Hey,to everyone who gave the round 2 of Lowes Codeathon. Could anyone give any idea (or hint) for the first question (the subset one).

Thanks in advance : )

The main observation was the Ai<=30. If you look at the possible subset that only have unique prime factors in their product then there won’t be that many as there are only 10 primes upto 30 and 8 more no.s which are just product of some primes with no primes coming more than once . So in my solution I just brute forces all the subset with pre computation of 2^18(the length of the array A in compute function will be 18) . For every test case I then just calculated the count for each subset which can be done by using a frequency map.

Code:

```
#include "bits/stdc++.h"
#define ll long long
using namespace std;
const int mod = 1e9+7;
vector<vector<int>>a;
void compute(){
vector<pair<int,vector<int>>>A;
for(int i = 2;i<31;i++){
int v = i,p=0;
vector<int>b;
while(v%2==0){
v/=2,p++;
}
if(p>1)continue;
if(p)b.push_back(2);
bool flag = true;
for(int j = 3;j<=i;j++){
if(v%j==0){
p = 0;
while(v%j==0){
v/=j,p++;
}
if(p>1){
flag = false;
break;
}
b.push_back(j);
}
}
if(flag)A.push_back({i,b});
}
ll l = A.size(),m = 1LL<<l;
for(int i=1;i<m;i++){
int j = i,k=0;
set<int>s;
bool flag = true;
vector<int>b;
while(j){
if(j&1){
for(int prime:A[k].second){
if(s.count(prime)){
flag = false;
break;
}
s.insert(prime);
}
b.push_back(A[k].first);
}
j>>=1,k++;
}
if(flag)a.push_back(b);
}
}
long long solve(int n,vector<int>&A){
map<int,int>d;
for(int v:A)d[v]++;
ll ans = 0;
for(auto arr:a){
ll val = 1;
for(int v:arr){
val = (val*d[v])%mod;
}
ans = (ans + val)%mod;
}
return ans;
}
int32_t main(){
ios_base::sync_with_stdio(0);cin.tie(0);
compute();
int t;cin>>t;
while(t--){
int n;cin>>n;
vector<int>a(n);
for(int i = 0;i<n;i++)cin>>a[i];
cout<<solve(n,a)<<"\n";
}
return 0;
}
```

Man do i feel dumb ;_;

Anyway thanks : ) its clear now.

Hi , In your while(j) loop before b.push_back(A[k].first); can we add the condition if(flag==false) break; ?

Thanks in advance.

Did you guys solved the second question of “Road Construction”? If yes! please share your approach ;_;

Yes u can

This is the only solution idea that I found.

Can anyone share the round 2 questions of Lowe’s Codeathon.

Thanks in advance.