素数C ++

Question

I have this code:

#include <iostream>
#include <cmath>

using namespace std;

int n, liczba;

int main()
{
    cin >> n;
    for (int i = 0; i < n; i++) {
        cin >> liczba;
        if (liczba < 2) {
            cout << "NIE" << endl;
        } else if (liczba == 2) {
            cout << "TAK" << endl;
        }

        for (int i = 2; i < liczba; i++) {
            if (liczba % i == 0) {
                cout << "NIE" << endl;
                break;
            } else if (liczba % i != 0) {
                cout << "TAK" << endl;
                break;
            }
        }
    }
    return 0;
}

This program is supposed to write yes "TAK" or no "NIE" whether the number you input is prime or isn't. Variable n is the number of numbers you want to input into program, and liczba is the number you want to check if it's prime or not. It seems to work fine expect one significant thing. If I input number 9 it says yes "TAK" instead of no "NIE" .. I discovered that this happens to numbers: 9,27,45,63,81 and so on.. if I add 18 starting from 9 it will happen every time.

What's wrong with my code?

Answer 1

You're break ing on BOTH sides of your if() test. Effectly you'll only ever test one divisor:

eg liczba = 9

1. if (liczba % 2 == 0) -> if (9 % 2 == 0) -> if (1 == 0) -> false
2. ...jump to else
3. if (liczba % 2 != 0) -> if (9 % 2 != 0) -> if (1 != 0) -> TRUE
4. spit out 'tak' and break out of the loop

You cannot break out of the loop "early" if you get a remainder. That means the divisor you tested is NOT a factor of the number. You can only break early if you DO get a remainder of 0 , which means the number's not prime - it's composite.

Answer 2

Hint:

All prime numbers (except 2 and 3) can be expressed in the form 6k+1 or 6k-1 , where k is a positive whole number.

Therefore, This should work:

bool IsPrime( int number )
{

 if ( ( (!(number & 1)) && number != 2 ) || (number < 2) || (number % 3 == 0 && number != 3) )
      return (false);

 for( int k = 1; 36*k*k-12*k < number;++k)
     if ( (number % (6*k+1) == 0) || (number % (6*k-1) == 0) )
         return (false);
     return true;
}

Taken from Determining if a number is prime .

Answer 3

You have not used a flag and thus it says NIE after first check. Also, you are missing an else statement. Try this instead:

#include <iostream>
#include <cmath>
using namespace std;
int n,liczba;
int main()
{
    cin >> n; //
    for(int i=0;i<n;i++)
        {
            cin>>liczba;
            if (liczba < 2)
                {
                cout << "NIE" << endl;
                }
            else if (liczba == 2)
            {
                cout << "TAK" << endl;
            }
            else
            {
                bool isPrime = true;
                for (int i=2;i<liczba;i++)
                {

                    if (liczba % i == 0)
                        {
                            isPrime = false;
                            break;
                        } 
                }
                if(isPrime)
                    cout<<"TAK";
                else
                    cout<<"NIE";
            }

        }
    return 0;
}

Currently, if you input 7, It will check if 7 % 2 == 0 . Since it is not, it will print "NIE" and break out of the loop.