A15504 | Make It Connected
时间限制1s
内存限制256MB
通过 / 提交0/0
题目描述
You are given a simple undirected graph consisting of $n$ vertices. The graph doesn't contain self-loops, there is at most one edge between each pair of vertices. Your task is simple: make the graph connected.
You can do the following operation any number of times (possibly zero):
- Choose a vertex $u$ arbitrarily.
- For each vertex $v$ satisfying $v\ne u$ in the graph individually, if $v$ is adjacent to $u$ , remove the edge between $u$ and $v$ , otherwise add an edge between $u$ and $v$ .
Find the minimum number of operations required to make the graph connected. Also, find any sequence of operations with the minimum length that makes the graph connected.
You can do the following operation any number of times (possibly zero):
- Choose a vertex $u$ arbitrarily.
- For each vertex $v$ satisfying $v\ne u$ in the graph individually, if $v$ is adjacent to $u$ , remove the edge between $u$ and $v$ , otherwise add an edge between $u$ and $v$ .
Find the minimum number of operations required to make the graph connected. Also, find any sequence of operations with the minimum length that makes the graph connected.
输入格式
Each test contains multiple test cases. The first line contains a single integer $t$ ( $1\leq t\leq 800$ ) — the number of test cases. The description of test cases follows.
The first line of each test case contains a single integer $n$ ( $2\leq n\leq 4000$ ) — the number of vertices in the graph.
Then $n$ lines follow. The $i$ -th row contains a binary string $s_i$ of length $n$ , where $s_{i,j}$ is '1' if there is an edge between vertex $i$ and $j$ initially, otherwise $s_{i,j}$ is '0'.
It is guaranteed that $s_{i,i}$ is always '0' and $s_{i,j}=s_{j,i}$ for $1\leq i,j\leq n$ .
It is guaranteed that the sum of $n$ over all test cases does not exceed $4000$ .
The first line of each test case contains a single integer $n$ ( $2\leq n\leq 4000$ ) — the number of vertices in the graph.
Then $n$ lines follow. The $i$ -th row contains a binary string $s_i$ of length $n$ , where $s_{i,j}$ is '1' if there is an edge between vertex $i$ and $j$ initially, otherwise $s_{i,j}$ is '0'.
It is guaranteed that $s_{i,i}$ is always '0' and $s_{i,j}=s_{j,i}$ for $1\leq i,j\leq n$ .
It is guaranteed that the sum of $n$ over all test cases does not exceed $4000$ .
输出格式
For each test case, in the first line, output an integer $m$ — the minimum number of operations required.
If $m$ is greater than zero, then print an extra line consisting of $m$ integers — the vertices chosen in the operations in your solution. If there are multiple solutions with the minimum number of operations, print any.
If $m$ is greater than zero, then print an extra line consisting of $m$ integers — the vertices chosen in the operations in your solution. If there are multiple solutions with the minimum number of operations, print any.
输入输出样例
输入 #1
4 3 011 100 100 3 000 001 010 4 0100 1000 0001 0010 6 001100 000011 100100 101000 010001 010010
输出 #1
0 1 1 2 3 4 3 2 5 6
In the first test case, the graph is connected at the beginning, so the answer is $0$ .
In the second test case, if we do the operation with vertex $1$ , we will get the following graph represented by an adjacency matrix:
$$ \begin{bmatrix} 0&1&1\\ 1&0&1\\ 1&1&0 \end{bmatrix} $$
It's obvious that the graph above is connected.
In the third test case, if we do the operation with vertex $3$ and $4$ , we will get the following graph represented by an adjacency matrix:
$$ \begin{bmatrix} 0&1&1&1\\ 1&0&1&1\\ 1&1&0&1\\ 1&1&1&0 \end{bmatrix} $$
It's obvious that the graph above is connected, and it can be proven that we can't perform less than $2$ operations to make the graph connected.
In the second test case, if we do the operation with vertex $1$ , we will get the following graph represented by an adjacency matrix:
$$ \begin{bmatrix} 0&1&1\\ 1&0&1\\ 1&1&0 \end{bmatrix} $$
It's obvious that the graph above is connected.
In the third test case, if we do the operation with vertex $3$ and $4$ , we will get the following graph represented by an adjacency matrix:
$$ \begin{bmatrix} 0&1&1&1\\ 1&0&1&1\\ 1&1&0&1\\ 1&1&1&0 \end{bmatrix} $$
It's obvious that the graph above is connected, and it can be proven that we can't perform less than $2$ operations to make the graph connected.
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