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davearonson's solution

to Sieve in the Elixir Track

Published at Jul 13 2018 · 0 comments
Instructions
Test suite
Solution

Note:

This solution was written on an old version of Exercism. The tests below might not correspond to the solution code, and the exercise may have changed since this code was written.

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.

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.

Running tests

Execute the tests with:

$ elixir sieve_test.exs

Pending tests

In the test suites, all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by commenting out the relevant @tag :pending with a # symbol.

For example:

# @tag :pending
test "shouting" do
  assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
end

Or, you can enable all the tests by commenting out the ExUnit.configure line in the test suite.

# ExUnit.configure exclude: :pending, trace: true

For more detailed information about the Elixir track, please see the help page.

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_test.exs

if !System.get_env("EXERCISM_TEST_EXAMPLES") do
  Code.load_file("sieve.exs", __DIR__)
end

ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)

defmodule SieveTest do
  use ExUnit.Case

  # @tag :pending
  test "a few primes" do
    assert Sieve.primes_to(10) == [2, 3, 5, 7]
  end

  @tag :pending
  test "primes to 1000" do
    result = [
      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
    ]

    assert Sieve.primes_to(1000) == result
  end
end
defmodule Sieve do

  @doc """
  Generates a list of primes up to a given limit.
  """
  @spec primes_to(non_neg_integer) :: [non_neg_integer]
  def primes_to(limit) do
    do_primes_to(limit, 2, %{})
    |> Enum.filter(&(elem(&1, 1)))
    |> Enum.map(&(elem(&1, 0)))
    |> Enum.sort
  end

  defp do_primes_to(limit, candidate, numbers) when candidate > limit do
    numbers
  end

  defp do_primes_to(limit, candidate, numbers) do
    next_numbers = if numbers[candidate] == false do  # known composite
                     numbers
                   else
                     # kinda cheating here -- instead of leaving the primes
                     # unmarked, I'm marking them in a different way.  could
                     # instead have put the marked ones in a set and subtracted
                     # them from a map of all or some such; this way just uses
                     # the same map to keep track of both.
                     mark_multiples(Map.put(numbers, candidate, true),
                                    candidate * 2,
                                    candidate,
                                    limit)
                   end
    do_primes_to(limit, candidate + 1, next_numbers)
  end

  defp mark_multiples(numbers, this_one, _, limit) when this_one > limit do
    numbers
  end

  defp mark_multiples(numbers, this_one, candidate, limit) do
    mark_multiples(Map.put(numbers, this_one, false),
                   this_one + candidate,
                   candidate,
                   limit)
  end

end

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