???Frequent Subsets Problem_综合

The frequent subset problem is defined as follows. Suppose $U$ ={1, 2, $\ldots$ ,N} is the universe, and $S_{1}$ , $S_{2}$ , $\ldots$ , $S_{M}$ are $M$ sets over $U$ . Given a positive constant $\alpha$ , $0<\alpha \leq 1$ , a subset $B$ ( $\neq 0$ ) is α-frequent if it is contained in at least $\alpha M$ sets of $S_{1}$ , $S_{2}$ , $\ldots$ , $S_{M}$ , i.e. $\left | \left \{ i:B\subseteq S_{i} \right \} \right | \geq \alpha M$ . The frequent subset problem is to find all the subsets that are α-frequent. For example, let $U=\{1, 2,3,4,5\}$ , $M = 3$ , $\alpha =0.5$ , and $S_{1}=\{1, 5\}$ , $S_{2}=\{1,2,5\}$ , $S_{3}=\{1,3,4\}$ . Then there are $3$ α-frequent subsets of $U$ , which are $\{1\}$ , $\{5\}$ and $\{1,5\}$ .

Input Format

The first line contains two numbers $N$ and $\alpha$ , where $N$ is a positive integers, and $\alpha$ is a floating-point number between 0 and 1. Each of the subsequent lines contains a set which consists of a sequence of positive integers separated by blanks, i.e., line $i + 1$ contains $S_{i}$ , $\le i \le M$ . Your program should be able to handle $N$ up to $20$ and $M$ up to $50$ .

Output Format

The number of $\alpha$ -frequent subsets.

样例输入

15 0.4
1 8 14 4 13 2
3 7 11 6
10 8 4 2
9 3 12 7 15 2
8 3 2 4 5

???Frequent Subsets Problem

Input Format

Output Format

样例输入

样例输出

题目来源