126. Word Ladder II

问题

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

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

Note:

• Return an empty list 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.

UPDATE (2017/1/20):
The wordList parameter had been changed to a list of strings (instead of a set of strings). Please reload the code definition to get the latest changes.

例子

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

分析

参考Word Ladder的思路，在two-sided bfs的基础上保存路径信息，然后用dfs打印出路径。

要点

1. bfs和dfs的差异以及各自的应用场景：bfs一般用来寻找最短路径，层级展开，迭代；dfs一般用来遍历所有路径，深入到底然后回溯，递归；
2. 可能有多条最短路径，two-sided bfs不能找到结果就立马返回，而且在单词表中删除单词的时机也要注意。详见代码注释。

时间复杂度

O(n)

空间复杂度

O(1)

代码

class Solution {
public:
    vector> findLadders(string beginWord, string endWord, vector& wordList) {
        vector> ladders;
        vector ladder;
        ladder.push_back(beginWord); // 加入起点
        
        unordered_set words(wordList.begin(), wordList.end());
        if (words.find(endWord) == words.end()) return ladders;
        words.erase(beginWord);
        words.erase(endWord);
        
        unordered_set beginWords, endWords;
        beginWords.insert(beginWord);
        endWords.insert(endWord);
        unordered_map> paths;
        
        if (twoSidedBfs(beginWords, endWords, words, paths))
            dfs(beginWord, endWord, paths, ladder, ladders);
        
        return ladders;
    }
    
private:
    bool twoSidedBfs(unordered_set &beginWords, unordered_set &endWords, 
        unordered_set &words, unordered_map> &paths) {
        unordered_set *p1 = &beginWords, *p2 = &endWords;
        
        while (!p1->empty() && !p2->empty()) {
            if (p1->size() > p2->size())
                swap(p1, p2);

            unordered_set tempWords;
            bool found = false; // 是否能在p2中找到单词
            for (string word : *p1) {
                string tempWord = word;
                for (int i = 0; i < word.size(); i++) {
                    char letter = word[i];
                    for (int j = 0; j < 26; j++) {
                        word[i] = 'a' + j;
                        
                        bool existsInP2 = p2->find(word) != p2->end();
                        bool existsInWords = words.find(word) != words.end();
                        if (existsInP2 || existsInWords) {
                            if (p1 == &beginWords)
                               paths[tempWord].push_back(word);
                            else
                               paths[word].push_back(tempWord);
                        }
                        if (existsInP2)
                            found = true; // 注意到没有在found=true的时候立刻返回，因为可能有多条最短路径
                        if (existsInWords)
                            // 不能在这里删除单词，否则会丢失一部分最短路径！
                            tempWords.insert(word);
                    }
                    word[i] = letter;
                }
            }
            
            if (found) return true;
            // 注意只能在遍历p1的循环外删除单词表的单词，因为可能有多条最短路径，所以每一层的单词允许有重复
            // 例如hit hot pot dot dit和hit hot hop dop dit，在第二层就有两个重复的hot
            for (string tempWord : tempWords)
                words.erase(tempWord);
            swap(*p1, tempWords);
        }
        return false;
    }
    
    void dfs(string beginWord, string endWord, unordered_map> &paths,
        vector &ladder, vector> &ladders) {
        if (beginWord == endWord) {
            ladders.push_back(ladder);
            return;
        }
        for (const string &nodeWord : paths[beginWord]) {
            ladder.push_back(nodeWord);
            dfs(nodeWord, endWord, paths, ladder, ladders);
            ladder.pop_back();
        }
    }
};