<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>

from collections import deque, defaultdict
 
class Solution:
    def findLadders(self, beginWord, endWord, wordList):
        wordSet = set(wordList)
        if endWord not in wordSet:
            return []
        wordSet.add(beginWord)
        # Initialize data structures
        parents = defaultdict(list)
        levels = {beginWord: 0}
        min_level = float('inf')
        queue = deque([beginWord])
        res = []
        word_len = len(beginWord)
        while queue:
            current_word = queue.popleft()
            current_level = levels[current_word]
            if current_level > min_level:
                break
            for i in range(word_len):
                for c in 'abcdefghijklmnopqrstuvwxyz':
                    if c == current_word[i]:
                        continue
                    next_word = current_word[:i] + c + current_word[i+1:]
                    if next_word in wordSet:
                        if next_word not in levels:
                            levels[next_word] = current_level + 1
                            queue.append(next_word)
                        if levels[next_word] == current_level + 1:
                            parents[next_word].append(current_word)
                            if next_word == endWord:
                                min_level = current_level + 1
        if endWord not in parents:
            return []
        # Backtracking to build paths
        res = []
        path = [endWord]
        def backtrack(word):
            if word == beginWord:
                res.append(path[::-1])
                return
            for parent in parents[word]:
                path.append(parent)
                backtrack(parent)
                path.pop()
        backtrack(endWord)
        return res
 
# Example usage:
# solution = Solution()
# sequences = solution.findLadders("hit", "cog", ["hot","dot","dog","lot","log","cog"])
# print(sequences)
# Output: [["hit","hot","dot","dog","cog"], ["hit","hot","lot","log","cog"]]


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