### Romok007's blog

By Romok007, history, 14 months ago, Hello everyone, I am stuck at this problem. I think we can use a Trie. But I am unable to handle the special character '?'. Please help me with this problem. Thanks in advance :).

There are N words in a dictionary such that each word is of fixed length M, and consists of only lower case english alphabets. A query word Q also has length M. Query word also contains only lower case english alphabets but at some places instead of an alphabet it has "?". match_count of Q, is the count of words in the dictionary (already populated with words of same length M) and contains the same english letters (excluding the letter that can be in the position of ?) in the same position as the letters are there in the query word Q. Your are given the query word Q and you have to find the match_count.

Input Format

First line contains two space seperated integers N and M denoting the number of words in the dictionary and the length of each word
Next N line contains the words in the dictionary
Next line Q contains the number of query words
Next Q lines contain one query word each

Output
For each query word output the match_count

Constrains
1<=N<=5x10^4
1<=M<=7
1<=Q<=10^5

Time Limit - 4 secs

Sample Input:
5 3
cat
map
bat
man
pen
4
?at
ma?
?a?
??n

Sample Output
2
2
4
2  Comments (5)
 » 14 months ago, # | ← Rev. 4 →   Length of words $M$ is small ($\le$ $7$), so you can do next approach:For each word generate $2^M$ binary masks, where $0$ at the $i$-th bit means that letter is replaced by '?' and $1$ means that $i$-th letter of the word used.For each mask you can calculate hash of transformed word — so you would have $O(N \cdot 2^M)$ hashes. Now for each query you need simply take all hashes for mask equal to mask of query (depending on positions '?') and look at the count of hashes equal to hash of the query.For reducing amount of needed memory you can do next: group all queries by their mask and process only one mask at the time — for each mask you calculate $O(N)$ hashes of input words, after you answer on all queries with the same mask.Total time complexity is $O(N \cdot 2^M + Q)$.
 » For every word in the dictionary, list all its possible ways of being replaced by ? and insert it into a Trie, than query as a usual trie.Then the complexity will be $O(n\cdot 2^m+q\cdot m)$, I think it will pass.