# 127. Word Ladder

#### Hard

***

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 *the **number of words** in the **shortest transformation sequence** from* `beginWord` *to* `endWord`*, or* `0` *if no such sequence exists.*

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**Example 1:**

```
Input: beginWord = "hit", endWord = "cog", wordList = ["hot","dot","dog","lot","log","cog"]
Output: 5
Explanation: One shortest transformation sequence is "hit" -> "hot" -> "dot" -> "dog" -> cog", which is 5 words long.
```

**Example 2:**

```
Input: beginWord = "hit", endWord = "cog", wordList = ["hot","dot","dog","lot","log"]
Output: 0
Explanation: The endWord "cog" is not in wordList, therefore there is no valid transformation sequence.
```

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**Constraints:**

* `1 <= beginWord.length <= 10`
* `endWord.length == beginWord.length`
* `1 <= wordList.length <= 5000`
* `wordList[i].length == beginWord.length`
* `beginWord`, `endWord`, and `wordList[i]` consist of lowercase English letters.
* `beginWord != endWord`
* All the words in `wordList` are **unique**.

```python
from collections import deque
class Solution:
    def ladderLength(self, beginWord: str, endWord: str, wordList: List[str]) -> int:
        # Got TLE
        # Next improvement can be is to convert wordList from List to Set
        # Since check "if exists" takes linear time in List and Constant in Set
        wordList = set(wordList)
        charSet = {w for word in wordList for w in word}
        queue = deque([[beginWord, 1]])
        while queue:
            word, length = queue.popleft()
            if word == endWord:
                return length
            for index in range(len(word)):
                for char in charSet:
                    new_word = word[:index] + char + word[index+1:]
                    if new_word in wordList:
                        wordList.remove(new_word)
                        queue.append([new_word, length+1])
        return 0
```