<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]]:
        wordSet = set(wordList)
 
        seq = []
        res = []
        alphabet = "abcdefghijklmnopqrstuvwxyz"

        def findNeighbors(word):
            nonlocal wordSet
            neis = []
            charList = list(word)
            for i,oldChar in enumerate(charList): # 5
                for c in alphabet: # 25
                    if c == oldChar:
                        continue
                    charList[i] = c
                    newWord = ''.join(charList)
                    if newWord in wordSet:
                        neis.append(newWord)
                    charList[i] = oldChar
            return neis


        dag = defaultdict(list)
        # let's build dag first
        # we will use level-by-level BFS to build the dag
        to_visit =set([beginWord])
        visited = set([beginWord])
        while to_visit:
            new_to_visit = set([])
            new_visited = set(visited)
            for node in to_visit:
                neis = findNeighbors(node)
                for word in neis:
                    if word in visited:
                        continue
                    dag[node].append(word)
                    new_to_visit.add(word)
                    new_visited.add(word)
            to_visit = new_to_visit
            visited = new_visited
        

        if endWord not in wordList:
            return []



        seq.append(beginWord)
        
        cache = dict()

        def find_paths(word):
            nonlocal endWord
            if word in cache:
                return cache[word]

            if word == endWord:
                cache[word] = [deque([word])]
                return [deque([word])]
            res = []
            for new_word in dag[word]:
                paths = find_paths(new_word)
                new_paths = []
                for path in paths:
                    new_paths.append(deque(path))
                for new_path in new_paths:
                    new_path.appendleft(word)
                    res.append(new_path)

            cache[word] = []
            for path in res:
                cache[word].append(deque(path))
            return res

        
        result = find_paths(beginWord)
        print(cache)

        return result
        
17800