【找规律】【DFS】XVII Open Cup named after E.V. Pankratiev Stage 14, Grand Prix of Tatarstan, Sunday, April 2, 2017 Problem A. Arithmetic Derivative

时间:2023-03-09 04:04:20
【找规律】【DFS】XVII Open Cup named after E.V. Pankratiev Stage 14, Grand Prix of Tatarstan, Sunday, April 2, 2017 Problem A. Arithmetic Derivative

【找规律】【DFS】XVII Open Cup named after E.V. Pankratiev Stage 14, Grand Prix of Tatarstan, Sunday, April 2, 2017 Problem A. Arithmetic Derivative

假设一个数有n个质因子a1,a2,..,an,那么n'=Σ(a1*a2*...*an)/ai。

打个表出来,发现一个数x,如果x'=Kx,那么x一定由K个“基础因子”组成。

这些基础因子是2^2,3^3,5^5,7^7,11^11,13^13。只有6个,K不超过30,于是可以dfs。

要注意搜索顺序(每次枚举的时候,都从大于等于前项的开始搜)和可行性剪枝(如果超过r则剪枝,虽说有可能爆long long,但其实整除就可以判,而且没有精度误差)。

#include<cstdio>
//#include<set>
#include<algorithm>
#include<cmath>
using namespace std;
//const long double EPS=0.0000000001;
typedef long long ll;
//set<ll>S;
ll base[11],path[1000010];
int pr[11];
int K,e;
ll r;
void dfs(int cur,int pre,ll now){
if(cur==K){
// if(S.find(now)==S.end()){
path[++e]=now;
// S.insert(now);
// }
return;
}
for(int i=pre;i<=6;++i){
if(base[i]>r/now){
break;
}
dfs(cur+1,i,now*base[i]);
}
}
int main(){
// freopen("a.in","r",stdin);
// freopen("a1.out","w",stdout);
pr[1]=2; pr[2]=3; pr[3]=5; pr[4]=7; pr[5]=11; pr[6]=13;
for(int i=1;i<=6;++i){
base[i]=1;
for(int j=1;j<=pr[i];++j){
base[i]*=(ll)pr[i];
}
}
while(scanf("%d%lld",&K,&r)!=EOF){
e=0;
// S.clear();
dfs(0,1,1ll);
printf("%d\n",e);
sort(path+1,path+e+1);
if(e){
for(int i=1;i<e;++i){
printf("%lld ",path[i]);
}
printf("%lld\n",path[e]);
}
}
return 0;
}