LeetCode-Word Ladder II

Word Ladder II

##题目

####Word Ladder II

Given two words (start and end), and a dictionary, find all shortest transformation sequence(s) from start to end, such that:

  1. Only one letter can be changed at a time
  2. Each intermediate word must exist in the dictionary
    For example,

Given:
start = "hit"
end = "cog"
dict = ["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.

##解题思路
这道题是LeetCode中AC率最低的题目，确实是比较难。一方面是因为对时间有比较严格的要求（容易超时），另一方面是它有很多细节需要实现。思路上和Word Ladder是比较类似的，但是因为是要求出所有路径，仅仅保存路径长度是不够的，而且这里还有更多的问题，那就是为了得到所有路径，不是每个结点访问一次就可以标记为visited了，因为有些访问过的结点也会是别的路径上的结点，所以访问的集合要进行回溯（也就是标记回未访问）。所以时间上不再是一次广度优先搜索的复杂度了，取决于结果路径的数量。同样空间上也是相当高的复杂度，因为我们要保存过程中满足的中间路径到某个数据结构中，以便最后可以获取路径，这里我们维护一个HashMap，把一个结点前驱结点都进行保存。
在LeetCode中用Java实现上述算法非常容易超时。为了提高算法效率，需要注意一下两点：
1）在替换String的某一位的字符时，先转换成char数组再操作；
2）如果按照正常的方法从start找end，然后根据这个来构造路径，代价会比较高，因为保存前驱结点容易，而保存后驱结点则比较困难。所以我们在广度优先搜索时反过来先从end找start，最后再根据生成的前驱结点映射从start往end构造路径，这样算法效率会有明显提高。

##算法代码
代码采用JAVA实现：

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
public class Solution {
    class StringWithLevel {
   String str;
   int level;
   public StringWithLevel(String str, int level) {
      this.str = str;
      this.level = level;
   }
}
public ArrayList<ArrayList<String>> findLadders(String start, String end, HashSet<String> dict) {
   ArrayList<ArrayList<String>> res = new ArrayList<ArrayList<String>>();
   HashSet<String> unvisitedSet = new HashSet<String>();
   unvisitedSet.addAll(dict);
   unvisitedSet.add(start);
   unvisitedSet.remove(end);
   Map<String, List<String>> nextMap = new HashMap<String, List<String>>();
   for (String e : unvisitedSet) {
      nextMap.put(e, new ArrayList<String>());
   }
   LinkedList<StringWithLevel> queue = new LinkedList<StringWithLevel>();
   queue.add(new StringWithLevel(end, 0));
   boolean found = false;
   int finalLevel = Integer.MAX_VALUE;
   int curLevel = 0;
   int preLevel = 0;
   HashSet<String> visitedCurLevel = new HashSet<String>();
   while (!queue.isEmpty()) {
      StringWithLevel cur = queue.poll();
      String curStr = cur.str;
      curLevel = cur.level;
      if(found && curLevel > finalLevel) {
         break;
      }
      if (curLevel > preLevel) {
         unvisitedSet.removeAll(visitedCurLevel);
      }
      preLevel = curLevel;
      char[] curStrCharArray = curStr.toCharArray();
      for (int i = 0; i < curStr.length(); ++i) {
         char originalChar = curStrCharArray[i];
         boolean foundCurCycle = false;
         for (char c = 'a'; c <= 'z'; ++c) {
            curStrCharArray[i] = c;
            String newStr = new String(curStrCharArray);
            if(c != originalChar && unvisitedSet.contains(newStr)) {
               nextMap.get(newStr).add(curStr);
               if(newStr.equals(start)) {
                  found = true;
                  finalLevel = curLevel;
                  foundCurCycle = true;
                  break;
               }
               if(visitedCurLevel.add(newStr)) {
                  queue.add(new StringWithLevel(newStr, curLevel + 1));
               }
            }
         }
         if(foundCurCycle) {
            break;
         }
         curStrCharArray[i] = originalChar;
     }
   }
   if(found) {
       ArrayList<String> list = new ArrayList<String>();
       list.add(start);
       getPaths(start, end, list, finalLevel + 1, nextMap, res);
   }
   return res;
}
private void getPaths(String cur, String end, ArrayList<String> list, int level, Map<String, List<String>> nextMap, ArrayList<ArrayList<String>> res) {
   if(cur.equals(end)){
      res.add(new ArrayList<String>(list));
   }
   else if(level > 0){
      List<String> parentsSet = nextMap.get(cur);
      for (String parent : parentsSet) {
         list.add(parent);
         getPaths(parent, end, list, level - 1, nextMap, res);
         list.remove(list.size() - 1);
      }
   }
}
}

Comments

▲