# DISTOPPSUMS - Editorial

Author: abhi_inav
Testers: tabr, iceknight1093
Editorialist: iceknight1093

TBD

None

# PROBLEM:

Given even N, print a permutation of length N such that all the values of P_i + P_{N+1-i} are distinct for 1 \leq i \leq \frac{N}{2}

# EXPLANATION:

There are many different constructions that will work. For the most part, the simplest way to come up with a construction is to try to make the values of P_i + P_{N+1-i} sorted in some order.

For example, we can do the following:

• Set P_1 = 1 and P_N = 2
• Set P_2 = 3 and P_{N-1} = 4
• Set P_3 = 5 and P_{N-2} = 6
\vdots
• Set P_i = 2i-1 and P_{N+1-i} = 2i

It’s easy to see that P_i + P_{N+1-i} = 4i-1, which is obviously distinct for each i.

The created permutation is [1, 3, 5, \ldots, N-1, N, N-2, N-4, \ldots, 6, 4, 2].

There are other constructions; for example, [1, 2, 3, \ldots, \frac{N}{2}, N, N-1, N-2, \ldots, \frac{N}{2}+2, \frac{N}{2}+1], which is what the code below implements.

# TIME COMPLEXITY

\mathcal{O}(N) per test case.

# CODE:

Editorialist's code (Python)
for _ in range(int(input())):
n = int(input())
print(*range(1, n//2+1), *reversed(range(n//2+1, n+1)))