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126. Word Ladder II

Description

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.

Solutions

Solution 1

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class Solution:
    def findLadders(
        self, beginWord: str, endWord: str, wordList: List[str]
    ) -> List[List[str]]:
        def dfs(path, cur):
            if cur == beginWord:
                ans.append(path[::-1])
                return
            for precursor in prev[cur]:
                path.append(precursor)
                dfs(path, precursor)
                path.pop()

        ans = []
        words = set(wordList)
        if endWord not in words:
            return ans
        words.discard(beginWord)
        dist = {beginWord: 0}
        prev = defaultdict(set)
        q = deque([beginWord])
        found = False
        step = 0
        while q and not found:
            step += 1
            for i in range(len(q), 0, -1):
                p = q.popleft()
                s = list(p)
                for i in range(len(s)):
                    ch = s[i]
                    for j in range(26):
                        s[i] = chr(ord('a') + j)
                        t = ''.join(s)
                        if dist.get(t, 0) == step:
                            prev[t].add(p)
                        if t not in words:
                            continue
                        prev[t].add(p)
                        words.discard(t)
                        q.append(t)
                        dist[t] = step
                        if endWord == t:
                            found = True
                    s[i] = ch
        if found:
            path = [endWord]
            dfs(path, endWord)
        return ans

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class Solution {
    private List<List<String>> ans;
    private Map<String, Set<String>> prev;

    public List<List<String>> findLadders(String beginWord, String endWord, List<String> wordList) {
        ans = new ArrayList<>();
        Set<String> words = new HashSet<>(wordList);
        if (!words.contains(endWord)) {
            return ans;
        }
        words.remove(beginWord);
        Map<String, Integer> dist = new HashMap<>();
        dist.put(beginWord, 0);
        prev = new HashMap<>();
        Queue<String> q = new ArrayDeque<>();
        q.offer(beginWord);
        boolean found = false;
        int step = 0;
        while (!q.isEmpty() && !found) {
            ++step;
            for (int i = q.size(); i > 0; --i) {
                String p = q.poll();
                char[] chars = p.toCharArray();
                for (int j = 0; j < chars.length; ++j) {
                    char ch = chars[j];
                    for (char k = 'a'; k <= 'z'; ++k) {
                        chars[j] = k;
                        String t = new String(chars);
                        if (dist.getOrDefault(t, 0) == step) {
                            prev.get(t).add(p);
                        }
                        if (!words.contains(t)) {
                            continue;
                        }
                        prev.computeIfAbsent(t, key -> new HashSet<>()).add(p);
                        words.remove(t);
                        q.offer(t);
                        dist.put(t, step);
                        if (endWord.equals(t)) {
                            found = true;
                        }
                    }
                    chars[j] = ch;
                }
            }
        }
        if (found) {
            Deque<String> path = new ArrayDeque<>();
            path.add(endWord);
            dfs(path, beginWord, endWord);
        }
        return ans;
    }

    private void dfs(Deque<String> path, String beginWord, String cur) {
        if (cur.equals(beginWord)) {
            ans.add(new ArrayList<>(path));
            return;
        }
        for (String precursor : prev.get(cur)) {
            path.addFirst(precursor);
            dfs(path, beginWord, precursor);
            path.removeFirst();
        }
    }
}

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func findLadders(beginWord string, endWord string, wordList []string) [][]string {
    var ans [][]string
    words := make(map[string]bool)
    for _, word := range wordList {
        words[word] = true
    }
    if !words[endWord] {
        return ans
    }
    words[beginWord] = false
    dist := map[string]int{beginWord: 0}
    prev := map[string]map[string]bool{}
    q := []string{beginWord}
    found := false
    step := 0
    for len(q) > 0 && !found {
        step++
        for i := len(q); i > 0; i-- {
            p := q[0]
            q = q[1:]
            chars := []byte(p)
            for j := 0; j < len(chars); j++ {
                ch := chars[j]
                for k := 'a'; k <= 'z'; k++ {
                    chars[j] = byte(k)
                    t := string(chars)
                    if v, ok := dist[t]; ok {
                        if v == step {
                            prev[t][p] = true
                        }
                    }
                    if !words[t] {
                        continue
                    }
                    if len(prev[t]) == 0 {
                        prev[t] = make(map[string]bool)
                    }
                    prev[t][p] = true
                    words[t] = false
                    q = append(q, t)
                    dist[t] = step
                    if endWord == t {
                        found = true
                    }
                }
                chars[j] = ch
            }
        }
    }
    var dfs func(path []string, begin, cur string)
    dfs = func(path []string, begin, cur string) {
        if cur == beginWord {
            cp := make([]string, len(path))
            copy(cp, path)
            ans = append(ans, cp)
            return
        }
        for k := range prev[cur] {
            path = append([]string{k}, path...)
            dfs(path, beginWord, k)
            path = path[1:]
        }
    }
    if found {
        path := []string{endWord}
        dfs(path, beginWord, endWord)
    }
    return ans
}

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