1926: Factovisors N的阶乘的质因子个数

1926: Factovisors

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Result	TIME Limit	MEMORY Limit	Run Times	AC Times	JUDGE
	3s	8192K	659	122	Standard

The factorial function, n! is defined thus for n a non-negative integer:

   0! = 1
   n! = n * (n-1)!   (n > 0)

We say that a divides b if there exists an integer k such that

   k*a = b

The input to your program consists of several lines, each containing two non-negative integers, n and m, both less than 2^31. For each input line, output a line stating whether or not m divides n!, in the format shown below.

Sample Input

6 9
6 27
20 10000
20 100000
1000 1009

Output for Sample Input

9 divides 6!
27 does not divide 6!
10000 divides 20!
100000 does not divide 20!
1009 does not divide 1000!

对于任意质数p，n！中有（n/p+n/p^2+n/p^3+...)个质因子p。

#include<iostream>
#include<cmath>
#include<cstring>
#include<cstdio>
using namespace std;
int prime[50000],is[50000];
int pl;
int a[50000],cnt[50000];
//对于任意质数p，n！中有（n/p+n/p^2+n/p^3+...)个质因子p。
int countc(int n,int p)
{
    int ans=0;
    while(n/p)
    {
        ans+=n/p;
        n/=p;
    }
    return ans;
}
int main()
{
    for(int i=2;i<50000;i++)
    {
        if(is[i]==0) prime[pl++]=i;
        for(int j=0;j<pl&&prime[j]*i<50000;j++)
        {
            is[i*prime[j]]=1;
            if(i%prime[j]==0) break;
        }
    }
    int n,m;
    while(cin>>n>>m)
    {
        if(m==0) {printf("%d does not divide %d!/n",m,n);continue;}
        if(n>=m) {printf("%d divides %d!/n",m,n);continue;}
        int mm=m;
        double k=sqrt(m);
        int num=0;
        memset(cnt,0,sizeof(cnt));
        for(int i=0;prime[i]<=k;i++)
        {
            if(m%prime[i]==0)
            {
                a[num]=prime[i];
                while(m%prime[i]==0)
                {
                    cnt[num]++;
                    m/=prime[i];
                }
                num++;
            }
        }
        if(m>1) a[num]=m,cnt[num++]=1;
        int flag=1;
        for(int i=0;i<num;i++)
        {
            if(countc(n,a[i])<cnt[i])
            {
                flag=0;
                break;
            }
        }
        if(flag) printf("%d divides %d!/n",mm,n);
        else printf("%d does not divide %d!/n",mm,n);
    }
    return 0;
}