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dsa-solutions/lc-solutions/0100-0199/0126-word-ladder-II.md

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+---
+id: word-ladder-II
+title: Word ladder II solution
+sidebar_label: 0126 Word ladder II
+tags:
+  - String
+  - BFS (Breadth-First Search)
+  - Backtracking
+  - Graph
+  - LeetCode
+  - Python
+  - Java
+  - C++
+description: "This is a solution to the word ladder II problem on LeetCode."
+---
+
+## Problem Description
+
+A transformation sequence from word beginWord to word endWord using a dictionary wordList is a sequence of words beginWord $s1 -> s2 -> ... -> sk$ such that:
+
+Every adjacent pair of words differs by a single letter.
+Every si for $1 <= i <= k$ is in wordList. Note that beginWord does not need to be in wordList.
+sk == endWord
+Given two words, beginWord and endWord, and a dictionary wordList, return all the shortest transformation sequences from beginWord to endWord, or an empty list if no such sequence exists. Each sequence should be returned as a list of the words [beginWord, s1, s2, ..., sk].
+
+### Examples
+
+**Example 1:**
+
+```
+Input: beginWord = "hit", endWord = "cog", wordList = ["hot","dot","dog","lot","log","cog"]
+Output: [["hit","hot","dot","dog","cog"],["hit","hot","lot","log","cog"]]
+Explanation: There are 2 shortest transformation sequences:
+"hit" -> "hot" -> "dot" -> "dog" -> "cog"
+"hit" -> "hot" -> "lot" -> "log" -> "cog"
+```
+
+**Example 2:**
+
+```
+Input: beginWord = "hit", endWord = "cog", wordList = ["hot","dot","dog","lot","log"]
+Output: []
+Explanation: The endWord "cog" is not in wordList, therefore there is no valid transformation sequence.
+```
+
+### Constraints
+
+- $1 <= beginWord.length <= 5$
+- $endWord.length == beginWord.length$
+- $1 <= wordList.length <= 500$
+- $wordList[i].length == beginWord.length$
+- beginWord, endWord, and wordList[i] consist of lowercase English letters.
+- beginWord != endWord
+- All the words in wordList are unique.
+- The sum of all shortest transformation sequences does not exceed 105.
+
+## Solution for Word Ladder II Problem
+
+<Tabs>
+  <TabItem value="Python 3" label="Python 3">
+
+### Approach :
+
+#### Intuition
+
+Define a helper function neighbors(word) that generates all the possible words by changing a single character in the given word.
+Initialize a variable words as a dictionary with beginWord as the key and a lambda function returning [[beginWord]] as the value. This dictionary will keep track of all possible transformation sequences.
+Initialize a set unvisited containing all words in wordList except beginWord.
+Perform BFS:
+While there are words in words and endWord is not yet found in words:
+Increment a counter i.
+Initialize a new dictionary new_words to store the next layer of words.
+Iterate through each word s in words:
+Generate all possible neighbors ss of s.
+If ss is in unvisited, create a lambda function get_seqs that appends ss to each sequence of words ending with s, and add ss and get_seqs to new_words.
+Update words to new_words.
+Remove the keys of new_words from unvisited.
+Return the transformation sequences ending with endWord.
+
+
+#### Code in Different Languages
+
+<Tabs>
+  <TabItem value="Python3" label="Python3">
+  <SolutionAuthor name="@mahek0620"/>
+   ```python3
+    class Solution:
+    def findLadders(
+        self, beginWord: str, endWord: str, wordList: List[str]
+    ) -> List[List[str]]:
+        def neighbors(word):
+            for i in range(len(word)):
+                for char in "abcdefghijklmnopqrstuvwxyz":
+                    yield word[:i] + char + word[i + 1 :]
+
+        i = 1
+        words = {beginWord: lambda: [[beginWord]]}
+        unvisited = set(wordList)
+        while words and endWord not in words:
+            i += 1
+            new_words = defaultdict(lambda: lambda: [])
+            for s in words:
+                for ss in neighbors(s):
+                    if ss in unvisited:
+
+                        def get_seqs(capture=(ss, new_words[ss], words[s])):
+                            ss, ss_get_seqs, s_get_seqs = capture
+                            seqs = ss_get_seqs()
+                            for seq in s_get_seqs():
+                                seq.append(ss)
+                                seqs.append(seq)
+                            return seqs
+
+                        new_words[ss] = get_seqs
+            words = new_words
+            unvisited -= words.keys()
+        return words[endWord]()
+
+    ```
+
+  </TabItem>
+  <TabItem value="Java" label="Java">
+  <SolutionAuthor name="@mahek0620"/>
+   ```java
+    class Solution {
+    public List<List<String>> findLadders(String beginWord, String endWord, List<String> wordList) {
+        List<List<String>> ans = new ArrayList<>(); 
+        Map<String, Set<String>> reverse = new HashMap<>(); // reverse graph start from endWord
+        Set<String> wordSet = new HashSet<>(wordList); // remove the duplicate words
+        wordSet.remove(beginWord); // remove the first word to avoid cycle path
+        Queue<String> queue = new LinkedList<>(); // store current layer nodes
+        queue.add(beginWord); // first layer has only beginWord
+        Set<String> nextLevel = new HashSet<>(); // store nextLayer nodes
+        boolean findEnd = false; // find endWord flag
+        while (!queue.isEmpty()) { // traverse current layer nodes
+            String word = queue.remove();
+            for (String next : wordSet) {
+                if (isLadder(word, next)) { // is ladder words
+					// construct the reverse graph from endWord
+                    Set<String> reverseLadders = reverse.computeIfAbsent(next, k -> new HashSet<>());
+                    reverseLadders.add(word); 
+                    if (endWord.equals(next)) {
+                        findEnd = true;
+                    }
+                    nextLevel.add(next); // store next layer nodes
+                }
+            }
+            if (queue.isEmpty()) { // when current layer is all visited
+                if (findEnd) break; // if find the endWord, then break the while loop
+                queue.addAll(nextLevel); // add next layer nodes to queue
+                wordSet.removeAll(nextLevel); // remove all next layer nodes in wordSet
+                nextLevel.clear();
+            }
+        }
+        if (!findEnd) return ans; // if can't reach endWord from startWord, then return ans.
+        Set<String> path = new LinkedHashSet<>();
+        path.add(endWord);
+		// traverse reverse graph from endWord to beginWord
+        findPath(endWord, beginWord, reverse, ans, path); 
+        return ans;
+    }
+
+
+    private void findPath(String endWord, String beginWord, Map<String, Set<String>> graph,
+                                 List<List<String>> ans, Set<String> path) {
+        Set<String> next = graph.get(endWord);
+        if (next == null) return;
+        for (String word : next) {
+            path.add(word);
+            if (beginWord.equals(word)) {
+                List<String> shortestPath = new ArrayList<>(path);
+                Collections.reverse(shortestPath); // reverse words in shortest path
+                ans.add(shortestPath); // add the shortest path to ans.
+            } else {
+                findPath(word, beginWord, graph, ans, path);
+            }
+            path.remove(word);
+        }
+    }
+
+    private boolean isLadder(String s, String t) {
+        if (s.length() != t.length()) return false;
+        int diffCount = 0;
+        int n = s.length();
+        for (int i = 0; i < n; i++) {
+            if (s.charAt(i) != t.charAt(i)) diffCount++;
+            if (diffCount > 1) return false;
+        }
+        return diffCount == 1;
+    }}
+    ```
+
+  </TabItem>
+  <TabItem value="C++" label="C++">
+  <SolutionAuthor name="@mahek0620"/>
+   ```cpp
+    class Solution {
+public:
+    vector<vector<string>> findLadders(string beginWord, string endWord, vector<string>& wordList) {
+        int n=wordList.size();
+
+        unordered_set<string> uset;
+        for(auto const &it:wordList){
+            if(it!=beginWord) uset.insert(it);
+        }
+
+        queue<string> q;
+        q.push(beginWord);
+
+        vector<pair<string,int>> levels;
+        int cnt=0;
+        bool flag=false;
+
+        while(!q.empty()){
+            int sz=q.size();
+
+            for(int i=0;i<sz;i++){
+                string node=q.front();
+                q.pop();
+
+                levels.push_back({node,cnt});
+
+                if(node==endWord){
+                    flag=true;
+                    break;
+                }
+
+                for(int i=0;i<node.length();i++){
+                    char original=node[i];
+                    for(char j='a';j<='z';j++){
+                        if(original==j) continue;
+
+                        node[i]=j;
+                        if(uset.find(node)!=uset.end()){
+                            q.push(node);
+                            uset.erase(node);
+                        }
+                    }
+                    node[i]=original;
+                }
+            }
+            if(flag) break;
+            cnt++;
+        }
+
+        vector<vector<string>> ans;
+
+        if(!flag){
+            return ans;
+        }
+
+        vector<pair<string,int>>::reverse_iterator it=levels.rbegin();
+
+        vector<string> vec;
+        dfs(endWord,levels,ans,vec,it,cnt,beginWord);
+
+        return ans;
+    }
+
+private:
+
+    void dfs(string str,vector<pair<string,int>> &levels,vector<vector<string>> &ans,vector<string> &vec,vector<pair<string,int>>::reverse_iterator it,int cnt,string &beginWord){
+        if(str==beginWord){
+            vec.push_back(str);
+            reverse(vec.begin(),vec.end());
+            ans.push_back(vec);
+            reverse(vec.begin(),vec.end());
+            vec.pop_back();
+
+            return;
+        }
+
+        while(it!=levels.rend() && it->second==cnt){
+            it++;
+        }
+
+        while(it!=levels.rend() && it->second==cnt-1){
+            if(isPossible(str,it->first)){
+                vec.push_back(str);
+                dfs(it->first,levels,ans,vec,it,cnt-1,beginWord);
+                vec.pop_back();
+            }
+            it++;
+        }
+    }
+
+    bool isPossible(string str1,string str2){
+        int n=str1.length();
+
+        int diff=0;
+        for(int i=0;i<n;i++){
+            if(str1[i]!=str2[i]){
+                diff++;
+            }
+
+            if(diff>1) return false;
+        }
+
+        return true;
+    }
+};
+    ```
+
+  </TabItem>
+</Tabs>
+
+
+</TabItem>
+
+</Tabs>
+
+## References
+
+- **LeetCode Problem**: [Word Ladder II](https://leetcode.com/problems/word-ladder-ii/)
+
+- **Solution Link**: [LeetCode Solution](https://leetcode.com/problems/word-ladder-ii/solution/)
+
+- **Authors GeeksforGeeks Profile:** [Mahek Patel](https://leetcode.com/u/mahekrpatel611/)