Word Ladder
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 intermediate word must exist in the word list
For example,
Given:
beginWord ="hit"
endWord ="cog"
wordList =["hot","dot","dog","lot","log"]
As one shortest transformation is"hit" -> "hot" -> "dot" -> "dog" -> "cog"
,
return its length5
.Note:
Return 0 if there is no such transformation sequence.
All words have the same length.
All words contain only lowercase alphabetic characters.
分析
典型的BFS题。一层一层的找,分别对应修改一个字符,两个字符,三个字符...直至发现结尾字符串, 注意用一个Set寸已经访问过的字符串,避免重复。
复杂度
time: O(n), space: O(n)
代码
public class Solution {
public int ladderLength(String beginWord, String endWord, Set<String> wordList) {
Queue<String> q = new LinkedList<String>();
q.add(beginWord);
Set<String> visited = new HashSet<String>();
visited.add(beginWord);
int level = 0;
while (!q.isEmpty()) {
int len = q.size();
level++;
for (int i = 0; i < len; i++) {
String word = q.remove();
for (int j = 0; j < word.length(); j++) {
char[] chars = word.toCharArray();
for (char c = 'a'; c <= 'z'; c++) {
chars[j] = c;
String nextWord = new String(chars);
if (nextWord.equals(endWord)) {
return level + 1;
}
if (!visited.contains(nextWord) && wordList.contains(nextWord)) {
q.add(nextWord);
visited.add(nextWord);
}
}
}
}
}
return 0;
}
}
Word Ladder II
Given two words (beginWord and endWord), and a dictionary's word list, find all shortest transformation sequence(s) from beginWord to endWord, such that:
Only one letter can be changed at a time
Each intermediate word must exist in the word list
For example,
Given:
beginWord ="hit"
endWord ="cog"
wordList =["hot","dot","dog","lot","log"]
Return[ ["hit","hot","dot","dog","cog"], ["hit","hot","lot","log","cog"] ]
Note:
All words have the same length.
All words contain only lowercase alphabetic characters.
分析
如果要返回所有的结果,问题变复杂了些。因为用BFS相对于DFS的劣势就是不方便存储结果。这种需要返回所有结果的,还是应该从DFS考虑,但是直接应用DFS复杂度会很高,因为这道题我们只要知道结尾就好了,不用继续往下搜。
所以问题就转化成怎样用DFS的同时又可以限制DFS的深度,所以我们可以BFS与DFS结合。先用BFS搜到结尾字符串,然后把中途所有的字符串及其跟起始字符的edit distance存在一个map里。这样的话,我们就可以从结尾字符串开始DFS,只有Map内的字符串才考虑继续DFS,直至搜到起始字符。
注意这里有个小技巧,就是为什么不从起始字符串开始DFS直至搜到结尾字符串,而是反过来。这里可以脑子里想像一个图,如果从起始字符串开始搜,到最后一层的话会有很多无效搜索,因为那层我们只需要找到结尾字符串,那么多无效的搜索到最一层太浪费时间。反之,如果我们从结尾字符串开始DFS, 我们把起始层控制在一个字符串,整个图先越来越宽,然后越来越窄直到起始字符串,而非一直越来越宽直到结尾字符串那层。
复杂度
time: O(n), space: O(n)
代码
public class Solution {
public List<List<String>> findLadders(String beginWord, String endWord, Set<String> wordList) {
Map<String, Integer> distMap = new HashMap<String, Integer>();
getDistance(beginWord, endWord, wordList, distMap);
List<List<String>> res = new ArrayList<List<String>>();
dfs(res, new ArrayList<String>(), distMap, wordList, endWord, beginWord);
return res;
}
public void dfs(List<List<String>> res, List<String> cur, Map<String, Integer> distMap, Set<String> wordList, String word, String des) {
if (word.equals(des)) {
List<String> list = new ArrayList<String>(cur);
list.add(des);
Collections.reverse(list);
res.add(list);
return;
}
cur.add(word);
for (int i = 0; i < word.length(); i++) {
char[] chars = word.toCharArray();
for (char c = 'a'; c <= 'z'; c++) {
chars[i] = c;
String nextWord = new String(chars);
// 不仅字典中含有,两字符串也是要在路径的相邻位置即距离差1
if (distMap.containsKey(nextWord) && distMap.get(nextWord) == distMap.get(word) - 1) {
dfs(res, cur, distMap, wordList, nextWord, des);
}
}
}
cur.remove(cur.size() - 1);
}
// 用Word Ladder I的方法把候选字符串及其距离存入map,缩小DFS范围。
public void getDistance(String beginWord, String endWord, Set<String> wordList, Map<String, Integer> distMap) {
distMap.put(beginWord, 1);
Queue<String> q = new LinkedList<String>();
q.add(beginWord);
while (!q.isEmpty()) {
String word = q.remove();
for (int j = 0; j < word.length(); j++) {
char[] chars = word.toCharArray();
for (char c = 'a'; c <= 'z'; c++) {
chars[j] = c;
String nextWord = new String(chars);
if (nextWord.equals(endWord)) {
distMap.put(nextWord, distMap.get(word) + 1);
return;
}
if (wordList.contains(nextWord) && !distMap.containsKey(nextWord)) {
distMap.put(nextWord, distMap.get(word) + 1);
q.add(nextWord);
}
}
}
}
}
}
**粗体** _斜体_ [链接](http://example.com) `代码` - 列表 > 引用
。你还可以使用@
来通知其他用户。