<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>all the <strong>shortest transformation sequences</strong> from</em> <code>beginWord</code> <em>to</em> <code>endWord</code><em>, or an empty list if no such sequence exists. Each sequence should be returned as a list of the words </em><code>[beginWord, s<sub>1</sub>, s<sub>2</sub>, ..., s<sub>k</sub>]</code>.</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> [[&quot;hit&quot;,&quot;hot&quot;,&quot;dot&quot;,&quot;dog&quot;,&quot;cog&quot;],[&quot;hit&quot;,&quot;hot&quot;,&quot;lot&quot;,&quot;log&quot;,&quot;cog&quot;]]
<strong>Explanation:</strong>&nbsp;There are 2 shortest transformation sequences:
&quot;hit&quot; -&gt; &quot;hot&quot; -&gt; &quot;dot&quot; -&gt; &quot;dog&quot; -&gt; &quot;cog&quot;
&quot;hit&quot; -&gt; &quot;hot&quot; -&gt; &quot;lot&quot; -&gt; &quot;log&quot; -&gt; &quot;cog&quot;
</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> []
<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;= 5</code></li>
	<li><code>endWord.length == beginWord.length</code></li>
	<li><code>1 &lt;= wordList.length &lt;= 500</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>
	<li>The <strong>sum</strong> of all shortest transformation sequences does not exceed <code>10<sup>5</sup></code>.</li>
</ul>

class Solution {
    inline int diff(string &a, string &b)
    {
        int n = a.size();
        int ans = 0;
        for(int i = 0; i < n; i++)
        {
            if(a[i] != b[i])
                ans++;
        }
        return ans;
    }

    void rec(vector<int> &curr, vector<string> &currW, int ind, vector<int> &dis, vector<vector<int>> &adj, vector<string>& wordList, vector<vector<string>> &ans)
    {
        int nd = curr[ind];
        if(dis[nd] == 0)
        {
            ans.push_back(currW);
            return;
        }
        for(int nr: adj[nd])
        {
            if(dis[nr] != dis[nd] - 1)
                continue;
            curr[ind + 1] = nr;
            currW[ind + 1] = wordList[nr];
            rec(curr, currW, ind + 1, dis, adj, wordList, ans);
        }
        return;
    }
public:
    vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
        int n = wordList.size();
        vector<vector<int>> adj(n);
        int start = n;
        int end = n;
        for(int i = 0; i < n; i++)
        {
            if(wordList[i] == beginWord)
                start = i;
            if(wordList[i] == endWord)
                end = i;
            for(int j = 0; j < n; j++)
            {
                if(diff(wordList[i], wordList[j]) == 1)
                    adj[i].push_back(j);
            }
        }
        if(end == n)
            return {};
        if(start == n)
        {
            adj.resize(n + 1);
            for(int i = 0; i < n; i++)
            {
                if(diff(beginWord, wordList[i]) == 1)
                {
                    adj[n].push_back(i);
                    adj[i].push_back(n);
                }
            }
            n++;
        }
        vector<int> dis(n, INT_MAX);
        queue<int> q;
        q.push(end);
        dis[end] = 0;
        while(!q.empty())
        {
            int nd = q.front();
            q.pop();
            if(nd == start)
                break;
            for(int nr: adj[nd])
            {
                if(dis[nr] <= dis[nd] + 1)
                    continue;
                dis[nr] = dis[nd] + 1;
                q.push(nr);
            }
        }
        if(dis[start] == INT_MAX)
            return {};
        vector<int> curr(dis[start] + 1);
        vector<string> currW(dis[start] + 1);
        vector<vector<string>> ans;
        currW[0] = beginWord;
        curr[0] = start;
        rec(curr, currW, 0, dis, adj, wordList, ans);
        return ans;
    }
};
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