UVA 10837 A Research Problem

时间:2023-03-09 20:01:58
UVA 10837 A Research Problem

https://vjudge.net/problem/UVA-10837

求最小的n,使phi(n)=m

#include<cstdio>
#include<algorithm>
#define N 10011
int prime[N],cnt;
bool v[N],vis[N];
int p[N],tot,ans;
void pre_prime()
{
for(int i=;i<N;i++)
{
if(!v[i]) prime[++cnt]=i;
for(int j=;j<=cnt;j++)
{
if(i*prime[j]>=N) break;
v[i*prime[j]]=;
if(i%prime[j]==) break;
}
}
}
int judge(int n)
{
if(n==) return ;
n++;
for(int i=;i<=cnt && prime[i]*prime[i]<=n;i++)
if(n%prime[i]==) return -;
for(int i=;i<=tot;i++)
if(vis[i] && n==p[i]) return -;
return n;
}
void dfs(int now,int left,int sum)
{
if(sum==tot+)
{
int ret=judge(left);
if(ret>) ans=std::min(ans,now*ret);
return;
}
dfs(now,left,sum+);
if(left%(p[sum]-)==)
{
vis[sum]=;
now*=p[sum];
left/=p[sum]-;
while()
{
dfs(now,left,sum+);
if(left%p[sum]) break;
left/=p[sum];now*=p[sum];
}
vis[sum]=;
}
}
void solve(int n)
{
tot=; ans=2e9;
for(int i=;i<=cnt && n>=(prime[i]-)*(prime[i]-);i++)
if(n%(prime[i]-)==)
p[++tot]=prime[i];
dfs(,n,);
}
int main()
{
pre_prime();
int n,t=;
while(scanf("%d",&n)!=EOF)
{
if(!n) return ;
solve(n);
printf("Case %d: %d %d\n",++t,n,ans);
}
}