The results:

Input the vector number:9
Put the 4 and 4on the balance.
Put the 4 and 4on the balance.
Put the 4 and 2on the balance.
The weight of is fake coin.is2

The codes:

#include <iostream>
#include <vector>
using namespace std;
void fill_vector(vector<double> &quantity, int n);
double  find_fake_coin(vector<double> quanity, int n);
int main()
{
    cout << "Input the vector number:";
    int number;
    cin >> number;
    vector<double> quantity;
    fill_vector(quantity, number);
    //cout << quantity[4];
    double fake_coin_weight;
    fake_coin_weight = find_fake_coin(quantity, number-1);
    cout << "The weight of " << "is fake coin.is" << fake_coin_weight;
    return 0;
}
void fill_vector(vector<double> &quantity, int n)
{
    for(int i=0; i<n; ++i){
            if(i==5){
                quantity.push_back(2);
            }else{
                quantity.push_back(4);
            }
    }
}
double  find_fake_coin(vector<double> quanity, int n)
{

    //if(n==1){
      //  return min(quanity[1],quanity[0]);
   // }
    cout << "Put the " <<quanity[n] << " and " << quanity[n-1] << "on the balance."<< endl ;
    if(quanity[n]!= quanity[n-1]) return min(quanity[n], quanity[n-1]);
    return min(quanity[n],find_fake_coin(quanity, --n));
}