<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 findLadders(self, beginWord: str, endWord: str, wordList: List[str]) -> List[List[str]]:
        if beginWord not in wordList:
            wordList.append(beginWord)
        wordSet = set(wordList)
        graph = defaultdict(list)
        for i in range(len(wordList)):
            word = wordList[i]
            for j in range(len(word)):
                for z in range(26):
                    char = chr(ord('a') + z)
                    if char == word[j]:
                        continue 
                    newWord = word[:j] + char + word[j+1:]
                    if newWord in wordSet:
                        graph[word].append(newWord)
        def bfs(beginWord,endWord):
            hashMap = {}
            visited = set()
            visited.add(beginWord)
            queue = deque([[beginWord,1]])
            while queue:
                node,moves = queue.popleft()
                hashMap[node] = moves
                if node == endWord:
                    return hashMap,moves 
                for neighbor in graph[node]:
                    if neighbor not in visited:
                        visited.add(neighbor)
                        queue.append([neighbor,moves + 1])
            return  {},0
        hashMap,length = bfs(beginWord,endWord)
        visited = set([endWord])
        result = []
        def dfs(cur):
            nonlocal length 
            nonlocal beginWord
            if len(cur) == length:
                result.append(cur.copy()[::-1])
                return 
            word = cur[-1]
            for j in range(len(word)):
                for z in range(26):
                    char = chr(ord('a') + z)
                    if char == word[j]:
                        continue 
                    newWord = word[:j] + char + word[j+1:]
                    if newWord in hashMap and newWord not in visited and hashMap[newWord] == length - len(cur):
                        cur.append(newWord)
                        visited.add(newWord)
                        dfs(cur)
                        visited.remove(newWord)
                        cur.pop()
        dfs([endWord])
        return result 
17600