<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>the <strong>number of words</strong> in the <strong>shortest transformation sequence</strong> from</em> <code>beginWord</code> <em>to</em> <code>endWord</code><em>, or </em><code>0</code><em> if no such sequence exists.</em></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> 5
<strong>Explanation:</strong> One shortest transformation sequence is &quot;hit&quot; -&gt; &quot;hot&quot; -&gt; &quot;dot&quot; -&gt; &quot;dog&quot; -&gt; cog&quot;, which is 5 words long.
</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> 0
<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;= 10</code></li>
	<li><code>endWord.length == beginWord.length</code></li>
	<li><code>1 &lt;= wordList.length &lt;= 5000</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>
</ul>

class Solution:
    def ladderLength(self, beginWord: str, endWord: str, wordList: List[str]) -> int:
        def form_groups(s: str):
            s_array = list(s)
            for pos, letter in enumerate(s_array):
                s_array[pos] = "*"
                yield "".join(s_array)
                s_array[pos] = letter
        group_lookup = defaultdict(list)
        member_lookup = defaultdict(list)
        def process(s: str):
            for group in form_groups(s):
                group_lookup[s].append(group)
                member_lookup[group].append(s)
        
        process(beginWord)
        endWord_found = False
        for word in wordList:
            if word == endWord:
                endWord_found = True
            if word != beginWord:
                process(word)
        
        if not endWord_found:
            return 0
        if sum(a != b for a, b in zip(beginWord, endWord)) == 1:
            return 2
        
        queue_start = deque([(beginWord, 1)])
        dist_lookup_start = {beginWord: 1}

        queue_end = deque([(endWord, 1)])
        dist_lookup_end = {endWord: 1}

        while queue_start and queue_end:
            curr_word_start, curr_dist_start = queue_start.popleft()
            curr_word_end, curr_dist_end = queue_end.popleft()
            
            if curr_word_start in dist_lookup_end:
                return curr_dist_start + dist_lookup_end[curr_word_start] - 1

            if curr_word_end in dist_lookup_start:
                return curr_dist_end + dist_lookup_start[curr_word_end] - 1
            
            next_dist = curr_dist_start + 1
            for group in group_lookup[curr_word_start]:
                for member in member_lookup[group]:
                    if member in dist_lookup_start:
                        continue
                    dist_lookup_start[member] = next_dist
                    queue_start.append((member, next_dist))
            
            next_dist = curr_dist_end + 1
            for group in group_lookup[curr_word_end]:
                for member in member_lookup[group]:
                    if member in dist_lookup_end:
                        continue
                    dist_lookup_end[member] = next_dist
                    queue_end.append((member, next_dist))
        return 0
25862