How many integers can you find

Time Limit: 12000/5000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4249    Accepted Submission(s):
1211

Problem Description
  Now you get a number N, and a M-integers set, you
should find out how many integers which are small than N, that they can divided
exactly by any integers in the set. For example, N=12, and M-integer set is
{2,3}, so there is another set {2,3,4,6,8,9,10}, all the integers of the set can
be divided exactly by 2 or 3. As a result, you just output the number 7.
 
Input
  There are a lot of cases. For each case, the first
line contains two integers N and M. The follow line contains the M integers, and
all of them are different from each other. 0<N<2^31,0<M<=10, and the
M integer are non-negative and won’t exceed 20.
 
Output
  For each case, output the number.
 
Sample Input
12 2
2 3
 
Sample Output
7
题意:给n个数字,最大不会超过20的非负数,0忽略它可以。给你一个数字M,
问1-M-1中,有多少个数字能被这n数字中任何一个整除(只要满足其中一个能整除就行)。统计个数输出。
 
思路:容斥,简单容斥。一开始做zoj的一道题,果断数据太水,方法是不对的也能ac。
原来的思路是这样的,对n个数字,筛选掉ai倍数的数字,然后就容斥,但是明显这样的数据有问题
4 6,  这样容斥后得到的结果是4 6 -24,不对的,应该是4 6 -12,所以应该是 4 6    -(4*6)/gcd(4,6)

略坑略坑。

 #include<iostream>
#include<stdio.h>
#include<cstring>
#include<cstdlib>
using namespace std; bool Hash[];
int f[],len,qlen;
__int64 Q[]; int gcd(int a,int b)
{
if(a<)a=-a;
if(b<)b=-b;
if(b==)return a;
int r;
while(b)
{
r=a%b;
a=b;
b=r;
}
return a;
}
void solve(__int64 m)
{
qlen = ;
Q[]=-;
for(int i=;i<=len;i++)
{
int k=qlen;
for(int j=;j<=k;j++)
Q[++qlen]=-*(Q[j]*f[i]/gcd(Q[j],f[i]));
}
__int64 sum = ;
for(int i=;i<=qlen;i++)
sum = sum+m/Q[i];
printf("%I64d\n",sum);
}
int main()
{
int m,x;
__int64 n;
while(scanf("%I64d%d",&n,&m)>)
{
n=n-;
memset(Hash,false,sizeof(Hash));
for(int i=;i<=m;i++)
{
scanf("%d",&x);
Hash[x]=true;
}
for(int i=;i<=;i++)
{
if(Hash[i]==true)
for(int j=i+i;j<=;j=j+i)
if(Hash[j]==true) Hash[j]=false;
}
len = ;
for(int i=;i<=;i++)if(Hash[i]==true) f[++len]=i;
solve(n);
}
return ;
}

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