Question:

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:

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 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: 5Explanation: 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: 0Explanation: The endWord "cog" is not in wordList, therefore no possible transformation.

Answer:

题目的意思如下：题目给出一个单词beginWord，一个单词列表wordList，一个单词endWord，要求我们从beginWord开始，每次只能变单词中的一个字母，使其成为wordList中的一个单词，重复若干次上述步骤直到变化成endWord，求最少的变化次数（若能成功变化成endWord）。

分析题目我们可以得到以下方案：

对beginWord，以wordList作为候选池，进行BFS，得到其下一层A
层A中的所有单词从候选池（wordList）中删去，避免搜索路径树出现环。而且其他将来可能经过该层单词的路径都将比层A发散出去的路径更长
将层A中的单词推进队列
队列头弹出一个单词，对其BFS，所有下一层的单词都从wordList中删去，并将该层单词推进队列。（从树根到队列头单词的下一层某单词K的步数肯定小于等于从树根到队列中其他单词到单词K的步数）
重复第四步，直到某队列头的下一层单词中有endWord（有解）或队列为空（无解）

在函数开始，先检测了endWord是否在wordList中，避免无谓的路径搜索。

声明了类State，有属性单词和属性步数，作为搜索的节点记录数据，相当于树的节点。方法中将State对象推进或弹出队列，对搜索到的下一层单词创建State对象记录其单词和步数（上一层+1）。

从wordList删除搜索到的下一层单词是为了后续搜索时能搜索更少的节点。

定义了方法check用于校验两个单词是否只差一个字母。

然后得到初步的代码如下（Python3）：

import time
import queue
import copyclass State:def __init__(self, on, times):self.now = onself.times = timesclass Solution:def ladderLength(self, beginWord, endWord, wordList):""":type beginWord: str:type endWord: str:type wordList: List[str]:rtype: int"""self.q = queue.Queue()if endWord not in wordList:return 0self.list = wordListself.end = endWordbegin = State(beginWord, 1)self.q.put(begin)while not self.q.empty():temp = self.q.get()i = 0while i < len(self.list):word = self.list[i]if self.check(word, temp.now):if word == self.end:return temp.times + 1if word != temp.now:self.q.put(State(word, temp.times+1))self.list.remove(word)else: i += 1return 0def check(self, wordA, wordB):flag = Truefor i in range(len(wordA)):if wordA[i] != wordB[i] and flag == True:flag = Falseelif wordA[i] != wordB[i] and flag == False:return Falsereturn True

然而当wordList中元素足够多（如以下代码中的29/39次test的2855个数据）时，提交反馈Time Limit Exceeded。这是因为搜索的效率低下。对于一个弹出的队列头单词A，搜索与他相似（指只相差一个字母）的单词需要遍历整个wordList，复杂度为O(n)，同时remove一个相似单词需要对所有后续元素进行移动。若用一个标识（如0）取代remove，在另一方面由加重了遍历的工作量（实际上通过time计时发现时间更长了）。由于python3中list的数据结构相当于一个动态数组，因此假如不改变算法，这将无可避免。曾考虑使用链表，然而只能优化remove而无法改变搜索需要的遍历。

以下代码为测试代码，其中wordList有2855个数据，用以上算法在VScode调试下计时得6-7s，步数为11。

test = Solution()
beginWord = "sand"
endWord = "acne"
wordList = ["slit","bunk","wars","ping","viva","wynn","wows","irks","gang","pool","mock","fort","heel","send","ship","cols","alec","foal","nabs","gaze","giza","mays","dogs","karo","cums","jedi","webb","lend","mire","jose","catt","grow","toss","magi","leis","bead","kara","hoof","than","ires","baas","vein","kari","riga","oars","gags","thug","yawn","wive","view","germ","flab","july","tuck","rory","bean","feed","rhee","jeez","gobs","lath","desk","yoko","cute","zeus","thus","dims","link","dirt","mara","disc","limy","lewd","maud","duly","elsa","hart","rays","rues","camp","lack","okra","tome","math","plug","monk","orly","friz","hogs","yoda","poop","tick","plod","cloy","pees","imps","lead","pope","mall","frey","been","plea","poll","male","teak","soho","glob","bell","mary","hail","scan","yips","like","mull","kory","odor","byte","kaye","word","honk","asks","slid","hopi","toke","gore","flew","tins","mown","oise","hall","vega","sing","fool","boat","bobs","lain","soft","hard","rots","sees","apex","chan","told","woos","unit","scow","gilt","beef","jars","tyre","imus","neon","soap","dabs","rein","ovid","hose","husk","loll","asia","cope","tail","hazy","clad","lash","sags","moll","eddy","fuel","lift","flog","land","sigh","saks","sail","hook","visa","tier","maws","roeg","gila","eyes","noah","hypo","tore","eggs","rove","chap","room","wait","lurk","race","host","dada","lola","gabs","sobs","joel","keck","axed","mead","gust","laid","ends","oort","nose","peer","kept","abet","iran","mick","dead","hags","tens","gown","sick","odis","miro","bill","fawn","sumo","kilt","huge","ores","oran","flag","tost","seth","sift","poet","reds","pips","cape","togo","wale","limn","toll","ploy","inns","snag","hoes","jerk","flux","fido","zane","arab","gamy","raze","lank","hurt","rail","hind","hoot","dogy","away","pest","hoed","pose","lose","pole","alva","dino","kind","clan","dips","soup","veto","edna","damp","gush","amen","wits","pubs","fuzz","cash","pine","trod","gunk","nude","lost","rite","cory","walt","mica","cart","avow","wind","book","leon","life","bang","draw","leek","skis","dram","ripe","mine","urea","tiff","over","gale","weir","defy","norm","tull","whiz","gill","ward","crag","when","mill","firs","sans","flue","reid","ekes","jain","mutt","hems","laps","piss","pall","rowe","prey","cull","knew","size","wets","hurl","wont","suva","girt","prys","prow","warn","naps","gong","thru","livy","boar","sade","amok","vice","slat","emir","jade","karl","loyd","cerf","bess","loss","rums","lats","bode","subs","muss","maim","kits","thin","york","punt","gays","alpo","aids","drag","eras","mats","pyre","clot","step","oath","lout","wary","carp","hums","tang","pout","whip","fled","omar","such","kano","jake","stan","loop","fuss","mini","byrd","exit","fizz","lire","emil","prop","noes","awed","gift","soli","sale","gage","orin","slur","limp","saar","arks","mast","gnat","port","into","geed","pave","awls","cent","cunt","full","dint","hank","mate","coin","tars","scud","veer","coax","bops","uris","loom","shod","crib","lids","drys","fish","edit","dick","erna","else","hahs","alga","moho","wire","fora","tums","ruth","bets","duns","mold","mush","swop","ruby","bolt","nave","kite","ahem","brad","tern","nips","whew","bait","ooze","gino","yuck","drum","shoe","lobe","dusk","cult","paws","anew","dado","nook","half","lams","rich","cato","java","kemp","vain","fees","sham","auks","gish","fire","elam","salt","sour","loth","whit","yogi","shes","scam","yous","lucy","inez","geld","whig","thee","kelp","loaf","harm","tomb","ever","airs","page","laud","stun","paid","goop","cobs","judy","grab","doha","crew","item","fogs","tong","blip","vest","bran","wend","bawl","feel","jets","mixt","tell","dire","devi","milo","deng","yews","weak","mark","doug","fare","rigs","poke","hies","sian","suez","quip","kens","lass","zips","elva","brat","cosy","teri","hull","spun","russ","pupa","weed","pulp","main","grim","hone","cord","barf","olav","gaps","rote","wilt","lars","roll","balm","jana","give","eire","faun","suck","kegs","nita","weer","tush","spry","loge","nays","heir","dope","roar","peep","nags","ates","bane","seas","sign","fred","they","lien","kiev","fops","said","lawn","lind","miff","mass","trig","sins","furl","ruin","sent","cray","maya","clog","puns","silk","axis","grog","jots","dyer","mope","rand","vend","keen","chou","dose","rain","eats","sped","maui","evan","time","todd","skit","lief","sops","outs","moot","faze","biro","gook","fill","oval","skew","veil","born","slob","hyde","twin","eloy","beat","ergs","sure","kobe","eggo","hens","jive","flax","mons","dunk","yest","begs","dial","lodz","burp","pile","much","dock","rene","sago","racy","have","yalu","glow","move","peps","hods","kins","salk","hand","cons","dare","myra","sega","type","mari","pelt","hula","gulf","jugs","flay","fest","spat","toms","zeno","taps","deny","swag","afro","baud","jabs","smut","egos","lara","toes","song","fray","luis","brut","olen","mere","ruff","slum","glad","buds","silt","rued","gelt","hive","teem","ides","sink","ands","wisp","omen","lyre","yuks","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time_start=time.time()
print(test.ladderLength(beginWord, endWord, wordList))
time_end=time.time()
print('time cost',time_end-time_start,'s')

最后参考题目的Discuss得到，可以通过对单词字母的广度优先搜索来避免对wordList的遍历。一个长度为m的单词，其所有相似单词共有25*m个。由于我们已经得到单词可能的搜索结果，只要查找其是否在wordList即可避免遍历。这样我们可以使用一个可哈希的数据结构存储wordList，这里使用了set。这样检测一个单词是否在wordList的耗时将缩减到最小。此时搜索的复杂度为O(1)。同样在搜索到一个相似单词时在set中删除它，这样可以避免维护一个容器来储存搜索过的单词。然后将代码优化如下：

import queue
import stringclass State:def __init__(self, on, times):self.now = onself.times = timesclass Solution:def ladderLength(self, beginWord, endWord, wordList):""":type beginWord: str:type endWord: str:type wordList: List[str]:rtype: int"""self.q = queue.Queue()self.list = set(wordList)if endWord not in self.list:return 0self.end = endWordbegin = State(beginWord, 1)self.q.put(begin)while not self.q.empty():temp = self.q.get()for index in range(len(temp.now)):for ch in string.ascii_lowercase:if ch == temp.now[index]:continueelse:nextWord = temp.now[:index] + str(ch) + temp.now[index+1:]if nextWord in self.list:if nextWord == self.end:return temp.times + 1else:self.q.put(State(nextWord, temp.times+1))self.list.discard(nextWord)return 0

这次提交的Runtime为1064 ms - 1804ms 间浮动（实际上主要在1600ms-1800ms间浮动）。VScode调试计时为0.3s+。

假如进一步优化，将queue换成collections.deque，VScode调试计时将减小为0.2s+，LeetCode的Runtime为952ms - 1120ms

优化后如下：

import time
import string
import collectionsclass Solution:def ladderLength(self, beginWord, endWord, wordList):""":type beginWord: str:type endWord: str:type wordList: List[str]:rtype: int"""self.list = set(wordList)if endWord not in self.list:return 0self.end = endWordself.q = collections.deque([(beginWord, 1)])while self.q:(w,t) = self.q.popleft()for index in range(len(w)):for ch in string.ascii_lowercase:if ch == w[index]:continueelse:nextWord = w[:index] + str(ch) + w[index+1:]if nextWord in self.list:if nextWord == self.end:return t + 1else:self.q.append((nextWord, t+1))self.list.discard(nextWord)return 0

VScode调试计时：

LeetCode下的Runtime：