Word Ladder
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Given two words (start and end), and a dictionary, find the length of shortest transformation sequence from start to end, such
that:
- Only one letter can be changed at a time
- Each intermediate word must exist in the dictionary
For example,
Given:
start = "hit"
end = "cog"
dict = ["hot","dot","dog","lot","log"]
As one shortest transformation is "hit",
-> "hot" -> "dot" -> "dog" -> "cog"
return its length 5.
Note:
- Return 0 if there is no such transformation sequence.
- All words have the same length.
- All words contain only lowercase alphabetic characters.
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此题是图的遍历问题。要找一条起始点到目标点最短的路径，假设存在这种路径则返回路径长度。否则返回0。 刚開始想到用深度优先搜索遍历，可是时间复杂度太大。于是转为用宽搜，把起始点放入队列中，队列中的节点是一个字符串。由于要找到最短路径，所以在取出队首节点时要知道该节点属于第几层被搜索的节点，即路径长度，我用了levels来保存当前遍历的是第几层的节点，然后扩展该节点，把编辑距离为1而且在字典中出现的字符串增加队尾。并从字典中删除该字符串。
在找编辑距离为1的字符串时，我试了两种方法，一种是遍历字典，找到编辑记录为1的字符串，假设字典数目非常大的话，每次都遍历字典耗时太多了。结果就是TLE，后来直接对节点字符串进行改动一个字符来得到扩展字符串才通过。
<span style="font-size:14px;">class Solution {
public:
typedef queue<string,deque<string>> qq;
int ladderLength(string start, string end, unordered_set<string> &dict) {
//Use queue to implement bfs operation
qq q;
q.push(start);
dict.erase(start);
int currLevelLens = 1, nextLevelLens;
int levels = 1; //To be returned answer, the total bfs levels be traversed
string front, str;
while (!q.empty()) {
nextLevelLens = 0;
while (currLevelLens--) { // Traverse the node of current level
string front = q.front();
q.pop();
if (front == end)
return levels;
for (int i=0; i<front.size(); ++i) {
for (char j='a'; j<='z'; ++j) { // transform
if (front[i]=='j')
continue;
str = front;
str[i] = j;
if (dict.find(str) != dict.end()) {
++nextLevelLens;
q.push(str);
dict.erase(str);
}
}
}
}
currLevelLens = nextLevelLens;
++levels;
}
return 0;
}
};
</span>
可是这个方案改变了dict的内容。有没有不改变dict的方法呢？我试了用一个unorder_set来保存被搜索过的字符串,可是耗时比前一种方法多。
class Solution {
public:
typedef queue<string,deque<string>> qq;
int ladderLength(string start, string end, unordered_set<string> &dict) {
//Use queue to implement bfs operation
qq q;
q.push(start);
int currLevelLens = 1, nextLevelLens;
int levels = 1; //To be returned answer, the total bfs levels be traversed
string front, str;
searchedStrs.insert(start);
while (!q.empty()) {
nextLevelLens = 0;
while (currLevelLens--) { // Traverse the node of current level
string front = q.front();
q.pop();
if (front == end)
return levels;
for (int i=0; i<front.size(); ++i) {
for (char j='a'; j<='z'; ++j) { // transform
if (front[i]==j)
continue;
str = front;
str[i] = j;
if (searchedStrs.find(str) == searchedStrs.end() && dict.find(str) != dict.end()) {
++nextLevelLens;
q.push(str);
//dict.erase(str);
searchedStrs.insert(str);
}
}
}
}
currLevelLens = nextLevelLens;
++levels;
}
return 0;
}
private:
unordered_set<string> searchedStrs;
};
Python解法：
有參考Google Norvig的拼写纠正样例：http://norvig.com/spell-correct.html
class Solution:
# @param word, a string
# @return a list of transformed words
def edit(self, word):
alphabet = string.ascii_lowercase
splits = [(word[:i],word[i:]) for i in range(len(word)+1)]
replaces = [a+c+b[1:] for a,b in splits for c in alphabet if b]
replaces.remove(word)
return replaces # @param start, a string
# @param end, a string
# @param dict, a set of string
# @return an integer
def ladderLength(self, start, end, dict):
currQueue = []
currQueue.append(start)
dict.remove(start)
ret = 0
while 1:
ret += 1
nextQueue = []
while len(currQueue):
s = currQueue.pop(0)
if s == end:
return ret
editWords = self.edit(s) for word in editWords:
if word in dict:
dict.remove(word)
nextQueue.append(word)
if len(nextQueue)==0:
return 0
currQueue = nextQueue
return 0