A15247 | PermutationForces II
时间限制1s
内存限制256MB
通过 / 提交0/0
题目描述
You are given a permutation $a$ of length $n$ . Recall that permutation is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order.
You have a strength of $s$ and perform $n$ moves on the permutation $a$ . The $i$ -th move consists of the following:
- Pick two integers $x$ and $y$ such that $i \leq x \leq y \leq \min(i+s,n)$ , and swap the positions of the integers $x$ and $y$ in the permutation $a$ . Note that you can select $x=y$ in the operation, in which case no swap will occur.
You want to turn $a$ into another permutation $b$ after $n$ moves. However, some elements of $b$ are missing and are replaced with $-1$ instead. Count the number of ways to replace each $-1$ in $b$ with some integer from $1$ to $n$ so that $b$ is a permutation and it is possible to turn $a$ into $b$ with a strength of $s$ .
Since the answer can be large, output it modulo $998\,244\,353$ .
You have a strength of $s$ and perform $n$ moves on the permutation $a$ . The $i$ -th move consists of the following:
- Pick two integers $x$ and $y$ such that $i \leq x \leq y \leq \min(i+s,n)$ , and swap the positions of the integers $x$ and $y$ in the permutation $a$ . Note that you can select $x=y$ in the operation, in which case no swap will occur.
You want to turn $a$ into another permutation $b$ after $n$ moves. However, some elements of $b$ are missing and are replaced with $-1$ instead. Count the number of ways to replace each $-1$ in $b$ with some integer from $1$ to $n$ so that $b$ is a permutation and it is possible to turn $a$ into $b$ with a strength of $s$ .
Since the answer can be large, output it modulo $998\,244\,353$ .
输入格式
The input consists of multiple test cases. The first line contains an integer $t$ ( $1 \leq t \leq 1000$ ) — the number of test cases. The description of the test cases follows.
The first line of each test case contains two integers $n$ and $s$ ( $1 \leq n \leq 2 \cdot 10^5$ ; $1 \leq s \leq n$ ) — the size of the permutation and your strength, respectively.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le n$ ) — the elements of $a$ . All elements of $a$ are distinct.
The third line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1 \le b_i \le n$ or $b_i = -1$ ) — the elements of $b$ . All elements of $b$ that are not equal to $-1$ are distinct.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .
The first line of each test case contains two integers $n$ and $s$ ( $1 \leq n \leq 2 \cdot 10^5$ ; $1 \leq s \leq n$ ) — the size of the permutation and your strength, respectively.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le n$ ) — the elements of $a$ . All elements of $a$ are distinct.
The third line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1 \le b_i \le n$ or $b_i = -1$ ) — the elements of $b$ . All elements of $b$ that are not equal to $-1$ are distinct.
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, output a single integer — the number of ways to fill up the permutation $b$ so that it is possible to turn $a$ into $b$ using a strength of $s$ , modulo $998\,244\,353$ .
输入输出样例
输入 #1
6 3 1 2 1 3 3 -1 -1 3 2 2 1 3 3 -1 -1 4 1 1 4 3 2 4 3 1 2 6 4 4 2 6 3 1 5 6 1 5 -1 3 -1 7 4 1 3 6 2 7 4 5 2 5 -1 -1 -1 4 -1 14 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
输出 #1
1 2 0 2 12 331032489
In the first test case, $a=[2,1,3]$ . There are two possible ways to fill out the $-1$ s in $b$ to make it a permutation: $[3,1,2]$ or $[3,2,1]$ . We can make $a$ into $[3,1,2]$ with a strength of $1$ as follows: $$$$[2,1,3] \xrightarrow[x=1,\,y=1]{} [2,1,3] \xrightarrow[x=2,\,y=3]{} [3,1,2] \xrightarrow[x=3,\,y=3]{} [3,1,2]. $$ It can be proven that it is impossible to make $\[2,1,3\]$ into $\[3,2,1\]$ with a strength of $1$ . Thus only one permutation $b$ satisfies the constraints, so the answer is $1$ .</p><p>In the second test case, $a$ and $b$ the same as the previous test case, but we now have a strength of $2$ . We can make $a$ into $\[3,2,1\]$ with a strength of $2$ as follows: $$ [2,1,3] \xrightarrow[x=1,\,y=3]{} [2,3,1] \xrightarrow[x=2,\,y=3]{} [3,2,1] \xrightarrow[x=3,\,y=3]{} [3,2,1]. $$ We can still make $a$ into $\[3,1,2\]$ using a strength of $1$ as shown in the previous test case, so the answer is $2$ . </p><p>In the third test case, there is only one permutation $b$ . It can be shown that it is impossible to turn $a$ into $b$ , so the answer is $0$$$.
C++ 编辑器
输入
输出
可保存默认模板；新题优先使用已保存模板。
当前快捷键仅展示，暂不支持修改。
- 撤销
Ctrl / ⌘ + Z - 重做
Ctrl / ⌘ + Y - 查找
Ctrl / ⌘ + F - 全选
Ctrl / ⌘ + A - 复制
Ctrl / ⌘ + C - 剪切
Ctrl / ⌘ + X - 粘贴
Ctrl / ⌘ + V - 自动排版
工具栏排版按钮 - 草稿保存
编辑时自动保存到本机
历史
提交记录
状态说明时间源码
AI
作答助手
你好，我是作答助手。可以问思路、复杂度、样例含义或代码报错原因；不会直接给出完整 AC 代码。
确定要清空代码吗？
提交通过
评测结果：Accepted