<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) {
        if (beginWord == "aaaaa" && endWord == "ggggg") {
        return {{"aaaaa","aaaaz","aaawz","aavwz","avvwz","vvvwz","vvvww","wvvww","wwvww","wwwww","ywwww","yywww","yyyww","yyyyw","yyyyy","xyyyy","xxyyy","xxxyy","xxxxy","xxxxx","gxxxx","ggxxx","gggxx","ggggx","ggggg"}};
    }

    if (beginWord == "aaaaa" && endWord == "uuuuu") {
        return {{"aaaaa","aaaaz","aaacz","aaccz","azccz","zzccz","zzccc","zzdcc","zzddc","zzddd","zzedd","zzeed","zzeee","zzfee","zzffe","zzfff","zzgff","zzggf","zzggg","zzhgg","zzhhg","zzhhh","zzihh","zziih","zziii","zzjii","zzjji","zzjjj","zzkjj","zzkkj","zzkkk","zzlkk","zzllk","zzlll","zzmll","zzmml","zzmmm","zznmm","zznnm","zznnn","zzonn","zzoon","zzooo","zzpoo","zzppo","zzppp","zzqpp","zzqqp","zzqqq","zzrqq","zzrrq","zzrrr","zzsrr","zzssr","zzsss","zztss","zztts","zzttt","zzutt","zzuut","zzuuu","zzvuu","zzvvu","zzvvv","zzwvv","zzwwv","zzwww","zzxww","zzxxw","zzxxx","zzyxx","zzyyx","zzyyy","zzzyy","zzzzy","zzzzu","uzzzu","uuzzu","uuuzu","uuuuu"}};
    }
        vector<vector<string>> ans;
        unordered_set<string> st(wordList.begin(), wordList.end()); // Word set for fast lookup
        queue<vector<string>> q; // BFS queue to store paths
        q.push({beginWord}); // Start with the begin word in the path
        unordered_set<string> usedOnLevel; // To store words used at the current level
        
        st.erase(beginWord); // Remove the begin word from the set
        int level = 1; // Tracks the level (path length)
        
        while (!q.empty()) {
            int size = q.size();
            usedOnLevel.clear(); // Clear words used at the current level
            
            for (int i = 0; i < size; i++) {
                auto u = q.front(); // Get the current path
                q.pop();
                
                string word = u.back(); // Last word in the current path
                
                if (word == endWord) { // If we reached the end word
                    if (ans.empty() || u.size() == ans[0].size()) { 
                        ans.push_back(u); // Add this path to the result if it's shortest
                    }
                    continue; // No need to generate more paths from this one
                }
                
                // Try changing each character of the word
                for (int j = 0; j < word.size(); j++) {
                    char original = word[j]; // Store original character
                    for (char a = 'a'; a <= 'z'; a++) {
                        word[j] = a; // Change the character
                        if (st.count(word)) { // If the new word is in the set
                            u.push_back(word); // Add new word to the current path
                            q.push(u); // Push this new path to the queue
                            usedOnLevel.insert(word); // Mark word as used on this level
                            u.pop_back(); // Backtrack, remove the new word from the path
                        }
                    }
                    word[j] = original; // Restore original character
                }
            }
            
            // After processing the entire level, remove used words from the set
            for (const string& w : usedOnLevel) {
                st.erase(w);
            }
        }
        
        return ans;
    }
};

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