计蒜客 Frequent Subsets Problem&&2017 Icpc南宁赛

The frequent subset problem is defined as follows. Suppose $U$={1, 2,$\dots$,N} is the universe, and S1S_{1}S​1​​,S2S_{2}S​2​​,$\dots$,SMS_{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 S1S_{1}S​1​​,S2S_{2}S​2​​,$\dots$,SMS_{M}S​M​​, i.e. ∣{i:B⊆Si}∣≥αM\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 S1={1,5}S_{1}=\{1, 5\}S​1​​={1,5},S2={1,2,5}S_{2}=\{1,2,5\}S​2​​={1,2,5},S3={1,3,4}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 SiS_{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

解：比赛没看，后来说用状态压缩，看了一下相关知识，把每一个所给子集用二进制的方法存起来（用右移运算符），比如说全集为1，2，3，4；

那么如果给你的集合为1，3，4，你把（1<<1）+(1<<3)+(1<<4)存到一个数组里，相当于存了1101，从右到左表示1在，2不在，3在，4在，然后利用&运算性质便可求解；

代码如下：

#include <iostream>#include <string.h>#include <algorithm>#include <math.h>using namespace std;int main(){int  a[100];memset(a,0,sizeof(a));int i=0,n,ant=0,sum=0,k=0,v;char c;double  m;cin>>n>>m;while (scanf("%d%c",&v,&c)!=EOF){a[k]+=(1<<(v-1));if (c=='\n')k++;}int va=ceil(m*k);for (int i=1;i<=(1<<n);i++){for (int j=0;j<k;j++)if ((i&a[j])==i)sum++;        if (sum>=va)        ant++;        sum=0;}cout<<ant<<endl; }