<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>

from queue import PriorityQueue


class Solution:
    def get_n_diff_chars(self, word, target):
        return len(list(filter(lambda p: p[0] != p[1], zip(word, target))))


    def get_adjacent(self, word):
        adjacent = []
        for potential_neighbor in self.wordList:
            n_diff_chars = self.get_n_diff_chars(word, potential_neighbor)
            if n_diff_chars == 1:
                adjacent.append(potential_neighbor)

        return adjacent

    
    def get_adjacent_2(self, word):
        adjacent = []
        for i in range(len(word)):
            for j in range(26):  # try all lowercase letters
                transformed_word = word[:i] + chr(ord('a') + j) + word[i+1:]
                if transformed_word in self.wordSet:
                    adjacent.append(transformed_word)
        return adjacent

    
    def heuristic(self, word, target):
        return self.get_n_diff_chars(word, target)

    
    def dijkstra(self, beginWord: str, endWord) -> int:
        dists = {}
        preds = {}
        
        queue = PriorityQueue()
        queue.put((0, beginWord))
        dists[beginWord] = 0
        preds[beginWord] = None

        while not queue.empty():
            dist, word = queue.get()

            if word == endWord:
                break
            
            for neighbor in self.get_adjacent_2(word):
                #new_dist = dists[word] + 1 + self.heuristic(neighbor, endWord)
                new_dist = dists[word] + 1
                if neighbor not in dists or new_dist < dists[neighbor]:
                    dists[neighbor] = new_dist
                    preds[neighbor] = word
                    queue.put((new_dist, neighbor))

        return dists, preds


    def ladderLength(self, beginWord: str, endWord: str, wordList: List[str]) -> int:
        self.wordList = wordList
        self.wordSet = set(wordList)

        dists, preds = self.dijkstra(beginWord, endWord)
        
        if endWord not in dists:
            return 0

        return dists[endWord] + 1
        
        path = [endWord]
        word = endWord
        while preds[word] is not None:
            word = preds[word]
            path = [word] + path

        return path
18362