Roof Construction

题意翻译

给定数组 $p$ 的长度 $n$。已知在该数组中，从 $0$ 到 $n-1$ 的这 $n$ 个整数都恰好出现了一次。现在，你想通过这 $n$ 个整数按照一定顺序重新排列，使得 $\max\limits_{1\leqslant i\leqslant n-1} p_i\oplus p_{i+1}$ 最小，其中 $\oplus$ 表示按位异或运算。请求出**任意一个**满足该要求的重新排列后的数组 $p$。 数据范围： - $t$ 组数据，$1\leqslant t\leqslant 10^4$。 - $2\leqslant n,\sum n\leqslant 2\times 10^5$。 Translated by Eason_AC 2022.1.31

题目描述

It has finally been decided to build a roof over the football field in School 179. Its construction will require placing $ n $ consecutive vertical pillars. Furthermore, the headmaster wants the heights of all the pillars to form a permutation $ p $ of integers from $ 0 $ to $ n - 1 $ , where $ p_i $ is the height of the $ i $ -th pillar from the left $ (1 \le i \le n) $ . As the chief, you know that the cost of construction of consecutive pillars is equal to the maximum value of the bitwise XOR of heights of all pairs of adjacent pillars. In other words, the cost of construction is equal to $ \max\limits_{1 \le i \le n - 1}{p_i \oplus p_{i + 1}} $ , where $ \oplus $ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Find any sequence of pillar heights $ p $ of length $ n $ with the smallest construction cost. In this problem, a permutation is an array consisting of $ n $ distinct integers from $ 0 $ to $ n - 1 $ in arbitrary order. For example, $ [2,3,1,0,4] $ is a permutation, but $ [1,0,1] $ is not a permutation ( $ 1 $ appears twice in the array) and $ [1,0,3] $ is also not a permutation ( $ n=3 $ , but $ 3 $ is in the array).

输入输出格式

输入格式

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). Description of the test cases follows. The only line for each test case contains a single integer $ n $ ( $ 2 \le n \le 2 \cdot 10^5 $ ) — the number of pillars for the construction of the roof. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

输出格式

For each test case print $ n $ integers $ p_1 $ , $ p_2 $ , $ \ldots $ , $ p_n $ — the sequence of pillar heights with the smallest construction cost. If there are multiple answers, print any of them.

输入输出样例

输入样例 #1

4
2
3
5
10

输出样例 #1

0 1
2 0 1
3 2 1 0 4
4 6 3 2 0 8 9 1 7 5

说明

For $ n = 2 $ there are $ 2 $ sequences of pillar heights: - $ [0, 1] $ — cost of construction is $ 0 \oplus 1 = 1 $ . - $ [1, 0] $ — cost of construction is $ 1 \oplus 0 = 1 $ . For $ n = 3 $ there are $ 6 $ sequences of pillar heights: - $ [0, 1, 2] $ — cost of construction is $ \max(0 \oplus 1, 1 \oplus 2) = \max(1, 3) = 3 $ . - $ [0, 2, 1] $ — cost of construction is $ \max(0 \oplus 2, 2 \oplus 1) = \max(2, 3) = 3 $ . - $ [1, 0, 2] $ — cost of construction is $ \max(1 \oplus 0, 0 \oplus 2) = \max(1, 2) = 2 $ . - $ [1, 2, 0] $ — cost of construction is $ \max(1 \oplus 2, 2 \oplus 0) = \max(3, 2) = 3 $ . - $ [2, 0, 1] $ — cost of construction is $ \max(2 \oplus 0, 0 \oplus 1) = \max(2, 1) = 2 $ . - $ [2, 1, 0] $ — cost of construction is $ \max(2 \oplus 1, 1 \oplus 0) = \max(3, 1) = 3 $ .