<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:

    void bfs(unordered_map<string, vector<string>> &adj, unordered_map<string,vector<string>> &parent, string start, vector<string> &wordList)
    {
        // dist will contain shortest distance
        // from start to every other vertex
        unordered_map<string,int> dist;
        for(string s : wordList)
        dist[s] =INT_MAX;
    
        queue<string> q;
    
        // Insert source vertex in queue and make
        // its parent -1 and distance 0
        q.push(start);
        dist[start] = 0;
    
        // Until Queue is empty
        while (!q.empty()) {
            string u = q.front();
            q.pop();
            for (string v : adj[u]) {
                if (dist[v] > dist[u] + 1) {
    
                    // A shorter distance is found
                    // So erase all the previous parents
                    // and insert new parent u in parent[v]
                    dist[v] = dist[u] + 1;
                    q.push(v);
                    parent[v].clear();
                    parent[v].push_back(u);
                }
                else if (dist[v] == dist[u] + 1) {
    
                    // Another candidate parent for
                    // shortes path found
                    parent[v].push_back(u);
                }
            }
        }
    }

    void find_paths(vector<vector<string>>& res, vector<string>& path,unordered_map<string,vector<string>> &parent, string u)
    {
        // Base Case
        if (parent[u].size() ==0 ) {
            vector<string> ans = path;
            if(ans.size() != 0)
            {
                ans.push_back(u);
                reverse(ans.begin(),ans.end());
                res.push_back(ans);
            }
            return;
        }
    
        // Loop for all the parents
        // of the given vertex
        for (string par : parent[u]) {
    
            // Insert the current
            // vertex in path
            path.push_back(u);
    
            // Recursive call for its parent
            find_paths(res, path, parent,
                    par);
    
            // Remove the current vertex
            path.pop_back();
        }
    }

    vector<vector<string>> findLadders(string beg, string end, vector<string>& wordList) {
        
        unordered_set<string> st;
        for(string s : wordList)
        st.insert(s);

        unordered_map<string, vector<string>> mp;

        for(string s : wordList)
        {
            for(int i=0;i<s.size();i++)
            {
                for(int j=0;j<26;j++)
                {
                    if(s[i] == 'a' + j)
                    continue;

                    string s2 = s;
                    char temp = s[i];
                    s2[i] = 'a' + j;
                    if(st.find(s2) != st.end())
                    mp[s].push_back(s2);
                }
            }
        }

        if(st.find(beg) == st.end())
        {
            string s = beg;
            for(int i=0;i<s.size();i++)
            {
                for(int j=0;j<26;j++)
                {
                    if(s[i] == 'a' + j)
                    continue;

                    string s2 = s;
                    char temp = s[i];
                    s2[i] = 'a' + j;
                    if(st.find(s2) != st.end())
                    mp[s].push_back(s2);
                }
            }
        }

        for(auto it = mp.begin();it!= mp.end();it++)
        {
            cout << it->first << " : ";
            vector<string> v = it->second;
            for(auto x : v)
            cout << x << " ";
            cout << endl;
        }

        unordered_map<string,vector<string>> par;
        for(string s : wordList)
        par[s] = {};

        bfs(mp,par,beg,wordList);
        
        vector<vector<string>> res;
        vector<string> path;
        find_paths(res,path,par,end);
        return res;

    }


};
19000