Spoj Problem-PERMUT2 - Ambiguous Permutations
PERMUT2 - Ambiguous Permutations [Java Program]
Link:-
Problem Statement:-
Some programming contest problems are really tricky: not only do they require a different output format from what you might have expected, but also the sample output does not show the difference. For an example, let us look at permutations.
A permutation of the integers 1 to n is an ordering of these integers. So the natural way to represent a permutation is to list the integers in this order. With n = 5, a permutation might look like 2, 3, 4, 5, 1.
However, there is another possibility of representing a permutation: You create a list of numbers where the i-th number is the position of the integer i in the permutation. Let us call this second possibility an inverse permutation. The inverse permutation for the sequence above is 5, 1, 2, 3, 4.
An ambiguous permutation is a permutation which cannot be distinguished from its inverse permutation. The permutation 1, 4, 3, 2 for example is ambiguous, because its inverse permutation is the same. To get rid of such annoying sample test cases, you have to write a program which detects if a given permutation is ambiguous or not.
A permutation of the integers 1 to n is an ordering of these integers. So the natural way to represent a permutation is to list the integers in this order. With n = 5, a permutation might look like 2, 3, 4, 5, 1.
However, there is another possibility of representing a permutation: You create a list of numbers where the i-th number is the position of the integer i in the permutation. Let us call this second possibility an inverse permutation. The inverse permutation for the sequence above is 5, 1, 2, 3, 4.
An ambiguous permutation is a permutation which cannot be distinguished from its inverse permutation. The permutation 1, 4, 3, 2 for example is ambiguous, because its inverse permutation is the same. To get rid of such annoying sample test cases, you have to write a program which detects if a given permutation is ambiguous or not.
Input Specification
The input contains several test cases.
The first line of each test case contains an integer n (1 ≤ n ≤ 100000). Then a permutation of the integers 1 to n follows in the next line. There is exactly one space character between consecutive integers. You can assume that every integer between 1and n appears exactly once in the permutation.
The last test case is followed by a zero.
The first line of each test case contains an integer n (1 ≤ n ≤ 100000). Then a permutation of the integers 1 to n follows in the next line. There is exactly one space character between consecutive integers. You can assume that every integer between 1and n appears exactly once in the permutation.
The last test case is followed by a zero.
Output Specification
For each test case output whether the permutation is ambiguous or not. Adhere to the format shown in the sample output.
Input
4
1 4 3 2
5
2 3 4 5 1
1
1
0
Output
ambiguous
not ambiguous
ambiguous
Java Program:-
/**
* @(#)PERMUT2.java
*
*
* @author Suyash Bhalla
* @version 1.00 2015/4/23
*/
import java.io.*;
class PERMUT2 {
public static void main(String args[])throws IOException{
BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
int n=Integer.parseInt(br.readLine());
while(n!=0){
int per[]=new int[n+1];
int inper[]=new int[n+1];
String str[]=br.readLine().split(" ");
for(int i=1;i<=n;i++){
per[i]=Integer.parseInt(str[i-1]);
inper[per[i]]=i;
}
boolean isAmbigous=true;
for(int i=1;i<=n;i++){
if(per[i]!=inper[i]){
isAmbigous=false;
break;
}
}
if(isAmbigous){
System.out.println("ambiguous");
}else{
System.out.println("not ambiguous");
}
n=Integer.parseInt(br.readLine());
}
}
}
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Labels: inverse permutation, Spoj Problem-PERMUT2 - Ambiguous Permutations
posted by Suyash @ April 22, 2015
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