# shmibs's solution

## to Sieve in the Crystal Track

Published at Dec 02 2018 · 0 comments
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).

## Setup

Follow the setup instructions for Crystal here:

http://exercism.io/languages/crystal

More help installing can be found here:

http://crystal-lang.org/docs/installation/index.html

## Making the Test Suit Pass

Execute the tests with:

``````\$ crystal spec
``````

In each test suite all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by changing `pending` to `it`.

## Source

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

## Submitting Incomplete Solutions

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

### sieve_spec.cr

``````require "spec"
require "../src/*"

describe "Primes" do
describe "#sieve" do
it "no primes under two" do
Primes.sieve(1).should eq [] of Int32
end
pending "find first prime" do
Primes.sieve(2).should eq [2]
end
pending "find primes up to 10" do
Primes.sieve(10).should eq [2, 3, 5, 7]
end
pending "limit is prime" do
Primes.sieve(13).should eq [2, 3, 5, 7, 11, 13]
end
pending "find primes up to 1000" do
Primes.sieve(1000).should eq [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]
end
end
end``````
``````require "bit_array"

module Primes

def self.sieve(max : Int) : Array(Int32)
b = BitArray.new(max, true)

# 1 s'not prime
b[0] = false

(2..b.size).each { |i|
case b[i-1]
when false
next
when true
j = i * 2
while j <= max
b[j-1] = false
j = j + i
end
end
}

a = [] of Int32
b.each.with_index.reject{|e| e[0] == false}.each{|e| a.push e[1]+1}
a

end

end``````