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from string import ascii_lowercase

class Solution(object):
    def ladderLength(self, beginWord, endWord, wordList):
        """
        :type beginWord: str
        :type endWord: str
        :type wordList: Set[str]
        :rtype: int
        """
        if beginWord == endWord:
            return 1
        
        wordList.remove(beginWord)
        wordList.remove(endWord)
        
        frontier = set([beginWord])
        otherside = set([endWord])
        visited = set()
        pathLength = 1
        while len(frontier) > 0 and len(otherside) > 0:
            pathLength += 1
            nexts = set()
            
            for cur in frontier:
                for perm in self.permutations(cur):
                    if perm in otherside:
                        return pathLength
                        
                    if perm not in visited and perm in wordList:
                        visited.add(perm)
                        nexts.add(perm)
            
            frontier = nexts
            if len(frontier) > len(otherside):
                frontier, otherside = otherside, frontier
        
        return 0
        
    def permutations(self, word):
        for i in range(len(word)):
            for c in ascii_lowercase:
                yield word[:i] + c + word[i+1:]