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单词接龙 II

Word Ladder II

专题
Algorithmic Programming / 算法编程
难度
L4
来源
Citadel

题目详情

问题：单词接龙 II

考察：图、字符串

来源：Citadel

链接：https://www.jointaro.com/interviews/questions/word-ladder-ii/

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].

 

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.
解析

思路：先用 BFS 从 beginWord 按层搜索到 endWord，同时记录每个单词的所有前驱，保证只保留最短路径层。之后从 endWord 回溯到 beginWord 枚举所有路径。

复杂度：时间和空间取决于单词数、长度和最短路径数量，建邻接通常为 O(NL^2)。