[220212] Word Ladder

from collections import defaultdict, deque


class Solution:
    def ladderLength(self, beginWord, endWord, wordList):

        if endWord not in wordList:
            return 0

        if beginWord not in wordList:
            wordList.append(beginWord)

        # record graph[pattern] = corresponding words
        # E.g., '*ot': ['hot', 'dot', 'lot']
        graph = defaultdict(list)
        for word in wordList:
            for i in range(len(word)):
                pattern = word[:i] + '*' + word[i+1:]
                graph[pattern].append(word)

        # BFS - q: deque to pop current word; path: record words already seen
        q = deque([beginWord])
        path = set()
        path.add(beginWord)
        count = 1

        while q:
            for i in range(len(q)):
                word = q.popleft()
                if word == endWord:
                    return count

                for j in range(len(word)):
                    pattern = word[:j] + '*' + word[j+1:]
                    # for each word following this pattern
                    for w in graph[pattern]:
                        if w not in path:
                            q.append(w)
                            path.add(w)
            # path length += 1
            count += 1

        return 0