<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 {

    unordered_set<string> dict;
    map<string,set<string>> adj;

    void find_edges(string &word)
    {
        for(int i=0;i<word.size();i++)
        {
            string temp = word;
            for(int j=0;j<26;j++)
            {
                temp[i] = 'a'+j;
                if(temp[i]!=word[i] && dict.find(temp)!=dict.end())
                {
                    // cout<<temp<<" ";
                    adj[word].insert(temp);
                    adj[temp].insert(word);
                }
            }
        }
        // cout<<endl;
    }

public:
    int ladderLength(string beginWord, string endWord, vector<string>& wordList) {
        
        for(auto word : wordList)
            dict.insert(word);

        find_edges(beginWord);
        
        for(auto word :wordList)
            find_edges(word);

        unordered_set<string> vis;
        queue<pair<string,int>> q;
        
        q.push({beginWord,0});
        vis.insert(beginWord);

        while(!q.empty())
        {
            string node = q.front().first;
            int dist = q.front().second;
            q.pop();
            
            // cout<<node<<" "<<dist<<endl;
            if(node==endWord)
                return dist+1;

            for(string nex: adj[node])
            {
                if(vis.find(nex)==vis.end())
                {
                    q.push({nex,dist+1});
                    vis.insert(nex);
                }
            }
        }

       return 0;
    }
};
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