<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 {
private:
    bool canGo(string w1, string w2){
        int n = w1.size();
        int count = 0;
        for(int i=0;i<n;i++){
            if(w1[i]!=w2[i]){
                count++;
            }
        }
        return count==1;
    }
public:
    vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
        vector<vector<string>>ans;
        int endIdx = -1;
        for(int i = 0;i<wordList.size();i++){
            if(wordList[i]==endWord){
                endIdx = i;
                break;
            }
        }
        if(endIdx==-1)return ans;
        wordList.push_back(beginWord);
        int n = wordList.size();
        vector<int>vis(n,1e7);
        vis[n-1]=1;
        vector<vector<int>>parent(n);
        queue<int>q;
        q.push(n-1);
        while(!q.empty()){
            int node = q.front();
            q.pop();
            for(int i=0;i<wordList.size()-1;i++){
                if(canGo(wordList[i],wordList[node]) && vis[node]+1<=vis[i]){
                    if(vis[i]>=(1e7)) {
                        q.push(i);
                    }
                    vis[i]=vis[node]+1;
                    parent[i].push_back(node);
                }
            }
        }
        vector<string>vt;
        vt.push_back(endWord);
        dfs(endIdx,parent,ans,vt,wordList);
        return ans;
    }
    void dfs(int node, vector<vector<int>>&parent, vector<vector<string>>&ans,vector<string>&temp,vector<string>& wordList){
        if(node == wordList.size()-1){
            ans.push_back(temp);
            reverse(ans.back().begin(),ans.back().end());
            return;
        }
        for(int i=0;i<parent[node].size();i++){
            temp.push_back(wordList[parent[node][i]]);
            dfs(parent[node][i],parent,ans,temp,wordList);
            temp.pop_back();
        }
    }
};
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