<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]]:
        d = defaultdict(list)
        for word in wordList:
            for i in range(len(word)):
                d[word[:i]+"*"+word[i+1:]].append(word)

        if endWord not in wordList:
            return []

        visited1 = defaultdict(list)
        q1 = deque([beginWord])
        visited1[beginWord] = []

        visited2 = defaultdict(list)
        q2 = deque([endWord])
        visited2[endWord] = []

        ans = []
        def dfs(v, visited, path, paths):
            path.append(v)
            if not visited[v]:
                if visited is visited1:
                    paths.append(path[::-1])
                else:
                    paths.append(path[:])
            for u in visited[v]:
                dfs(u, visited, path, paths)
            path.pop()

        def bfs(q, visited1, visited2, frombegin):
            level_visited = defaultdict(list)
            for _ in range(len(q)):
                u = q.popleft()

                for i in range(len(u)):
                    for v in d[u[:i]+"*"+u[i+1:]]:
                        if v in visited2:
                            paths1 = []
                            paths2 = []
                            dfs(u, visited1, [], paths1)
                            dfs(v, visited2, [], paths2)
                            if not frombegin:
                                paths1, paths2 = paths2, paths1
                            for a in paths1:
                                for b in paths2:
                                    ans.append(a+b)
                        elif v not in visited1:
                            if v not in level_visited:
                                q.append(v)
                            level_visited[v].append(u)
            visited1.update(level_visited)

        while q1 and q2 and not ans:
            if len(q1) <= len(q2):
                bfs(q1, visited1, visited2, True)
            else:
                bfs(q2, visited2, visited1, False)

        return ans
        
        
17200