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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._

**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. 

**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**.




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