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Published at Jul 13 2018
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Instructions

Test suite

Solution

Use the Sieve of Eratosthenes to find all the primes from 2 up to a given number.

The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e. not prime) the multiples of each prime, starting with the multiples of 2. It does not use any division or remainder operation.

Create your range, starting at two and continuing up to and including the given limit. (i.e. [2, limit])

The algorithm consists of repeating the following over and over:

- take the next available unmarked number in your list (it is prime)
- mark all the multiples of that number (they are not prime)

Repeat until you have processed each number in your range.

When the algorithm terminates, all the numbers in the list that have not been marked are prime.

The wikipedia article has a useful graphic that explains the algorithm: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Notice that this is a very specific algorithm, and the tests don't check that you've implemented the algorithm, only that you've come up with the correct list of primes. A good first test is to check that you do not use division or remainder operations (div, /, mod or % depending on the language).

You can run all the tests for an exercise by entering

```
$ gradle test
```

in your terminal.

Sieve of Eratosthenes at Wikipedia http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
import org.junit.Test;
import org.junit.Ignore;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import static org.junit.Assert.assertEquals;
public class SieveTest {
@Test
public void noPrimesUnder2(){
Sieve sieve = new Sieve(1);
List<Integer> expectedOutput = Collections.emptyList();
assertEquals(expectedOutput, sieve.getPrimes());
}
@Ignore("Remove to run test")
@Test
public void findFirstPrime() {
Sieve sieve = new Sieve(2);
List<Integer> expectedOutput = Collections.singletonList(2);
assertEquals(expectedOutput, sieve.getPrimes());
}
@Ignore("Remove to run test")
@Test
public void findPrimesUpTo10() {
Sieve sieve = new Sieve(10);
List<Integer> expectedOutput = Arrays.asList(2, 3, 5, 7);
assertEquals(expectedOutput, sieve.getPrimes());
}
@Ignore("Remove to run test")
@Test
public void limitIsPrime(){
Sieve sieve = new Sieve(13);
List<Integer> expectedOutput = Arrays.asList(2, 3, 5, 7, 11, 13);
assertEquals(expectedOutput, sieve.getPrimes());
}
@Ignore("Remove to run test")
@Test
public void findPrimesUpTo1000() {
Sieve sieve = new Sieve(1000);
List<Integer> expectedOutput = Arrays.asList(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283,
293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421,
431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563,
569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683,
691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829,
839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983,
991, 997);
assertEquals(expectedOutput, sieve.getPrimes());
}
}
```

```
import java.util.List;
import java.util.ArrayList;
public final class Sieve {
private Integer limit;
private List<Integer> primes;
public Sieve(Integer limit) {
this.limit = limit;
primes = findPrimes();
}
public List<Integer> getPrimes() {
return primes;
}
private List<Integer> findPrimes() {
List<Integer> primes = new ArrayList<Integer>();
List<Integer> possible = findPossible();
while (!possible.isEmpty()) {
Integer curr = possible.remove(0);
possible = removeMultiples(curr, possible);
primes.add(curr);
}
return primes;
}
private List<Integer> findPossible() {
List<Integer> possible = new ArrayList<Integer>();
for (int i = 2; i <= limit; i++) {
possible.add(i);
}
return possible;
}
private List<Integer> removeMultiples(Integer curr, List<Integer> possible) {
List<Integer> multiples = new ArrayList<Integer>();
Integer multiplier = 2;
while (!possible.isEmpty() &&
curr * multiplier <= possible.get(possible.size() - 1)) {
multiples.add(curr * multiplier);
multiplier += 1;
}
possible.removeAll(multiples);
return possible;
}
}
```

A huge amount can be learned from reading other peopleโs code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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