E. Number With The Given Amount Of Divisors

http://codeforces.com/problemset/problem/27/E

假设P(i)代表某个素数a(i)代表这个素数的幂

那么任何一个数都可以分解成  ( P(1)^a(1) )*( P(2)^a(2) )*( P(3)^a(3) )*.............*( P(k)^a(k) )

而且这个数的约数的数量为  (a(1)+1)*(a(2)+1)*(a(3)+1)*.............*(a(k)+1)

代码：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<map>
#include<set>
#include<vector>
#include<stack>
#include<queue>
#include<algorithm>
#include<cmath>

#define LL long long
#define ULL unsigned long long
using namespace std;
const int INF=0x3f3f3f3f;
const long long LINF=ceil(1e18);
int p[11]={1,2,3,5,7,11,13,17,19,23,29};
long long ans;
void dfs(int x,int n,long long M)
{//cout<<x<<" "<<n<<" "<<M<<endl;
    if(n==1)
    {ans=min(ans,M);return ;}
    long long k=p[x];
    for(int l=1;l<n&&k<LINF;++l,k=k*p[x])
    if(n%(l+1)==0)
    {//cout<<x<<" "<<l<<" "<<M*k<<endl;
        if(M*k>LINF||M*k<=0)
        break;
        dfs(x+1,n/(l+1),M*k);
    }
}
int main()
{
    //freopen("data.in","r",stdin);
    int n;
    while(cin>>n)
    {
        ans=LINF;
        dfs(1,n,1);
        cout<<ans<<endl;
    }
    return 0;
}