PrimeSieve.java


Below is the syntax highlighted version of PrimeSieve.java from §1.4 Arrays.


/******************************************************************************
 *  Compilation:  javac PrimeSieve.java
 *  Execution:    java -Xmx1100m PrimeSieve n
 *  
 *  Computes the number of primes less than or equal to n using
 *  the Sieve of Eratosthenes.
 *
 *  % java PrimeSieve 25
 *  The number of primes <= 25 is 9
 *
 *  % java PrimeSieve 100
 *  The number of primes <= 100 is 25
 *
 *  % java -Xmx100m PrimeSieve 100000000
 *  The number of primes <= 100000000 is 5761455
 *
 *  % java PrimeSieve -Xmx1100m 1000000000 
 *  The number of primes <= 1000000000 is 50847534
 * 
 *
 *  The 110MB and 1100MB is the amount of memory you want to allocate
 *  to the program. If your computer has less, make this number smaller,
 *  but it may prevent you from solving the problem for very large
 *  values of n.
 *
 *
 *                  n     Primes <= n
 *  ---------------------------------
 *                 10               4   
 *                100              25  
 *              1,000             168  
 *             10,000           1,229  
 *            100,000           9,592  
 *          1,000,000          78,498  
 *         10,000,000         664,579  
 *        100,000,000       5,761,455  
 *      1,000,000,000      50,847,534  
 *
 ******************************************************************************/


public class PrimeSieve {
    public static void main(String[] args) { 
        int n = Integer.parseInt(args[0]);

        // initially assume all integers are prime
        boolean[] isPrime = new boolean[n+1];
        for (int i = 2; i <= n; i++) {
            isPrime[i] = true;
        }

        // mark non-primes <= n using Sieve of Eratosthenes
        for (int factor = 2; factor*factor <= n; factor++) {

            // if factor is prime, then mark multiples of factor as nonprime
            // suffices to consider mutiples factor, factor+1, ...,  n/factor
            if (isPrime[factor]) {
                for (int j = factor; factor*j <= n; j++) {
                    isPrime[factor*j] = false;
                }
            }
        }

        // count primes
        int primes = 0;
        for (int i = 2; i <= n; i++) {
            if (isPrime[n]) primes++;
        }
        System.out.println("The number of primes <= " + n + " is " + primes);
    }
}


Copyright © 2000–2011, Robert Sedgewick and Kevin Wayne.
Last updated: Thu Jun 16 10:59:13 EDT 2016.