第二十篇英文翻译
重点单词：
coordinate n.坐标； v.协调，配合； adj.同等重要的；
line coordinate n .坐标轴；
出处：https://acs.jxnu.edu.cn/contest/24/board/challenge/D
Divan and a New Project
描述：
The company "Divan's Sofas" is planning to build n+1n+1 different buildings on a coordinate line so that:
“Divan沙发”公司计划在一条坐标线上建造n+1栋不同的建筑，并做到如下要求：
- the coordinate of each building is an integer number;
- no two buildings stand at the same point.
- 每栋建筑的坐标是一个整数；
-
没有两栋建筑站在同一个点上。
Let xixi be the coordinate of the ii-th building. To get from the building ii to the building jj, Divan spends |xi−xj||xi−xj| minutes, where |y||y| is the absolute value of yy.
让xi作为每一个建筑坐标的代表。为了从建筑i到建筑j，Divan花了| xi−xj |分钟，|y|是y的绝对值。
All buildings that Divan is going to build can be numbered from 00 to nn. The businessman will live in the building 00, the new headquarters of "Divan's Sofas". In the first ten years after construction Divan will visit the ii-th building aiai times, each time spending 2⋅|x0−xi|2⋅|x0−xi| minutes for walking.
Divan将要建造的所有建筑都可以从0到n编号。这位商人将住在0号建筑，“Divan沙发”的新总部。在施工后的前十年里，Divan将参观ai建筑，每次花费2⋅|x0−xi | 步行分钟。
Divan asks you to choose the coordinates for all n+1n+1 buildings so that over the next ten years the businessman will spend as little time for walking as possible.
Divan要求您为所有n+1建筑选择坐标，以便在未来十年内，商人将尽可能少地花费时间步行。
输入：
Each test contains several test cases. The first line contains one integer number tt (1≤t≤1031≤t≤103) — the number of test cases.
The first line of each case contains an integer nn (1≤n≤2⋅1051≤n≤2⋅105) — the number of buildings that "Divan's Sofas" is going to build, apart from the headquarters.
The second line contains the sequence a1,a2,…,ana1,a2,…,an (0≤ai≤1060≤ai≤106), where aiai is the number of visits to the ii-th building.
It is guaranteed that the sum of nn over all test cases does not exceed 2⋅1052⋅105.
每个测试包含几个测试用例。第一行包含一个整数t（1≤T≤1031≤T≤103）-测试用例的数量。
每种情况的第一行包含一个整数nn（1≤N≤2.⋅1051≤N≤2.⋅105）-除总部外，“Divan’s Sofas”将建造的建筑数量。
第二行包含序列a1，a2，…，ana1，a2，…，an（0≤ai≤1060），其中ai是第二栋楼的参观次数。
保证所有测试用例的nn之和不超过2⋅1052⋅105
输出：
For each test case, on the first line print the number TT — the minimum time Divan will spend walking.
On the second line print the sequence x0,x1,…,xnx0,x1,…,xn of n+1n+1 integers, where xixi (−106≤xi≤106−106≤xi≤106) is the selected coordinate of the ii-th building. It can be shown that an optimal answer exists with coordinates not exceeding 106106.
If there are multiple answers, print any of them.
对于每个测试用例，在第一行打印数字T——Divan行走的最短时间。
在第二行打印n+1n+1整数的序列x0，x1，…，xnx0，x1，…，xn，其中xixi(−106≤席≤106−106≤席≤106）是第二栋建筑的选定坐标。可以证明，在坐标不超过106106的情况下，存在一个最优答案。
如果有多个答案，请打印其中任何一个。
样例输入：
4 3 1 2 3 5 3 8 10 6 1 5 1 1 1 1 1 1 0
样例输出：
14 2 4 1 3 78 1 -1 0 2 3 4 18 3 6 1 5 2 4 0 1 2
注释：
Let's look at the first example.
Divan will visit the first building a1=1a1=1 times, the second a2=2a2=2 times and the third a3=3a3=3 times. Then one of the optimal solution will be as follows:
- the headquarters is located in x0=2x0=2;
- x1=4x1=4: Divan will spend 2⋅|x0−x1|⋅a1=2⋅|2−4|⋅1=42⋅|x0−x1|⋅a1=2⋅|2−4|⋅1=4 minutes walking to the first building;
- x2=1x2=1: Divan will spend 2⋅|x0−x2|⋅a2=2⋅|2−1|⋅2=42⋅|x0−x2|⋅a2=2⋅|2−1|⋅2=4 minutes walking to the second building;
- x3=3x3=3: Divan will spend 2⋅|x0−x3|⋅a3=2⋅|2−3|⋅3=62⋅|x0−x3|⋅a3=2⋅|2−3|⋅3=6 minutes walking to the third building.
In total, Divan will spend 4+4+6=144+4+6=14 minutes. It can be shown that it is impossible to arrange buildings so that the businessman spends less time.
Among others, x=[1,3,2,0]x=[1,3,2,0], x=[−5,−3,−6,−4]x=[−5,−3,−6,−4] are also correct answers for the first example.
让我们来看第一个例子。
Divan将参观第一栋建筑a1=1a1=1次，第二栋建筑a2=2a2=2次，第三栋建筑a3=3a3=3次。然后，最佳解决方案之一如下所示：
总部位于x0=2x0=2；
x1=4x1=4:Divan将花费2⋅|x0−x1|⋅a1=2⋅|2.−4|⋅1=42⋅|x0−x1|⋅a1=2⋅|2.−4|⋅1=步行4分钟到第一栋建筑；
x2=1x2=1:Divan将花费2⋅|x0−x2|⋅a2=2⋅|2.−1|⋅2=42⋅|x0−x2|⋅a2=2⋅|2.−1|⋅2=步行4分钟到第二栋建筑；
x3=3x3=3:Divan将花费2⋅|x0−x3|⋅a3=2⋅|2.−3|⋅3=62⋅|x0−x3|⋅a3=2⋅|2.−3|⋅3=步行6分钟到第三栋建筑。
总的来说，Divan将花费4+4+6=144+4+6=14分钟。可以证明，不可能安排建筑物，以便商人花费更少的时间。
其中，x=[1,3,2,0]x=[1,3,2,0]，x=[−5.−3.−6.−4] x=[−5.−3.−6.−4] 这也是第一个例子的正确答案。
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