<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 dfs(string curr, vector<string> path, unordered_map<string, int>& mp,
             vector<vector<string>>& ans) {
        if (mp[curr] == 0) {
            reverse(path.begin(), path.end());
            ans.push_back(path);
            return;
        }
        int n = curr.size();
        string w = curr;
        for (int i = 0; i < n; i++) {
            char org = curr[i];
            for (char c = 'a'; c <= 'z'; c++) {
                if (c == org)
                    continue;
                curr[i] = c;
                if (mp.count(curr) && mp[curr] == mp[w] - 1) {
                    vector<string> new_path(path);
                    new_path.push_back(curr);
                    dfs(curr, new_path, mp, ans);
                }
            }
            curr[i] = org;
        }
    }

    vector<vector<string>> findLadders(string startWord, string endWord,
                                       vector<string>& wordList) {
        vector<vector<string>> ans;
        unordered_set<string> wordSet(wordList.begin(), wordList.end());
        if (!wordSet.count(endWord))
            return ans;

        vector<vector<int>> paths;
        wordSet.insert(startWord);
        queue<string> q;
        unordered_map<string, int> mp;
        wordSet.erase(startWord);
        q.push(startWord);
        int lvl = 1, tar_lvl = INT_MAX;
        mp[startWord] = 0;
        while (!q.empty()) {
            int sz = q.size();
            for (int i = 0; i < sz; i++) {
                auto word = q.front();
                q.pop();

                int n = word.size();
                for (int i = 0; i < n; i++) {
                    char org = word[i];

                    for (char c = 'a'; c <= 'z'; c++) {
                        if (c == org)
                            continue;

                        word[i] = c;

                        if (word == endWord) {
                            tar_lvl = lvl;
                            mp[word] = lvl;
                            continue;
                        }

                        if (wordSet.count(word)) {
                            mp[word] = lvl;
                            q.emplace(word);
                            wordSet.erase(word);
                        }
                    }
                    word[i] = org;
                }
            }

            if (tar_lvl == lvl) {
                break;
            }
            lvl++;
        }

        if (tar_lvl != INT_MAX)
            dfs(endWord, vector<string>{endWord}, mp, ans);

        return ans;
    }
};

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