simple sieve vs sieve of eratosthenes code example
Example 1: sieve in java
class SieveOfEratosthenes
{
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.
boolean prime[] = new boolean[n+1];
for(int i=0;i<n;i++)
prime[i] = true;
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*p; i <= n; i += p)
prime[i] = false;
}
}
// Print all prime numbers
for(int i = 2; i <= n; i++)
{
if(prime[i] == true)
System.out.print(i + " ");
}
}
// Driver Program to test above function
public static void main(String args[])
{
int n = 30;
System.out.print("Following are the prime numbers ");
System.out.println("smaller than or equal to " + n);
SieveOfEratosthenes g = new SieveOfEratosthenes();
g.sieveOfEratosthenes(n);
}
}
Example 2: how to get the prime number in c++ where time complexity is 0(log n)
// 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 greater than or
// equal to the square of it
// numbers which are multiple of p and are
// less than p^2 are already been marked.
for (int i=p*p; 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;
}