Factor_Combinations.cpp

// Ms ALEENA is working on numbers; she is fascinated by number factors.
// She is given a number N, she wants to find out all possible ways of 
// obtaining N as multiple of its factors.
// For example given N =12
// can be written as multiple of 2,3 and 4.
// and the ways to obtains 12 from ots factors are: 2*2*3, 2*6, 3*4

// Your task is to help Ms ALEENA to find the all possible ways of obtaining N 
// from its factors and return all the possible ways as shown in the samples.

// Input Format:
// -------------
// An integer N, value of N.

// Output Format:
// --------------
// Print the list of possiblilties.


// Sample Input-1:
// ---------------
// 12

// Sample Output-1:
// ----------------
// [[2, 2, 3], [2, 6], [3, 4]]


// Sample Input-2:
// ---------------
// 16

// Sample Output-2:
// ----------------
// [[2, 2, 2, 2], [2, 2, 4], [2, 8], [4, 4]]


// Sample Input-3:
// ---------------
// 32

// Sample Output-3:
// ----------------
// [[2, 2, 2, 2, 2], [2, 2, 2, 4], [2, 2, 8], [2, 4, 4], [2, 16], [4, 8]]





#include<bits/stdc++.h>
using namespace std;
vector<vector<int>> res;
void solve(vector<int> &v,int n,int ind){
    if(n==1){
        if(v.size()>1){
            res.push_back(v);
        }
        return;
    }
    for(int i=ind;i<=n;i++){
        if(n%i==0){
            v.push_back(i);
            solve(v,n/i,i);
            v.pop_back();
        }
    }
}
int main(){
    int n;
    cin>>n;
    vector<int> v;
    solve(v,n,2);
    for(auto p:res){
        for(int i:p){
            cout<<i<<" ";
        }
        cout<<endl;
    }
}