Permutation Creation Codechef Solution

Problem

JJ gives you a number $N$ and challenges you to construct a permutation $P$ of length $N$ such that:

• |P_{i + 1} – P_i| \ge 2∣Pi+1​−Pi​∣≥2 for all $1\le i\le N-1$ (Here $|x|$ denotes the absolute value of $x$)

Can you complete JJ’s challenge?

As a reminder, a permutation of length $N$ is an array where every integer from $1$ to $N$ occurs exactly once.

Input Format

• The first line contains a single integer $T$ — the number of test cases. Then the test cases follow.
• The first and only line of each test case contains one integer $N$ — the length of the permutation $P$ to be constructed.

Output Format

For each test case, output $N$ space-separated integers P_1, P_2, \ldots, P_NP1​,P2​,…,PN​ denoting the permutation $P$ which satisfies the given conditions.

If no such permutation exists, output $-1$.

If there are multiple answers, print any.

Constraints

Sample 1:

2
2
6

-1
1 4 2 5 3 6

Explanation:

Test Case 1: It can be proven that no permutation of length $2$ exists that satisfies the given conditions.

Test Case 2: $[1,4,2,5,3,6]$ satisfies the given condition, since |P_{i + 1} – P_i| \ge 2∣Pi+1​−Pi​∣≥2 for all $1\le i\le N-1$