<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 {
public:
    int vis[5000 + 1];
    bool diff_one(const string& s1, const string& s2) {
        bool d = false;
        for (int i = 0; i < s1.size(); ++i) {
            if (!d && s1[i] != s2[i]) d = true;
            else if (d && s1[i] != s2[i]) return false;
        }
        return d;
    }
    int path(vector<string>& wordList, int w1, int w2, map<int, vector<int>>& graph) {
        queue<pair<int, int>> q;
        q.push({w1, 1});
        
        while (q.size() > 0) {
            pair<int, int> curr = q.front();
            q.pop();
            if (vis[curr.first] == 0 || curr.second < vis[curr.first]) vis[curr.first] = curr.second;
            if (curr.first != w2) {
                for (auto i : graph[curr.first]) {
                    if (vis[i] == 0 || vis[i] > curr.second + 1) {
                        q.push({i, curr.second + 1});
                    }
                }
            }
        }
        return vis[w2];
    }
    int ladderLength(string beginWord, string endWord, vector<string>& wordList) {
        map<int, vector<int>> graph;
        int start = -1, end = -1;
        for (int i = 0; i < wordList.size(); ++i) {
            if (wordList[i] == beginWord) start = i;
            else if (wordList[i] == endWord) end = i;
            for (int j = i + 1; j < wordList.size(); ++j) {
                if (diff_one(wordList[i], wordList[j])) {
                    graph[i].push_back(j);
                    graph[j].push_back(i);
                }
            }
        }
        if (end == -1) return 0;
        if (start == -1) {
            wordList.push_back(beginWord);
            start = wordList.size() - 1;
            for (int j = 0; j < start; ++j) {
                if (diff_one(beginWord, wordList[j])) {
                    graph[start].push_back(j);
                    graph[j].push_back(start);
                }
            }
        }
        int res = path(wordList, start, end, graph);
        return res == INT_MAX ? 0 : res;
    }
};
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