F. AND Graph

Codeforces

IDCF987F

Time4000ms

Memory256MB

Difficulty—

bitmasksdfs and similargraphs

English · Original

Chinese · Translation

Formal · Original

You are given a set of size $m$ with integer elements between $0$ and $2^{n}-1$ inclusive. Let's build an undirected graph on these integers in the following way: connect two integers $x$ and $y$ with an edge if and only if $x \& y = 0$. Here $\&$ is the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). Count the number of connected components in that graph. ## Input In the first line of input there are two integers $n$ and $m$ ($0 \le n \le 22$, $1 \le m \le 2^{n}$). In the second line there are $m$ integers $a_1, a_2, \ldots, a_m$ ($0 \le a_{i} < 2^{n}$) — the elements of the set. All $a_{i}$ are distinct. ## Output Print the number of connected components. [samples] ## Note Graph from first sample: ![image](https://espresso.codeforces.com/2ae9959ec95b178e60e27e28f5d62c1099bb9ef1.png) Graph from second sample: ![image](https://espresso.codeforces.com/9f9eee8f2409bbd78cce726875915c405af8a07e.png)

给你一个大小为 $m$ 的集合，其中的整数元素在 $0$ 到 $2^n - 1$ 之间（包含两端）。我们按照以下方式构建一个无向图：当且仅当 $x & y = 0$ 时，在两个整数 $x$ 和 $y$ 之间连一条边。这里 $&$ 表示按位与运算。请计算该图中连通分量的数量。输入的第一行包含两个整数 $n$ 和 $m$（$0 lt.eq n lt.eq 22$，$1 lt.eq m lt.eq 2^n$）。第二行包含 $m$ 个整数 $a_1, a_2, dots.h, a_m$（$0 lt.eq a_i < 2^n$）——集合的元素，所有 $a_i$ 互不相同。请输出连通分量的数量。第一个样例的图：第二个样例的图： ## Input 输入的第一行包含两个整数 $n$ 和 $m$（$0 lt.eq n lt.eq 22$，$1 lt.eq m lt.eq 2^n$）。第二行包含 $m$ 个整数 $a_1, a_2, dots.h, a_m$（$0 lt.eq a_i < 2^n$）——集合的元素，所有 $a_i$ 互不相同。 ## Output 请输出连通分量的数量。 [samples] ## Note 第一个样例的图：第二个样例的图：

Let $ S \subseteq \{0, 1, \dots, 2^n - 1\} $ with $ |S| = m $, and define an undirected graph $ G = (S, E) $ where: $$ E = \{ \{x, y\} \mid x, y \in S,\ x \ne y,\ x \mathbin{\&} y = 0 \} $$ Count the number of connected components in $ G $.

Samples

Input #1

2 3
1 2 3

Output #1

Input #2

5 5
5 19 10 20 12

Output #2

API Response (JSON)

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  "problem": {
    "name": "F. AND Graph",
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      "content": "You are given a set of size $m$ with integer elements between $0$ and $2^{n}-1$ inclusive. Let's build an undirected graph on these integers in the following way: connect two integers $x$ and $y$ with",
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    },
    "platform": "Codeforces",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
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    "difficulty": "None",
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    "is_sync": true,
    "sync_url": null,
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      "content": "You are given a set of size $m$ with integer elements between $0$ and $2^{n}-1$ inclusive. Let's build an undirected graph on these integers in the following way: connect two integers $x$ and $y$ with...",
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      "statement_type": "Markdown",
      "content": "给你一个大小为 $m$ 的集合，其中的整数元素在 $0$ 到 $2^n - 1$ 之间（包含两端）。我们按照以下方式构建一个无向图：当且仅当 $x & y = 0$ 时，在两个整数 $x$ 和 $y$ 之间连一条边。这里 $&$ 表示按位与运算。请计算该图中连通分量的数量。\n\n输入的第一行包含两个整数 $n$ 和 $m$（$0 lt.eq n lt.eq 22$，$1 lt.eq m lt.eq ...",
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