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davearonson's solution

to Prime Factors 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.

Compute the prime factors of a given natural number.

A prime number is only evenly divisible by itself and 1.

Note that 1 is not a prime number.

Example

What are the prime factors of 60?

  • Our first divisor is 2. 2 goes into 60, leaving 30.
  • 2 goes into 30, leaving 15.
    • 2 doesn't go cleanly into 15. So let's move on to our next divisor, 3.
  • 3 goes cleanly into 15, leaving 5.
    • 3 does not go cleanly into 5. The next possible factor is 4.
    • 4 does not go cleanly into 5. The next possible factor is 5.
  • 5 does go cleanly into 5.
  • We're left only with 1, so now, we're done.

Our successful divisors in that computation represent the list of prime factors of 60: 2, 2, 3, and 5.

You can check this yourself:

  • 2 * 2 * 3 * 5
  • = 4 * 15
  • = 60
  • Success!

Running tests

Execute the tests with:

$ elixir prime_factors_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

The Prime Factors Kata by Uncle Bob http://butunclebob.com/ArticleS.UncleBob.ThePrimeFactorsKata

Submitting Incomplete Solutions

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

prime_factors_test.exs

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

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

defmodule PrimeFactorsTest do
  use ExUnit.Case

  # @tag :pending
  test "1" do
    assert PrimeFactors.factors_for(1) == []
  end

  @tag :pending
  test "2" do
    assert PrimeFactors.factors_for(2) == [2]
  end

  @tag :pending
  test "3" do
    assert PrimeFactors.factors_for(3) == [3]
  end

  @tag :pending
  test "4" do
    assert PrimeFactors.factors_for(4) == [2, 2]
  end

  @tag :pending
  test "6" do
    assert PrimeFactors.factors_for(6) == [2, 3]
  end

  @tag :pending
  test "8" do
    assert PrimeFactors.factors_for(8) == [2, 2, 2]
  end

  @tag :pending
  test "9" do
    assert PrimeFactors.factors_for(9) == [3, 3]
  end

  @tag :pending
  test "27" do
    assert PrimeFactors.factors_for(27) == [3, 3, 3]
  end

  @tag :pending
  test "625" do
    assert PrimeFactors.factors_for(625) == [5, 5, 5, 5]
  end

  @tag :pending
  test "901255" do
    assert PrimeFactors.factors_for(901_255) == [5, 17, 23, 461]
  end

  @tag :pending
  test "93819012551" do
    assert PrimeFactors.factors_for(93_819_012_551) == [11, 9539, 894_119]
  end

  @tag :pending
  # @tag timeout: 2000
  #
  # The timeout tag above will set the below test to fail unless it completes
  # in under two sconds. Uncomment it if you want to test the efficiency of your
  # solution.
  test "10000000055" do
    assert PrimeFactors.factors_for(10_000_000_055) == [5, 2_000_000_011]
  end
end
defmodule PrimeFactors do
  @doc """
  Compute the prime factors for 'number'.

  The prime factors are prime numbers that when multiplied give the desired
  number.

  The prime factors of 'number' will be ordered lowest to highest.
  """
  @spec factors_for(pos_integer) :: [pos_integer]
  def factors_for(number) do
    do_factors_for(2, number, trunc(:math.sqrt(number)), [], []) |> Enum.reverse
  end

  def do_factors_for(_, 1, _, _, acc), do: acc

  def do_factors_for(candidate, number, limit, _, acc) when candidate > limit do
    [number|acc]
  end

  def do_factors_for(candidate, number, limit, primes, acc, known_prime \\ false) do
    next = if candidate > 2, do: candidate + 2, else: candidate + 1
    if known_prime || is_prime?(candidate, trunc(:math.sqrt(candidate)), primes) do
      # ++ is slow, but we should only have to do it rarely
      primes = if known_prime, do: primes, else: primes ++ [candidate]
      if rem(number, candidate) == 0 do
        new_number = trunc(number/candidate)
        do_factors_for(candidate,
                       new_number,
                       trunc(:math.sqrt(new_number)),
                       primes,
                       [candidate|acc], true)
      else
        do_factors_for(next, number, limit, primes, acc)
      end
    else
      do_factors_for(next, number, limit, primes, acc)
    end
  end

  def is_prime?(_, limit, [prime|_]) when prime > limit, do: true
  def is_prime?(_, _    , []       )                   , do: true

  def is_prime?(candidate, limit, [prime|more_primes]) do
    case rem(candidate, prime) do
      0 -> false
      _ -> is_prime?(candidate, limit, more_primes)
    end
  end

end

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