.discard(beginWord)

        self.b = beginWord
        self.mpp[beginWord] = 1
        wordLen = len(beginWord)

        while q:
            word = q.popleft()
            steps = self.mpp[word]
            if(word == endWord):
                break
            
            for i in range(wordLen):
                wordArr = list(word)
                origChar = wordArr[i]
                for ch in range(ord('a'), ord('z')+1):
                    wordArr[i] = chr(ch)
                    newWord = ''.join(wordArr)
                    if(newWord in wordSet):
                        wordSet.discard(newWord)
                        q.append(newWord)
                        self.mpp[newWord] = steps+1

                wordArr[i] = origChar
        
        if(endWord in self.mpp.keys()):
            seq = [endWord]
            self.dfs(endWord,seq)

        return self.ans
        
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