第二十二篇英语翻译

重点单词：

prime adj.素数的，主要的，最优的， 理想的

vertice n.顶点

出处：https://acs.jxnu.edu.cn/contest/24/board/challenge/F

Not Assigning
描述：
You are given a tree of n vertices numbered from 1 to n, with edges numbered from 1 to n−1. A tree is a connected undirected graph without cycles. You have to assign integer weights to each edge of the tree, such that the resultant graph is a prime tree.

您被给了一棵由n个顶点组成的树，编号从1到n，边编号从1到n−1.树是一个没有循环的连通无向图。必须为树的每条边指定整数权重，以便生成的图是素数树。

A prime tree is a tree where the weight of every path consisting of one or two edges is prime. A path should not visit any vertex twice. The weight of a path is the sum of edge weights on that path.

素数树是指由一条或两条边组成的每条路径的权重为素数的树。路径不应访问任何顶点两次。路径的权重是该路径上的边权重之和。

Consider the graph below. It is a prime tree as the weight of every path of two or less edges is prime. For example, the following path of two edges: 2→1→3 has a weight of 11+2=13, which is prime. Similarly, the path of one edge: 4→3 has a weight of 5, which is also prime.

请考虑下面的图表。它是一棵素数树，因为两条或更少边的每条路径的权重都是素数。例如，以下两条边的路径：2→1.→3的权重为11+2=13，即素数。同样，一条边的路径为：4→3的权重为5，也就是素数。

 

Print any valid assignment of weights such that the resultant tree is a prime tree. If there is no such assignment, then print −1. It can be proven that if a valid assignment exists, one exists with weights between 1 and 105 as well.

打印任何有效的权重分配，使生成的树成为素数树。如果没有这样的任务，请打印−1.可以证明，如果存在有效的赋值，那么也存在权重在1到105之间的赋值。

输入：
The input consists of multiple test cases. The first line contains an integer t (1≤t≤104) — the number of test cases. The description of the test cases follows.

输入由多个测试用例组成。第一行包含一个整数t（1≤T≤104）-测试用例的数量。测试用例的描述如下。

 

The first line of each test case contains one integer n (2≤n≤105) — the number of vertices in the tree.

Then, n−1 lines follow. The i-th line contains two integers u and v (1≤u,v≤n) denoting that edge number i is between vertices u and v. It is guaranteed that the edges form a tree.

It is guaranteed that the sum of n over all test cases does not exceed 105.

每个测试用例的第一行包含一个整数n（2≤N≤105）-树中的顶点数。

 

然后，n−下面是一行。第i行包含两个整数u和v（1≤u、 五≤n） 表示边数i在顶点u和v之间。保证边形成一棵树。

 

保证所有测试用例中n的总和不超过105。

输出：
For each test case, if a valid assignment exists, then print a single line containing n−1 integers a1,a2,…,an−1 (1≤ai≤105), where ai denotes the weight assigned to the edge numbered i. Otherwise, print −1.

If there are multiple solutions, you may print any.

对于每个测试用例，如果存在有效的赋值，则打印一行，其中包含n−1整数a1，a2，…，an−1 (1≤人工智能≤105），其中ai表示分配给编号为i的边缘的重量。否则，打印−1.

 

如果有多个解决方案，您可以打印任何解决方案。

样例输入：
3
2
1 2
4
1 3
4 3
2 1
7
1 2
1 3
3 4
3 5
6 2
7 2
复制
样例输出：
17
2 5 11
-1
复制
注释：
For the first test case, there are only two paths having one edge each: 1→2 and 2→1, both having a weight of 17, which is prime.

 

The second test case is described in the statement.

It can be proven that no such assignment exists for the third test case.

对于第一个测试用例，只有两条路径各有一条边：1→2和2→1，两者的重量都是17，这就是质数。

声明中描述了第二个测试用例。

可以证明，对于第三个测试用例，不存在这样的分配。