A13519 | Ehab's Last Corollary
时间限制1s
内存限制256MB
通过 / 提交0/0
题目描述
Given a connected undirected graph with $n$ vertices and an integer $k$ , you have to either:
- either find an independent set that has exactly $\lceil\frac{k}{2}\rceil$ vertices.
- or find a simple cycle of length at most $k$ .
An independent set is a set of vertices such that no two of them are connected by an edge. A simple cycle is a cycle that doesn't contain any vertex twice.
I have a proof that for any input you can always solve at least one of these problems, but it's left as an exercise for the reader.
- either find an independent set that has exactly $\lceil\frac{k}{2}\rceil$ vertices.
- or find a simple cycle of length at most $k$ .
An independent set is a set of vertices such that no two of them are connected by an edge. A simple cycle is a cycle that doesn't contain any vertex twice.
I have a proof that for any input you can always solve at least one of these problems, but it's left as an exercise for the reader.
输入格式
The first line contains three integers $n$ , $m$ , and $k$ ( $3 \le k \le n \le 10^5$ , $n-1 \le m \le 2 \cdot 10^5$ ) — the number of vertices and edges in the graph, and the parameter $k$ from the statement.
Each of the next $m$ lines contains two integers $u$ and $v$ ( $1 \le u,v \le n$ ) that mean there's an edge between vertices $u$ and $v$ . It's guaranteed that the graph is connected and doesn't contain any self-loops or multiple edges.
Each of the next $m$ lines contains two integers $u$ and $v$ ( $1 \le u,v \le n$ ) that mean there's an edge between vertices $u$ and $v$ . It's guaranteed that the graph is connected and doesn't contain any self-loops or multiple edges.
输出格式
If you choose to solve the first problem, then on the first line print $1$ , followed by a line containing $\lceil\frac{k}{2}\rceil$ distinct integers not exceeding $n$ , the vertices in the desired independent set.
If you, however, choose to solve the second problem, then on the first line print $2$ , followed by a line containing one integer, $c$ , representing the length of the found cycle, followed by a line containing $c$ distinct integers not exceeding $n$ , the vertices in the desired cycle, in the order they appear in the cycle.
If you, however, choose to solve the second problem, then on the first line print $2$ , followed by a line containing one integer, $c$ , representing the length of the found cycle, followed by a line containing $c$ distinct integers not exceeding $n$ , the vertices in the desired cycle, in the order they appear in the cycle.
输入输出样例
输入 #1
4 4 3 1 2 2 3 3 4 4 1
输出 #1
1 1 3
输入 #2
4 5 3 1 2 2 3 3 4 4 1 2 4
输出 #2
2 3 2 3 4
输入 #3
4 6 3 1 2 2 3 3 4 4 1 1 3 2 4
输出 #3
2 3 1 2 3
输入 #4
5 4 5 1 2 1 3 2 4 2 5
输出 #4
1 1 4 5
In the first sample:
Notice that printing the independent set $\{2,4\}$ is also OK, but printing the cycle $1-2-3-4$ isn't, because its length must be at most $3$ .
In the second sample:
Notice that printing the independent set $\{1,3\}$ or printing the cycle $2-1-4$ is also OK.
In the third sample:
In the fourth sample:
Notice that printing the independent set $\{2,4\}$ is also OK, but printing the cycle $1-2-3-4$ isn't, because its length must be at most $3$ .
In the second sample:
Notice that printing the independent set $\{1,3\}$ or printing the cycle $2-1-4$ is also OK.
In the third sample:
In the fourth sample:
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