<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 {
public:
    int diff(string a, string b){
        int tot =0 ;
        for(int i=0;i<a.size();i++) if(a[i]!=b[i]) tot++;
        return tot;
    }
    vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
        unordered_map<string, int> mapping;
        int n = wordList.size();
        for(int i=0;i<n;i++) mapping[wordList[i]] = i;
        if(mapping.find(endWord)==mapping.end()) return {};
        vector<vector<int>> edges(n+1, vector<int>(n,0));
        mapping[beginWord] = n;
        for(int i=0;i<n;i++){
            for(int j=i+1;j<n;j++){
                if(diff(wordList[i], wordList[j])==1) edges[i][j] = edges[j][i] = 1;
            }
        }
        for(int i=0;i<n;i++) if(diff(beginWord, wordList[i])==1) edges[n][i] = 1;
        unordered_set<int> s;
        vector<int>visited(n,0);
        queue<string> q;
        vector<vector<string>> ans;
        vector<vector<int>>prev(n+1, vector<int>(0));
        q.push(beginWord);
        bool flag_end = false;
        while(!q.empty()){
            if(flag_end) break;
            int l = q.size();
            unordered_set<int>tmp_visited;
            for(int i=0;i<l;i++){
                auto now = q.front();
                q.pop();
                if(now == endWord) {
                    flag_end = 1;
                }
                else{
                    int x = mapping[now];
                    for(int j=0;j<n;j++) if((!visited[j])&&edges[x][j]){
                        prev[j].push_back(x);
                        if(tmp_visited.find(j) == tmp_visited.end()){
                            q.push(wordList[j]);
                            tmp_visited.insert(j);
                        }
                    }
                }
            }
            for(auto i: tmp_visited) visited[i] = 1;
        }
        queue<vector<string>> qq;
        if(prev[mapping[endWord]].size()){
            qq.push({endWord});
            while(!qq.empty()){
                int l = qq.size();
                for(int i=0;i<l;i++){
                    auto now = qq.front();
                    qq.pop();
                    if(now.back()==beginWord){
                        reverse(now.begin(), now.end());
                        ans.push_back(now);
                    }
                    else{
                        for(auto i: prev[mapping[now.back()]]){
                            vector<string>tmp = now;
                            if(i<n)
                            tmp.push_back(wordList[i]);
                            else tmp.push_back(beginWord);
                            qq.push(tmp);
                        }
                    }
                }
                
            }
        }
        
        return ans;
    }
};
19900