127. Word Ladder

Problem

Given two words (beginWord and endWord), and a dictionary's word list, find the length of shortest transformation sequence from beginWord to endWord, such that:

1. Only one letter can be changed at a time.
2. Each transformed word must exist in the word list. Note that beginWord is not a transformed word.

Note:

• Return 0 if there is no such transformation sequence.
• All words have the same length.
• All words contain only lowercase alphabetic characters.
• You may assume no duplicates in the word list.
• You may assume beginWord and endWord are non-empty and are not the same.

Example 1:

Input:
beginWord = "hit",
endWord = "cog",
wordList = ["hot","dot","dog","lot","log","cog"]

Output: 5

Explanation: As one shortest transformation is "hit" -> "hot" -> "dot" -> "dog" -> "cog",
return its length 5.

Example 2:

Input:
beginWord = "hit"
endWord = "cog"
wordList = ["hot","dot","dog","lot","log"]

Output: 0

Explanation: The endWord "cog" is not in wordList, therefore no possible transformation.

Problem Summary

Given two words (beginWord and endWord) and a dictionary, find the length of the shortest transformation sequence from beginWord to endWord. The transformation must follow these rules:

1. Only one letter can be changed at a time.
2. The intermediate words during the transformation must be words in the dictionary.

Notes:

• If no such transformation sequence exists, return 0.
• All words have the same length.
• All words consist only of lowercase letters.
• There are no duplicate words in the dictionary.
• You may assume beginWord and endWord are non-empty and are not the same.

Solution Approach

• This problem requires outputting the shortest number of transformations from beginWord to endWord. BFS can be used. Start from beginWord, change each letter of the word once using 'a'~'z', and look up the generated words in wordList; here, use a Map to record the lookup. If found, enqueue it; if not found, output 0. After enqueuing, traverse sequentially according to the BFS algorithm. When all words have been dequeued and len(queue)<=0, the whole program ends.
• Although the problem says to find a shortest path, the method for finding the shortest path has actually already been given:
  1. Change only one letter at a time
  2. Each transformation must be in wordList
     So there is no need to separately consider which method is the shortest.

Code

package leetcode

func ladderLength(beginWord string, endWord string, wordList []string) int {
	wordMap, que, depth := getWordMap(wordList, beginWord), []string{beginWord}, 0
	for len(que) > 0 {
		depth++
		qlen := len(que)
		for i := 0; i < qlen; i++ {
			word := que[0]
			que = que[1:]
			candidates := getCandidates(word)
			for _, candidate := range candidates {
				if _, ok := wordMap[candidate]; ok {
					if candidate == endWord {
						return depth + 1
					}
					delete(wordMap, candidate)
					que = append(que, candidate)
				}
			}
		}
	}
	return 0
}

func getWordMap(wordList []string, beginWord string) map[string]int {
	wordMap := make(map[string]int)
	for i, word := range wordList {
		if _, ok := wordMap[word]; !ok {
			if word != beginWord {
				wordMap[word] = i
			}
		}
	}
	return wordMap
}

func getCandidates(word string) []string {
	var res []string
	for i := 0; i < 26; i++ {
		for j := 0; j < len(word); j++ {
			if word[j] != byte(int('a')+i) {
				res = append(res, word[:j]+string(int('a')+i)+word[j+1:])
			}
		}
	}
	return res
}