<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:
    vector<vector<string>> findLadders(string beginWord, string endWord,
                                       vector<string>& wordList) {
        unordered_map<string, vector<string>> neighborMap;
        bool isIn = false;
        bool endIn = false;
        int N = wordList.size();
        for (int i = 0; i < N; i++) {
            if (wordList[i] == beginWord) {
                isIn = true;
            } else if (wordList[i] == endWord) {
                endIn = true;
            }
        }

        if (!endIn) {
            return {};
        }

        if (!isIn) {
            wordList.push_back(beginWord);
        }
        generateNeighborMap(wordList, neighborMap);

        unordered_map<string, int> beginDisMap;
        unordered_map<string, int> endDisMap;
        generateDisMap(beginWord, neighborMap, beginDisMap);
        generateDisMap(endWord, neighborMap, endDisMap);

        if (beginDisMap.find(endWord) == beginDisMap.end()) {
            return {};
        }

        int dis = beginDisMap[endWord];
        vector<vector<string>> ans;
        vector<string> path(dis + 1, "");

        process(beginWord, endWord, beginWord, path, 0, neighborMap,
                beginDisMap, endDisMap, ans);

        return ans;
    }

    void process(string& beginWord, string& endWord, string& curword,
                 vector<string>& path, int curpos,
                 unordered_map<string, vector<string>>& neighborMap,
                 unordered_map<string, int>& beginDisMap,
                 unordered_map<string, int>& endDisMap,
                 vector<vector<string>>& ans) {

        path[curpos] = curword;

        if (curpos == path.size() - 1) {
            ans.push_back(path);
            return;
        }

        for (string w : neighborMap[curword]) {
            if (beginDisMap[w] == (beginDisMap[curword] + 1) &&
                endDisMap[w] == (endDisMap[curword] - 1)) {
                process(beginWord, endWord, w, path, curpos + 1, neighborMap,
                        beginDisMap, endDisMap, ans);
            }
        }

        return;
    }

    void
    generateNeighborMap(vector<string>& wordList,
                        unordered_map<string, vector<string>>& neighborMap) {

        unordered_set<string> wordSet(wordList.begin(), wordList.end());

        for (string word : wordList) {
            neighborMap[word] = {};
            int N = word.size();
            for (int i = 0; i < N; i++) {
                char cur = word[i];
                for (int c = 0; c < 26; c++) {
                    if (c != (cur - 'a')) {
                        string tmp = word;
                        tmp[i] = c + 'a';
                        if (wordSet.find(tmp) != wordSet.end()) {
                            neighborMap[word].push_back(tmp);
                        }
                    }
                }
            }
        }

        return;
    }

    void generateDisMap(string& word,
                        unordered_map<string, vector<string>>& neighborMap,
                        unordered_map<string, int>& disMap) {

        unordered_set<string> wS;

        int dis = 0;
        queue<string> mQ;
        mQ.push(word);
        wS.emplace(word);

        while (!mQ.empty()) {
            int sz = mQ.size();
            for (int i = 0; i < sz; i++) {
                string cur = mQ.front();
                mQ.pop();
                disMap.emplace(cur, dis);

                for (string nw : neighborMap[cur]) {
                    if (wS.find(nw) == wS.end()) {
                        mQ.push(nw);
                        wS.emplace(nw);
                    }
                }
            }
            dis++;
        }

        return;
    }
};
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