# Print all possible shortest chains to reach a target word

• Difficulty Level : Expert
• Last Updated : 25 May, 2021

Given two strings start and target(both of the same length) and a list of strings str[], the task is to print all possible smallest sequences starting from start to target if it exists, such that adjacent words in the sequence only differ by a single character and each word in the sequence is present in the given list.

Note: It may be assumed that the target word is present in the list and the length of all the words is the same. If multiple sequences occur, print all of them.

Example:

Input: str[] = {poon, plee, same, poie, plea, plie, poin}, start = “toon”, target = “plea”
Output: [[toon, poon, poin, poie, plee, plea]]
Explanation: toon → poon → poin → poie → plee → plea

Input: str[] = { ted, tex, red, tax, tad, den, rex, pee}, start = “red”, target = “tax”
Output [[“red”, “ted”, “tad”, “tax”], [“red”, “ted”, “tex”, “tax”], [“red”, “rex”, “tex”, “tax”]]

Approach: The problem can be solved using BFS.The tricky part here is to do the BFS of the path instead of words. Follow the steps below to solve the problem:

1. Initialize a variable, say res, to store all possible shortest paths.
2. Create a Set to store all the visited words in current path and once the current path is completed, erase all the visited words.
3. For each current word, find the possible next words present in str[] by changing each character from ‘a’ to ‘z’ and find all possible paths.
4. Finally, print all the possible path.

## C++

 `// C++ Program to implement` `// the above approach` `#include ` `using` `namespace` `std;`   `// Function to print all possible shortest` `// sequences starting from start to target.` `void` `displaypath(vector >& res)` `{` `    ``for` `(``int` `i = 0; i < res.size(); i++) {` `        ``cout << ``"[ "``;` `        ``for` `(``int` `j = 0; j < res[0].size(); j++) {` `            ``cout << res[i][j] << ``", "``;` `        ``}` `        ``cout << ``" ]\n"``;` `    ``}` `}` `// Find words differing by a single` `// character with word` `vector addWord(` `    ``string word,` `    ``unordered_set& dict)` `{` `    ``vector res;`   `    ``// Find next word in dict by changing` `    ``// each element from 'a' to 'z'` `    ``for` `(``int` `i = 0; i < word.size(); i++) {` `        ``char` `s = word[i];` `        ``for` `(``char` `c = ``'a'``; c <= ``'z'``; c++) {` `            ``word[i] = c;` `            ``if` `(dict.count(word))` `                ``res.push_back(word);` `        ``}` `        ``word[i] = s;` `    ``}` `    ``return` `res;` `}`   `// Function to get all the shortest possible` `// sequences starting from 'start' to 'target'` `vector > findLadders(` `    ``vector& Dict,` `    ``string beginWord,` `    ``string endWord)` `{` `    ``// Store all the shortest path.` `    ``vector > res;`   `    ``// Store visited words in list` `    ``unordered_set visit;`   `    ``// Queue used to find the shortest path` `    ``queue > q;`   `    ``// Stores the distinct words from given list` `    ``unordered_set dict(Dict.begin(),` `                               ``Dict.end());` `    ``q.push({ beginWord });`   `    ``// Stores whether the shortest` `    ``// path is found or not` `    ``bool` `flag = ``false``;`   `    ``while` `(!q.empty()) {` `        ``int` `size = q.size();` `        ``for` `(``int` `i = 0; i < size; i++) {`   `            ``// Explore the next level` `            ``vector cur = q.front();` `            ``q.pop();` `            ``vector newadd;`   `            ``// Find words differing by a` `            ``// single character` `            ``newadd = addWord(cur.back(), dict);`   `            ``// Add words to the path.` `            ``for` `(``int` `j = 0; j < newadd.size(); j++) {` `                ``vector newline(cur.begin(),` `                                       ``cur.end());`   `                ``newline.push_back(newadd[j]);`   `                ``// Found the target` `                ``if` `(newadd[j] == endWord) {` `                    ``flag = ``true``;` `                    ``res.push_back(newline);` `                ``}`   `                ``visit.insert(newadd[j]);` `                ``q.push(newline);` `            ``}` `        ``}`   `        ``// If already reached target` `        ``if` `(flag) {` `            ``break``;` `        ``}`   `        ``// Erase all visited words.` `        ``for` `(``auto` `it : visit) {` `            ``dict.erase(it);` `        ``}`   `        ``visit.clear();` `    ``}` `    ``return` `res;` `}`   `// Driver Code` `int` `main()` `{` `    ``vector str{ ``"ted"``, ``"tex"``, ``"red"``,` `                        ``"tax"``, ``"tad"``, ``"den"``,` `                        ``"rex"``, ``"pee"` `};` `    ``string beginWord = ``"red"``;` `    ``string endWord = ``"tax"``;`   `    ``vector > res` `        ``= findLadders(str, beginWord, endWord);`   `    ``displaypath(res);` `}`

## Python3

 `# Python Program to implement` `# the above approach` `from` `collections ``import` `deque` `from` `typing ``import` `Deque, ``List``, ``Set`   `# Function to print all possible shortest` `# sequences starting from start to target.` `def` `displaypath(res: ``List``[``List``[``str``]]):` `    ``for` `i ``in` `res:` `        ``print``(``"[ "``, end``=``"")` `        ``for` `j ``in` `i:` `            ``print``(j, end``=``", "``)` `        ``print``(``"]"``)`   `# Find words differing by a single` `# character with word` `def` `addWord(word: ``str``, ``Dict``: ``Set``):` `    ``res: ``List``[``str``] ``=` `[]` `    ``wrd ``=` `list``(word)` `    `  `    ``# Find next word in dict by changing` `    ``# each element from 'a' to 'z'` `    ``for` `i ``in` `range``(``len``(wrd)):` `        ``s ``=` `wrd[i]` `        ``c ``=` `'a'` `        ``while` `c <``=` `'z'``:` `            ``wrd[i] ``=` `c` `            ``if` `''.join(wrd) ``in` `Dict``:` `                ``res.append(''.join(wrd))` `            ``c ``=` `chr``(``ord``(c) ``+` `1``)` `        ``wrd[i] ``=` `s` `    ``return` `res`   `# Function to get all the shortest possible` `# sequences starting from 'start' to 'target'` `def` `findLadders(Dictt: ``List``[``str``], beginWord: ``str``, endWord: ``str``):`   `    ``# Store all the shortest path.` `    ``res: ``List``[``List``[``str``]] ``=` `[]`   `    ``# Store visited words in list` `    ``visit ``=` `set``()`   `    ``# Queue used to find the shortest path` `    ``q: Deque[``List``[``str``]] ``=` `deque()`   `    ``# Stores the distinct words from given list` `    ``Dict` `=` `set``()` `    ``for` `i ``in` `Dictt:` `        ``Dict``.add(i)` `    ``q.append([beginWord])`   `    ``# Stores whether the shortest` `    ``# path is found or not` `    ``flag ``=` `False` `    ``while` `q:` `        ``size ``=` `len``(q)` `        ``for` `i ``in` `range``(size):`   `            ``# Explore the next level` `            ``cur ``=` `q[``0``]` `            ``q.popleft()` `            ``newadd ``=` `[]`   `            ``# Find words differing by a` `            ``# single character` `            ``newadd ``=` `addWord(cur[``-``1``], ``Dict``)`   `            ``# Add words to the path.` `            ``for` `j ``in` `range``(``len``(newadd)):` `                ``newline ``=` `cur.copy()` `                ``newline.append(newadd[j])`   `                ``# Found the target` `                ``if` `(newadd[j] ``=``=` `endWord):` `                    ``flag ``=` `True` `                    ``res.append(newline)`   `                ``visit.add(newadd[j])` `                ``q.append(newline)`   `        ``# If already reached target` `        ``if` `(flag):` `            ``break`   `        ``# Erase all visited words.` `        ``for` `it ``in` `visit:` `            ``Dict``.remove(it)` `        ``visit.clear()` `    ``return` `res`   `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:`   `    ``string ``=` `[``"ted"``, ``"tex"``, ``"red"``, ``"tax"``, ``"tad"``, ``"den"``, ``"rex"``, ``"pee"``]` `    ``beginWord ``=` `"red"` `    ``endWord ``=` `"tax"`   `    ``res ``=` `findLadders(string, beginWord, endWord)`   `    ``displaypath(res)`   `# This code is contributed by sanjeev2552`

Output:

```[ red, ted, tad, tax,  ]
[ red, ted, tex, tax,  ]
[ red, rex, tex, tax,  ]```

Time complexity: O(N²*M), where M is the number of strings in the given list and N is the length of each string.

Auxiliary Space:O(M*N)

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