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POFinding prime numbers with the Sieve of Eratosthenes (Originally: Is there a better way to prepare this array?)
 

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  1. POFinding prime numbers with the Sieve of Eratosthenes (Originally: Is there a better way to prepare this array?)
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    <p><strong>Note:</strong> Version 2, below, uses the Sieve of Eratosthenes. There are several answers that helped with what I originally asked. I have chosen the Sieve of Eratosthenes method, implemented it, and changed the question title and tags appropriately. Thanks to everyone who helped!</p> <h2>Introduction</h2> <p>I wrote this fancy little method that generates an array of int containing the prime numbers less than the specified upper bound. It works very well, but I have a concern.</p> <h2>The Method</h2> <pre><code>private static int [] generatePrimes(int max) { int [] temp = new int [max]; temp [0] = 2; int index = 1; int prime = 1; boolean isPrime = false; while((prime += 2) &lt;= max) { isPrime = true; for(int i = 0; i &lt; index; i++) { if(prime % temp [i] == 0) { isPrime = false; break; } } if(isPrime) { temp [index++] = prime; } } int [] primes = new int [index]; while(--index &gt;= 0) { primes [index] = temp [index]; } return primes; } </code></pre> <h2>My Concern</h2> <p>My concern is that I am creating an array that is far too large for the final number of elements the method will return. The trouble is that I don't know of a good way to correctly guess the number of prime numbers less than a specified number.</p> <h2>Focus</h2> <p>This is how the program uses the arrays. This is what I want to improve upon.</p> <ol> <li>I create a temporary array that is large enough to hold every number less than the limit.</li> <li>I generate the prime numbers, while keeping count of how many I have generated.</li> <li>I make a new array that is the right dimension to hold just the prime numbers.</li> <li>I copy each prime number from the huge array to the array of the correct dimension.</li> <li>I return the array of the correct dimension that holds just the prime numbers I generated.</li> </ol> <h2>Questions</h2> <ol> <li>Can I copy the whole chunk (at once) of <code>temp[]</code> that has nonzero elements to <code>primes[]</code> without having to iterate through both arrays and copy the elements one by one?</li> <li>Are there any data structures that behave like an array of primitives that can grow as elements are added, rather than requiring a dimension upon instantiation? What is the performance penalty compared to using an array of primitives?</li> </ol> <hr> <p>Version 2 (thanks to <a href="https://stackoverflow.com/users/22656/jon-skeet">Jon Skeet</a>):</p> <pre><code>private static int [] generatePrimes(int max) { int [] temp = new int [max]; temp [0] = 2; int index = 1; int prime = 1; boolean isPrime = false; while((prime += 2) &lt;= max) { isPrime = true; for(int i = 0; i &lt; index; i++) { if(prime % temp [i] == 0) { isPrime = false; break; } } if(isPrime) { temp [index++] = prime; } } return Arrays.copyOfRange(temp, 0, index); } </code></pre> <hr> <p>Version 3 (thanks to <a href="https://stackoverflow.com/users/3333/paul-tomblin">Paul Tomblin</a>) which uses the <a href="http://en.wikipedia.org/wiki/Sieve%5Fof%5FErastosthenes" rel="nofollow noreferrer">Sieve of Erastosthenes</a>:</p> <pre><code>private static int [] generatePrimes(int max) { boolean[] isComposite = new boolean[max + 1]; for (int i = 2; i * i &lt;= max; i++) { if (!isComposite [i]) { for (int j = i; i * j &lt;= max; j++) { isComposite [i*j] = true; } } } int numPrimes = 0; for (int i = 2; i &lt;= max; i++) { if (!isComposite [i]) numPrimes++; } int [] primes = new int [numPrimes]; int index = 0; for (int i = 2; i &lt;= max; i++) { if (!isComposite [i]) primes [index++] = i; } return primes; } </code></pre>
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    1. COwhy do you need a fixed size array?
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    2. COMatt Davison: I don't want to return an array that has a bunch of zero elements at the end, it feels so sloppy.
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    3. COOne micro-optimization I'd make: replace "for (int j = i; i*j..." with "for (int j = i; j <= max; j+=i) { isComposite[j] = true;}"
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