<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:
    const vector<vector<string>> EMPTY;
    const int INVALID = -1;

    vector<vector<string>> buildAns(string beginWord, string endWord, map<string,
        vector<string>>& wordPrevMap) {
        vector<vector<string>> ans;
        if (beginWord == endWord) {
            vector<string> now = {beginWord};
            ans.push_back(now);
            return ans;
        }

        vector<string>& prevList = wordPrevMap[endWord];
        for (auto i = prevList.begin(); i != prevList.end(); i ++) {
            vector<vector<string>> lastAns = buildAns(beginWord, *i, wordPrevMap);
            for (int j = 0; j < lastAns.size(); j ++) {
                lastAns[j].push_back(endWord);
                ans.push_back(lastAns[j]);
            }
        }
        return ans;
    }

public:
    vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
        map<string, int> wordMap; // map word, minLength
        map<string, vector<string>> wordPrevMap;
        for (auto i = wordList.begin(); i != wordList.end(); i ++) {
            wordMap[*i] = INVALID;
        }
        if (wordMap.find(endWord) == wordMap.end()) {
            return EMPTY;
        }

        wordMap[beginWord] = 1;
        if (beginWord == endWord) {
            return buildAns(beginWord, endWord, wordPrevMap);
        }
        queue<string> queue;
        queue.push(beginWord);
        while (!queue.empty()) {
            string now = queue.front();
            queue.pop();
            int newLen = wordMap[now] + 1;
            if (wordMap[endWord] != INVALID &&
                wordMap[endWord] < newLen) {
                return buildAns(beginWord, endWord, wordPrevMap);
            }
            for (int i = 0; i < now.size(); i ++) {
                for (char c = 'a'; c <= 'z'; c ++) {
                    string next = now;
                    next[i] = c;
                    if (wordMap.find(next) != wordMap.end()) {
                        if (wordMap[next] == INVALID) {
                            wordMap[next] = newLen;
                            queue.push(next);
                        }
                        if (wordMap[next] == newLen) {
                            wordPrevMap[next].push_back(now);
                        }
                    }
                }
            }
        }
        return EMPTY;
    }
};
/*
hit -> cog
wordMap:
    hit [[hit]]
    hot [[hit, hot]]
    dot [[hit, hot, dot]]
    dog [[hit, hot, dot, dog]]
    lot [[hit, hot, lot]]
    log [[hit, hot, lot, log]]
    cog [[hit, hot, dot, dog, cog], [hit, hot, lot, log, cog]]
queue:
    [dot, lot]
now: hot
nowSolution: [[hit, hot]]
next: dot, lot
solution: [hit, hot]
*/
15100