Alternate Primes till N in C++?

Here we will see how to print all alternate prime numbers till N. The alternate prime numbers are like below. Suppose N = 15. So the prime numbers till N are {2, 3, 5, 7, 11, 13}. The alternate prime numbers are {2, 5, 11}. Let us see how we can solve this problem.

Algorithm

printAlternatePrime(N)

Begin
   define one Boolean array prime of size N + 1, and fill with 1.
   for p := 2, p^2 is less than N, increase p by 1, do
      if prime[p] is true, then
         for all multiples of p, make the position 0 in prime array
      end if
   done
   set the flag
   for p := 2 to n, do
      if prime[p] is true, then
         if flag is set, then
            print p, and reset the flag
         else
            set the flag
         end if
      end if
   done
End

Example

 Live Demo

#include<iostream>
using namespace std;
void printAlternatePrime(int n) {
   bool prime[n + 1];
   for(int i = 0; i<=n; i++) {
      prime[i] = true;
   }
   for (int p = 2; p * p <= n; p++) {
      if (prime[p]) {
         for (int i = p * 2; i <= n; i += p) //all multiples will be false
            prime[i] = false;
      }
   }
   bool prime_flag = true;
   for (int p = 2; p <= n; p++) {
      if (prime[p]) {
         if (prime_flag) {
            cout << p << " ";
            prime_flag = false;
         } else {
            prime_flag = true; //set to print next prime
         }
      }
   }
}
main() {
   int n;
   cout << "Enter upper limit: ";
   cin >> n;
   cout << "Alternate prime numbers are: ";
   printAlternatePrime(n);
}

Output

Enter upper limit: 20
Alternate prime numbers are: 2 5 11 17