# Need to explain what is Ambiguous Permutations and why the solution works . c++

Please, explain what is Ambiguous Permutations.  why does the solution works ?  I mean I know how operator ^ works, I just do not understand how mathematically define ambiguous/ non ambiguous permutation.

May there is some youtube video.

//// Ambiguous Permutations
//
//All submissions for this problem are available.
//
//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

``````#include <iostream>
using namespace std;
int main()
{
int n, i, j, k;
long long int s;

cin >> n;
while (n)
{
s = 0;
for (j = 1;j <= n;j++)
{
cin >> k;
if (k != j)
{
s ^= (k*j);
}
}
(s == 0) ? printf("ambiguous\n") : printf("not ambiguous\n");

cin >> n;
}
return 0;
}
``````
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Software ArchitectCommented:
Here is the explanation of ambiguous permutation
Sample : 1 6 3 4 2 5
This sample is some permutation of 6 numbers(from 1 to 6).
Now, for the inverse you start looking from 1 to 6 the numbers in the example, I mean:
The number 1 in wich position is located at 1 6 3 4 2 5? It is located first. So, the first number in the inverse is 1.
Inverse so far: 1XXXXX
The number 2 in wich position is located at 1 6 3 4 2 5? It is located 5th. So, the second number in the inverse is 5.
Inverse so far:15XXXX
.
.
.
The number 6 in wich position is located at 1 6 3 4 2 5? It is located 2nd. So, the 6th position in the inverse is 2.
Inverse so far:153462
This means this permutation is not ambiguous. Because 1 6 3 4 2 5 !=1 5 3 4 6 2.
Now, with 1 4 3 2(from 1 to 4)
In wich position is located 1 at 1 4 3 2. It's first, so the first number in the inverse is 1
In wich position is located 2 at 1 4 3 2. It's 4th, so the second number in inverse is 4
In wich position is located 3 at 1 4 3 2. It's 3rd, so the third numberse in the inverse is 3
In wich position is located 4 at 1 4 3 2. It's 2nd, so the fourth number in the inverse is 2
1 4 3 2 = 1 4 3 2, so this is an ambiguos permutation.
Notice that you need start looking from 1 until n.
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Software ArchitectCommented:
Basically inverse of a permutation is the position of each number in ascending order. (if permutation is of numbers 1 to 5, then it's inverse is position of each number starting from 1 till 5)
And if inverse matches the input permutation then it is an ambiguous permutation.
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Software ArchitectCommented:
Sunny, any response? Do you still need any help in understanding what is ambiguous permutation?
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