Sphere Online Judge

SPOJ Problem Set (classical)

379. Ambiguous Permutations

Problem code: PERMUT2


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.

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 1 and 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.

Sample Input

4
1 4 3 2
5
2 3 4 5 1
1
1
0

Sample Output

ambiguous
not ambiguous
ambiguous

Added by:Adrian Kuegel
Date:2005-06-24
Time limit:10s
Source limit:50000B
Memory limit:256MB
Cluster: Pyramid (Intel Pentium III 733 MHz)
Languages:All except: NODEJS PERL 6
Resource:own problem, used in University of Ulm Local Contest 2005

hide comments
2014-06-27 19:37:09 Shubham Jain
i sbmittd it on codechef
wen i was doing ds question again
got my mistake
2014-06-27 19:36:18 Shubham Jain
check on dis
10
1 4 3 2 5 7 8 6 9 10
0
http://ideone.com/66rFrP
i made a mistake in dis code bt it got submitted
check on d above test case
2014-06-25 06:32:20 ANKIT
http://ideone.com/06YOzQ
why it is giving wa :(
2014-06-07 15:44:36 sHaShAnK sHeKhAr
@novicecoder: it can be simply done in O(n).Think of a different approach.

Last edit: 2014-06-07 15:45:24
2014-06-03 12:45:04 yash
Piece of cake!!
2014-05-26 08:49:28 Saniya Najeeb
The spelling of ambiguous cost me a WA! :-/
2014-05-23 10:32:43 Abhishek
Is there any special case to check? , i have correct output for the sample input but Spoj gives me Wrong answer.

Here it is on ideone
https://ideone.com/79IJkP
2014-05-20 07:58:44 novicecoder
logic right?
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
{
if(a[j]==i+1)
{b[i]=j+1;

}
}
}
2014-05-20 07:57:48 novicecoder
time limit exceeded :(
2014-05-16 13:22:58 मोहन
@Alexandra refer to the comment by Adrian Kuegel
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