计蒜客 Frequent Subsets Problem（状态压缩）

The frequent subset problem is defined as follows. Suppose $U$={1, 2,$\dots$,N} is the universe, and S_{1}S​1​​, S_{2}S​2​​,$\dots$,S_{M}S​M​​are $M$ sets over $U$. Given a positive constant $\alpha$, $0<\alpha \le 1$, a subset $B$ ($B\ne 0$) is α-frequent if it is contained in at least $\alpha M$ sets of S_{1}S​1​​, S_{2}S​2​​,$\dots$,S_{M}S​M​​, i.e. \left | \left \{ i:B\subseteq S_{i} \right \} \right | \geq \alpha M∣{i:B⊆S​i​​}∣≥αM. 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​1​​={1,5}, S_{2}=\{1,2,5\}S​2​​={1,2,5}, S_{3}=\{1,3,4\}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}S​i​​, $1\le i\le M$ . 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 0.41 8 14 4 13 23 7 11 610 8 4 29 3 12 7 15 28 3 2 4 5

样例输出

11

题目来源

2017 ACM-ICPC 亚洲区（南宁赛区）网络赛

#include<iostream>#include<stdio.h>#include<string.h>using namespace std;int s[55];int main(){memset(s,0,sizeof(s));int n,m=0;double a;scanf("%d%lf",&n,&a);int x;char p;while(scanf("%d%c",&x,&p)!=EOF){s[m]+=(1<<(x-1));if(p=='\n')m++;}int g=m*a+(bool)(m*a-(int)(m*a));     //代表至少为g个给定集合的子集 int ans=0;for(int i=1;i<(1<<n);i++)           //二进制表示状态，枚举所有集合 {int sum=0;for(int j=0;j<m;j++)            //跑遍所有给定m个集合判断是不是子集关系 {if((i&s[j])==i)sum++;}if(sum>=g)ans++;}printf("%d\n",ans);}