A16444 | Multiple Lamps
时间限制1s
内存限制256MB
通过 / 提交0/0
题目描述
[Kid2Will - Fire Aura](https://soundcloud.com/xgp/kid2will-fire-aura)
⠀
You have $n$ lamps, numbered from $1$ to $n$ . Initially, all the lamps are turned off.
You also have $n$ buttons. The $i$ -th button toggles all the lamps whose index is a multiple of $i$ . When a lamp is toggled, if it was off it turns on, and if it was on it turns off.
You have to press some buttons according to the following rules.
- You have to press at least one button.
- You cannot press the same button multiple times.
- You are given $m$ pairs $(u_i, v_i)$ . If you press the button $u_i$ , you also have to press the button $v_i$ (at any moment, not necessarily after pressing the button $u_i$ ). Note that, if you press the button $v_i$ , you don't need to press the button $u_i$ .
You don't want to waste too much electricity. Find a way to press buttons such that at the end at most $\lfloor n/5 \rfloor$ lamps are on, or print $-1$ if it is impossible.
⠀
You have $n$ lamps, numbered from $1$ to $n$ . Initially, all the lamps are turned off.
You also have $n$ buttons. The $i$ -th button toggles all the lamps whose index is a multiple of $i$ . When a lamp is toggled, if it was off it turns on, and if it was on it turns off.
You have to press some buttons according to the following rules.
- You have to press at least one button.
- You cannot press the same button multiple times.
- You are given $m$ pairs $(u_i, v_i)$ . If you press the button $u_i$ , you also have to press the button $v_i$ (at any moment, not necessarily after pressing the button $u_i$ ). Note that, if you press the button $v_i$ , you don't need to press the button $u_i$ .
You don't want to waste too much electricity. Find a way to press buttons such that at the end at most $\lfloor n/5 \rfloor$ lamps are on, or print $-1$ if it is impossible.
输入格式
Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 10^4$ ). The description of the test cases follows.
The first line of each test case contains two integers $n$ and $m$ ( $1 \leq n \leq 2 \cdot 10^5$ , $0 \leq m \leq 2 \cdot 10^5$ ) — the number of lamps and the number of pairs, respectively.
Each of the next $m$ lines contains two integers $u_i$ , $v_i$ ( $1 \leq u_i, v_i \leq n$ , $u_i \neq v_i$ ). If you press the button $u_i$ , you also have to press the button $v_i$ . It is guaranteed that the pairs $(u_i, v_i)$ are distinct.
It is guaranteed that the sum of $n$ and the sum of $m$ over all test cases do not exceed $2 \cdot 10^5$ .
The first line of each test case contains two integers $n$ and $m$ ( $1 \leq n \leq 2 \cdot 10^5$ , $0 \leq m \leq 2 \cdot 10^5$ ) — the number of lamps and the number of pairs, respectively.
Each of the next $m$ lines contains two integers $u_i$ , $v_i$ ( $1 \leq u_i, v_i \leq n$ , $u_i \neq v_i$ ). If you press the button $u_i$ , you also have to press the button $v_i$ . It is guaranteed that the pairs $(u_i, v_i)$ are distinct.
It is guaranteed that the sum of $n$ and the sum of $m$ over all test cases do not exceed $2 \cdot 10^5$ .
输出格式
For each test case:
- If there is no choice of buttons that makes at most $\lfloor n/5 \rfloor$ lamps on at the end, output a single line containing $-1$ .
- Otherwise, output two lines. The first line should contain an integer $k$ ( $1 \le k \le n$ ) — the number of pressed buttons. The second line should contain $k$ integers $b_1, b_2, \dots, b_k$ ( $1 \le b_i \le n$ ) — the indices of the pressed buttons (in any order). The $b_i$ must be distinct, and at the end at most $\lfloor n/5 \rfloor$ lamps must be turned on.
- If there is no choice of buttons that makes at most $\lfloor n/5 \rfloor$ lamps on at the end, output a single line containing $-1$ .
- Otherwise, output two lines. The first line should contain an integer $k$ ( $1 \le k \le n$ ) — the number of pressed buttons. The second line should contain $k$ integers $b_1, b_2, \dots, b_k$ ( $1 \le b_i \le n$ ) — the indices of the pressed buttons (in any order). The $b_i$ must be distinct, and at the end at most $\lfloor n/5 \rfloor$ lamps must be turned on.
输入输出样例
输入 #1
4 4 0 5 2 4 1 5 1 15 9 7 8 8 9 9 10 10 9 11 1 12 2 13 3 14 4 15 5 5 4 1 2 2 3 3 4 4 5
输出 #1
-1 4 3 5 1 2 3 8 9 10 1 5
In the first test case, you need to turn at most $\lfloor 4/5 \rfloor$ lamps on, which means that no lamp can be turned on. You can show that no choice of at least one button turns $0$ lamps on.
In the second test case, you can press buttons $3$ , $5$ , $1$ , $2$ .
- Initially, all the lamps are off;
- after pressing button $3$ , the lamps whose index is a multiple of $3$ (i.e., $3$ ) are toggled, so lamp $3$ is turned on;
- after pressing button $5$ , the lamps whose index is a multiple of $5$ (i.e., $5$ ) are toggled, so lamps $3$ , $5$ are turned on;
- after pressing button $1$ , the lamps whose index is a multiple of $1$ (i.e., $1$ , $2$ , $3$ , $4$ , $5$ ) are toggled, so lamps $1$ , $2$ , $4$ are turned on;
- after pressing button $2$ , the lamps whose index is a multiple of $2$ (i.e., $2$ , $4$ ) are toggled, so lamp $1$ is turned on.
This is valid because
- you pressed at least one button;
- you pressed all the buttons at most once;
- you pressed button $u_2 = 5$ , which means that you had to also press button $v_2 = 1$ : in fact, button $1$ has been pressed;
- at the end, only lamp $1$ is on.
In the third test case, pressing the buttons $8$ , $9$ , $10$ turns only the lamps $8$ , $9$ , $10$ on.
In the second test case, you can press buttons $3$ , $5$ , $1$ , $2$ .
- Initially, all the lamps are off;
- after pressing button $3$ , the lamps whose index is a multiple of $3$ (i.e., $3$ ) are toggled, so lamp $3$ is turned on;
- after pressing button $5$ , the lamps whose index is a multiple of $5$ (i.e., $5$ ) are toggled, so lamps $3$ , $5$ are turned on;
- after pressing button $1$ , the lamps whose index is a multiple of $1$ (i.e., $1$ , $2$ , $3$ , $4$ , $5$ ) are toggled, so lamps $1$ , $2$ , $4$ are turned on;
- after pressing button $2$ , the lamps whose index is a multiple of $2$ (i.e., $2$ , $4$ ) are toggled, so lamp $1$ is turned on.
This is valid because
- you pressed at least one button;
- you pressed all the buttons at most once;
- you pressed button $u_2 = 5$ , which means that you had to also press button $v_2 = 1$ : in fact, button $1$ has been pressed;
- at the end, only lamp $1$ is on.
In the third test case, pressing the buttons $8$ , $9$ , $10$ turns only the lamps $8$ , $9$ , $10$ on.
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