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Update SieveOfEratosthenes.java (#4149)

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Rohan Anand 2023-04-07 18:20:43 +05:30 committed by GitHub
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1 changed files with 5 additions and 27 deletions
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src/main/java/com/thealgorithms/others/SieveOfEratosthenes.java
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@ -4,45 +4,24 @@ import java.util.Arrays;
/** /**
* Sieve of Eratosthenes is an ancient algorithm for finding all prime numbers * Sieve of Eratosthenes is an ancient algorithm for finding all prime numbers
* up to any given limit. It does so by iteratively marking as composite (i.e., * up to any given limit.
* not prime) the multiples of each prime, starting with the first prime number,
* 2. The multiples of a given prime are generated as a sequence of numbers
* starting from that prime, with constant difference between them that is equal
* to that prime. This is the sieve's key distinction from using trial division
* to sequentially test each candidate number for divisibility by each prime.
* Once all the multiples of each discovered prime have been marked as
* composites, the remaining unmarked numbers are primes.
* <p>
* Poetry about Sieve of Eratosthenes:
* <p>
* <i>Sift the Two's and Sift the Three's:</i></p>
* <p>
* <i>The Sieve of Eratosthenes.</i></p>
* <p>
* <i>When the multiples sublime,</i></p>
* <p>
* <i>The numbers that remain are Prime.</i></p>
* *
* @see <a href="https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes">Wiki</a> * @see <a href="https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes">Wiki</a>
*/ */
public class SieveOfEratosthenes { public class SieveOfEratosthenes {
/** /**
* @param n The number till which we have to check for prime Prints all the * Finds all prime numbers till n.
* prime numbers till n. Should be more than 1. *
* @return array of all prime numbers between 0 to n * @param n The number till which we have to check for primes. Should be more than 1.
* @return Array of all prime numbers between 0 to n.
*/ */
public static int[] findPrimesTill(int n) { public static int[] findPrimesTill(int n) {
// Create array where index is number and value is flag - is that number a prime or not.
// size of array is n + 1 cause in Java array indexes starts with 0
Type[] numbers = new Type[n + 1]; Type[] numbers = new Type[n + 1];
// Start with assumption that all numbers except 0 and 1 are primes.
Arrays.fill(numbers, Type.PRIME); Arrays.fill(numbers, Type.PRIME);
numbers[0] = numbers[1] = Type.NOT_PRIME; numbers[0] = numbers[1] = Type.NOT_PRIME;
double cap = Math.sqrt(n); double cap = Math.sqrt(n);
// Main algorithm: mark all numbers which are multiples of some other values as not prime
for (int i = 2; i <= cap; i++) { for (int i = 2; i <= cap; i++) {
if (numbers[i] == Type.PRIME) { if (numbers[i] == Type.PRIME) {
for (int j = 2; i * j <= n; j++) { for (int j = 2; i * j <= n; j++) {
@ -51,7 +30,6 @@ public class SieveOfEratosthenes {
} }
} }
//Write all primes to result array
int primesCount = (int) Arrays int primesCount = (int) Arrays
.stream(numbers) .stream(numbers)
.filter(element -> element == Type.PRIME) .filter(element -> element == Type.PRIME)