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Find Permutation

Posted: 18 Feb, 2021
Difficulty: Moderate


Try Problem

You are given an integer ‘N’. You need to find an array of size 2*N that satisfies the following two conditions.

1. All numbers from 1 to N should appear exactly twice in the array.

2. The distance between the second occurrence and the first occurrence of any number should exactly be equal to the value of that number.

The distance between two numbers at indices ‘i’ and ‘j’ is defined as (j-i-1) where i < j.

If no such array exists, then you should return an empty array.

For example :
For N = 3 one valid array is [3,1,2,1,3,2].
Input Format :
The first line of input contains an integer ‘T’, denoting the number of test cases. The test cases follow.

The first and the only line of each test case contains a single integer ‘N’.
Output Format :
The checker will print “Valid” if the returned permutation is valid and follows all the conditions, otherwise, it will print “Invalid”. If an empty array is returned, the checker will print -1.

Print the output of each test case in a new line.
Note :
You do not need to print anything. It has already been taken care of. Just implement the given function.
Constraints :
1<= T <= 5
1 <= N <= 8

where ’T’ is the number of test cases and ‘N’  is the given integer.

Time Limit: 1 sec