SieveOfEratosthenes.java

/*
 *  Following implementation of sieve of eratosthenes returns a boolean array which contains true is its index is prime
 *  less than or equal to a number n.
 *  Space complexity : O(n).
 *  Time complexity : O(n).
 */

public class SieveOfEratosthenes {

    public static boolean[] sieveOfEratosthenes(int n) {
        int sqrtOfn = (int)Math.sqrt(n) + 1;
        boolean[] primes = new boolean[n + 1];
        for (int i = 2; i < n + 1; ++i) {
            primes[i] = true;
        }
        for (int i = 2; i <= sqrtOfn; ++i) {
            if (primes[i]) {
                for (int j = 2 * i; j < n + 1; j += i) {
                    primes[j] = false;
                }
            }
        }
        return primes;
    }

    public static void main(String[] args) {
        int n = 100;
        boolean[] primes = sieveOfEratosthenes(n);
        for (int i = 2; i < n + 1; ++i) {
            if (primes[i]) {
                System.out.print(i + " ");
            }
        }
    }
}