Word Ladder
<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>
Breadth-First Search; Hash Table; String
using System.Collections;
using System.Collections.Generic;
using System.Linq;

public class Solution {
    public int LadderLength(string beginWord, string endWord, IList<string> wordList) {
        var words = Enumerable.Repeat(beginWord, 1).Concat(wordList).Select((word, i) => new { Word = word, Index = i }).ToList();
        var endWordIndex = words.Find(w => w.Word == endWord)?.Index;
        if (endWordIndex == null) {
            return 0;
        }

        var paths = new List<int>[words.Count];
        for (var i = 0; i < paths.Length; ++i)
        {
            paths[i] = new List<int>();
        }
        for (var i = 0; i < beginWord.Length; ++i)
        {
            var hashMap = new Hashtable();
            foreach (var item in words)
            {
                var newWord = string.Format("{0}_{1}", item.Word.Substring(0, i), item.Word.Substring(i + 1));
                List<int> similars;
                if (!hashMap.ContainsKey(newWord))
                {
                    similars = new List<int>();
                    hashMap.Add(newWord, similars);
                }
                else
                {
                    similars = (List<int>)hashMap[newWord];
                }
                foreach (var similar in similars)
                {
                    paths[similar].Add(item.Index);
                    paths[item.Index].Add(similar);
                }
                similars.Add(item.Index);
            }
        }

        var left = words.Count - 1;
        var lastRound = new List<int> { 0 };
        var visited = new bool[words.Count];
        visited[0] = true;
        for (var result = 2; left > 0; ++result)
        {
            var thisRound = new List<int>();
            foreach (var index in lastRound)
            {
                foreach (var next in paths[index])
                {
                    if (!visited[next])
                    {
                        visited[next] = true;
                        if (next == endWordIndex) return result;
                        thisRound.Add(next);
                    }
                }
            }
            if (thisRound.Count == 0) break;
            lastRound = thisRound;
        }

        return 0;
    }
}