A11318. Prefix Max Set Counting
编程题
普及/提高-
知识点
题目描述
Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 10^5$ ) — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer $n$ ( $1 \leq n \leq 10^6$ ) — the number of vertices.
The following next $n-1$ lines contain two integers $u$ and $v$ ( $1 \leq u, v \leq n$ , $u \neq v$ ) — denoting an edge between nodes $u$ and $v$ . It is guaranteed that the given edges form a tree.
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$ .
The first line of each test case contains a single integer $n$ ( $1 \leq n \leq 10^6$ ) — the number of vertices.
The following next $n-1$ lines contain two integers $u$ and $v$ ( $1 \leq u, v \leq n$ , $u \neq v$ ) — denoting an edge between nodes $u$ and $v$ . It is guaranteed that the given edges form a tree.
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$ .
输入格式
For each test case, output the number of distinct values of $f(a)$ modulo $998\,244\,353$ that you can get.
输出格式
In the first test case, the only valid pre-order is $a=[1]$ . So the only possible value of $f(a)$ is $[1]$ .
In the second test case, the only valid pre-order is $a=[1,2]$ . So the only possible value $f(a)$ is $[1,2]$ .
In the third test case, the two valid pre-orders are $a=[1,2,3]$ and $a=[1,3,2]$ . So the possible values of $f(a)$ are $[1,2,3]$ and $[1,3]$ .
In the fifth test case, the possible values of $f(a)$ are:
- $[1,5]$ ;
- $[1,2,5]$ ;
- $[1,3,5]$ ;
- $[1,4,5]$ ;
- $[1,2,3,5]$ ;
- $[1,2,4,5]$ ;
- $[1,3,4,5]$ ;
- $[1,2,3,4,5]$ .
In the second test case, the only valid pre-order is $a=[1,2]$ . So the only possible value $f(a)$ is $[1,2]$ .
In the third test case, the two valid pre-orders are $a=[1,2,3]$ and $a=[1,3,2]$ . So the possible values of $f(a)$ are $[1,2,3]$ and $[1,3]$ .
In the fifth test case, the possible values of $f(a)$ are:
- $[1,5]$ ;
- $[1,2,5]$ ;
- $[1,3,5]$ ;
- $[1,4,5]$ ;
- $[1,2,3,5]$ ;
- $[1,2,4,5]$ ;
- $[1,3,4,5]$ ;
- $[1,2,3,4,5]$ .
输入输出样例
输入 #1
6 1 2 1 2 3 1 2 1 3 3 1 2 2 3 5 1 2 1 3 1 4 1 5 10 1 2 2 3 1 4 2 5 2 6 4 7 5 8 4 9 9 10
输出 #1
1 1 2 1 8 6
说明/提示
In the first test case, the only valid pre-order is $a=[1]$ . So the only possible value of $f(a)$ is $[1]$ .
In the second test case, the only valid pre-order is $a=[1,2]$ . So the only possible value $f(a)$ is $[1,2]$ .
In the third test case, the two valid pre-orders are $a=[1,2,3]$ and $a=[1,3,2]$ . So the possible values of $f(a)$ are $[1,2,3]$ and $[1,3]$ .
In the fifth test case, the possible values of $f(a)$ are:
- $[1,5]$ ;
- $[1,2,5]$ ;
- $[1,3,5]$ ;
- $[1,4,5]$ ;
- $[1,2,3,5]$ ;
- $[1,2,4,5]$ ;
- $[1,3,4,5]$ ;
- $[1,2,3,4,5]$ .
In the second test case, the only valid pre-order is $a=[1,2]$ . So the only possible value $f(a)$ is $[1,2]$ .
In the third test case, the two valid pre-orders are $a=[1,2,3]$ and $a=[1,3,2]$ . So the possible values of $f(a)$ are $[1,2,3]$ and $[1,3]$ .
In the fifth test case, the possible values of $f(a)$ are:
- $[1,5]$ ;
- $[1,2,5]$ ;
- $[1,3,5]$ ;
- $[1,4,5]$ ;
- $[1,2,3,5]$ ;
- $[1,2,4,5]$ ;
- $[1,3,4,5]$ ;
- $[1,2,3,4,5]$ .