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;

}