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C++ Program for Sieve of Eratosthenes

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  • Difficulty Level : Easy
  • Last Updated : 15 Jun, 2022
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Given a number n, print all primes smaller than or equal to n. It is also given that n is a small number. For example, if n is 10, the output should be “2, 3, 5, 7”. If n is 20, the output should be “2, 3, 5, 7, 11, 13, 17, 19”.

CPP




// C++ program to print all primes smaller than or equal to
// n using Sieve of Eratosthenes
#include <bits/stdc++.h>
using namespace std;
 
void SieveOfEratosthenes(int n)
{
    // Create a boolean array "prime[0..n]" and initialize
    // all entries it as true. A value in prime[i] will
    // finally be false if i is Not a prime, else true.
    bool prime[n+1];
    memset(prime, true, sizeof(prime));
 
    for (int p=2; p*p<=n; p++)
    {
        // If prime[p] is not changed, then it is a prime
        if (prime[p] == true)
        {
            // Update all multiples of p
            for (int i=p*2; i<=n; i += p)
                prime[i] = false;
        }
    }
 
    // Print all prime numbers
    for (int p=2; p<=n; p++)
       if (prime[p])
          cout << p << " ";
}
 
// Driver Program to test above function
int main()
{
    int n = 30;
    cout << "Following are the prime numbers smaller "
         << " than or equal to " << n << endl;
    SieveOfEratosthenes(n);
    return 0;
}


Output:

Following are the prime numbers below 30
2 3 5 7 11 13 17 19 23 29

Time Complexity : O ( n* log(logn))

Auxiliary Space : O ( 1 )

Please refer complete article on Sieve of Eratosthenes for more details!

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