Merging nodes at same level in recursion tree - c++

Question

I have understood the approach to solving this problem.
Problem A. Is it co-prime?
Alex has a 1 indexed secret array A of size N (1 ≤ N ≤ 1000).
You have to guess whether all the elements in A are pairwise co-prime,
that is for all 1 ≤ i < j ≤ N,
gcd(Ai, Aj ) = 1.
You can ask Alex at most 15 questions, for each question you give him
two disjoint subsets of {1,2,3,...N}, say S1 and S2, and Alex will
compute P1 = ∏ Ai, and P2 = ∏ Ai and tell you if (i∈S1 i∈S2) gcd(P1,
P2) = 1 or not.
For his own convenience, Alex defined the product of the empty set as 1.
Interestingly, Alex is nowhere to be found, and instead we are here to judge your solution for this problem.
Input
A single integer N, the size of the array A, at the beginning of the
interaction. See section Interaction Protocol for Interaction
protocol.
Output
Copying from Interaction for clarity. Each query is of the format Q I1
I2 I3 . . . In(space separated integers), where Ij ∈ {0, 1, 2}. The
final answer is of the format “A coprime” or “A no”. (Read Interaction
Protocol section for explanation)
Interaction Protocol
For each query print a line of the format Q I1 I2 I3 . . . In(space
separated integers), where Ij ∈ {0, 1, 2} to stdout. • Ifj∈S1,Ij
shouldbe1. • Ifj∈S2,Ij shouldbe2. • IfjisnotinS1 orS2,Ij shouldbe0.
Then, read from stdin a single integer, which is 1 if gcd(P1, P2) = 1,
and 0 otherwise. Once you know the answer, print “A coprime” if you
think A is pairwise co-prime, print “A no” otherwise (without quotes).
Note that you do not have to ask 15 queries, you may print your answer
as soon as you know it, and then exit.
Also, after printing every query, and even your answer, you must do a
flush on stdout. You can use fflush(stdout) in C++, and google to find
what works in other languages.
However I am having trouble how to implement the algorithm and solve the question.
My working: Divide the secret array into two smaller arrays which form S1 and S2. If output by online judge is 1, then go on to divide each smaller array like the bigger array. This keeps going on till we get a singly occupied array. At any point if output by judge is 0, whole program terminates and outputs: "A no". This is O(N) and I have written the following code for this purpose:
#include<iostream>
using namespace std;
bool ask(int n,int start,int end)
{
if (end-start == 0)
return true;
int middle = (start+end)/2;
cout<<"Q"<<" ";
for (int i=1;i<=start-1;i++)
cout<<0<<" ";
for (int i=start;i<=middle;i++)
cout<<1<<" ";
for (int i=middle+1;i<=end;i++)
cout<<2<<" ";
for (int i=end+1;i<=n;i++)
cout<<0<<" ";
cout<<endl;
int answer;
cin>>answer;
if (answer == 1)
return (ask(n,start,middle) and ask(n,middle+1,end));
else
return false;
}
int main()
{
int n;
cin>>n;
if (ask(n,1,n) == true)
cout<<"A coprime"<<endl;
else
cout<<"A no"<<endl;
return 0;
}
However this clearly needs further optimisation and can be done so by combining the nth level nodes (which represent the nth level breakdown of array) by taking the first array of all the nth level nodes as S1 and correspondingly the second array as S2. This has time complexity O(logN) and should work.
But I am having problem with its implementation as it would require for the computer to remember all the nth level nodes and combine them together and so would be hard solving recursively the way I have.
Please note: This appeared in 2016 Exun Prelims hosted on CodeForces and I am doing this solely for the purpose of learning.