2013
11-12

# Obfuscation

It is a well-known fact that if you mix up the letters of a word, while leaving the first and last letters in their places, words still remain readable. For example, the sentence “tihs snetncee mkaes prfecet sesne”, makes perfect sense to most people.

If you remove all spaces from a sentence, it still remains perfectly readable, see for example: “thissentencemakesperfectsense”, however if you combine these two things, first shuffling, then removing spaces, things get hard. The following sentence is harder to decipher: “tihssnetnceemkaesprfecetsesne”.

You’re given a sentence in the last form, together with a dictionary of valid words and are asked to decipher the text.

On the first line one positive number: the number of testcases, at most 100. After that per testcase:

• One line with a string s: the sentence to decipher. The sentence consists of lowercase letters and has a length of at least 1 and at most 1 000 characters.

• One line with an integer n with 1 ≤ n10 000: the number of words in the dictionary.

• n lines with one word each. A word consists of lowercase letters and has a length of at least 1 and at most 100 characters. All the words are unique.

Per testcase:

• One line with the deciphered sentence, if it is possible to uniquely decipher it. Otherwise “impossible” or “ambiguous”, depending on which is the case.

3
tihssnetnceemkaesprfecetsesne
5
makes
perfect
sense
sentence
this
hitehre
2
there
hello
hitehre
3
hi
there
three

this sentence makes perfect sense
impossible
ambiguous

//* @author:alpc12
import java.util.*;

public class Main {
public static Scanner in=new Scanner(System.in).useLocale(Locale.US);

public void run() {
boolean[] singles=new boolean[26];
Map< String,String>[][] words=new Map[26][26];
for(int i=0;i< 26;++i) for(int j=0;j< 26;++j) words[i][j]=new HashMap< String,String>();
Set< String>[][] doublewords=new Set[26][26];
for(int i=0;i< 26;++i)
for(int j=0;j< 26;++j)
doublewords[i][j]=new HashSet< String>();
String s=in.next();
int n=in.nextInt();
for(int i=0;i< n;++i) {
String word=in.next();
if(word.length()==1) {
singles[word.charAt(0)-'a']=true;
} else {
int a=word.charAt(0)-'a',b=word.charAt(word.length()-1)-'a';
char[] letters=word.substring(1,1+word.length()-2).toCharArray();
Arrays.sort(letters);
if(words[a][b].containsKey(new String(letters)))
else words[a][b].put(new String(letters),word);
}
}
String[] prev=new String[s.length()+1];
int[] ways=new int[s.length()+1]; ways[0]=1;
for(int i=0;i< s.length();++i) if(ways[i]>0) {
if(singles[s.charAt(i)-'a']) {
ways[i+1]=Math.min(2,ways[i+1]+ways[i]);
prev[i+1]=""+s.charAt(i);
}
for(int len=2;i+len<=s.length() && len<=100;++len) {
int a=s.charAt(i)-'a',b=s.charAt(i+len-1)-'a';
char[] letters=s.substring(i+1,i+1+len-2).toCharArray();
Arrays.sort(letters);
String word=new String(letters);
if(doublewords[a][b].contains(word))
ways[i+len]=Math.min(2,ways[i+len]+2*ways[i]);
else if(words[a][b].containsKey(word)) {
ways[i+len]=Math.min(2,ways[i+len]+ways[i]);
prev[i+len]=words[a][b].get(word);
}
}
}
if(ways[s.length()]==0) System.out.println("impossible");
else if(ways[s.length()]==2) System.out.println("ambiguous");
else {
List< String> ret=new ArrayList< String>();
Collections.reverse(ret);
for(int i=0;i< ret.size();++i) {
if(i!=0) System.out.print(" ");
System.out.print(ret.get(i));
}
System.out.println();
}

}

public static void main(String[] args) {
int n=in.nextInt();
for(int i=0;i< n;++i)
new Main().run();
}
}