<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) {
        int idx = -1;
        int n = wordList.size();
        for(int i=0; i<n; i++) {
            if (endWord.compare(wordList[i]) == 0) {
                idx = i;
                break;
            }
        }
        if (idx == -1) {
            return {};
        }
        vector<vector<int>> adj(n+1);
        for(int i=0; i<n; i++) {
            for(int j=0; j<i; j++) {
                if (oneLetterDiff(wordList[i], wordList[j])) {
                    adj[i].push_back(j);
                    adj[j].push_back(i);
                }
            }
            if(oneLetterDiff(wordList[i], beginWord)) {
                adj[n].push_back(i);
                adj[i].push_back(n);
            }
        }
        vector<bool> vis(n+1, false);
        vector<int> dis(n+1, 1e9);
        vector<vector<int>> parents(n+1);
        dis[n] = 0;
        queue<int> q;
        q.push(n);
        vis[n] = true;
        while (!q.empty()) {
            auto f = q.front();
            q.pop();
            for(auto c: adj[f]) {
                if (vis[c]) {
                    if (dis[f] + 1 == dis[c]) {
                        parents[c].push_back(f);
                    }
                } else {
                    q.push(c);
                    vis[c] = true;
                    dis[c] = 1 + dis[f];
                    parents[c].push_back(f);
                }
            }
        }
        vector<vector<string>> results;
        vector<string> build;
        vector<bool> nvis(n, false);
        recursivelyCollect(parents, idx, build, nvis, wordList, results, beginWord);
        return results;
    }

    void recursivelyCollect(vector<vector<int>> &parents, int node, vector<string> &build, vector<bool> &vis, vector<string>& wordList, vector<vector<string>> &results, string &beginWord) {
        if (node == parents.size()-1) {
            vector<string> store = vector<string>(build);
            store.push_back(beginWord);
            reverse(store.begin(), store.end());
            results.push_back(store);
            return;
        }
        build.push_back(wordList[node]);
        vis[node] = true;
        for(auto p: parents[node]) {
            if (!vis[p])
                recursivelyCollect(parents, p, build, vis, wordList, results, beginWord);
        }
        build.pop_back();
        vis[node] = false;
    }

    bool oneLetterDiff(string &s1, string &s2) {
        int n = s1.length();
        int charDiff = 0;
        for(int i=0; i<n; i++) {
            if (s1[i] != s2[i]) charDiff++;
        }
        return charDiff == 1;
    }
};
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