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to Collatz Conjecture in the Elixir Track

Published at Jun 29 2019 · 0 comments
Test suite

The Collatz Conjecture or 3x+1 problem can be summarized as follows:

Take any positive integer n. If n is even, divide n by 2 to get n / 2. If n is odd, multiply n by 3 and add 1 to get 3n + 1. Repeat the process indefinitely. The conjecture states that no matter which number you start with, you will always reach 1 eventually.

Given a number n, return the number of steps required to reach 1.


Starting with n = 12, the steps would be as follows:

  1. 12
  2. 6
  3. 3
  4. 10
  5. 5
  6. 16
  7. 8
  8. 4
  9. 2
  10. 1

Resulting in 9 steps. So for input n = 12, the return value would be 9.

Running tests

Execute the tests with:

$ mix test

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!"

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

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

If you're stuck on something, it may help to look at some of the available resources out there where answers might be found.


An unsolved problem in mathematics named after mathematician Lothar Collatz https://en.wikipedia.org/wiki/3x_%2B_1_problem

Submitting Incomplete Solutions

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


defmodule CollatzConjectureTest do
  use ExUnit.Case

  test "zero steps for one" do
    assert CollatzConjecture.calc(1) == 0

  @tag :pending
  test "zero is an error" do
    assert_raise FunctionClauseError, fn -> CollatzConjecture.calc(0) end

  @tag :pending
  test "divide if even" do
    assert CollatzConjecture.calc(16) == 4

  @tag :pending
  test "even and odd steps" do
    assert CollatzConjecture.calc(12) == 9

  @tag :pending
  test "Large number of even and odd steps" do
    assert CollatzConjecture.calc(1_000_000) == 152

  @tag :pending
  test "start with odd step" do
    assert CollatzConjecture.calc(21) == 7

  @tag :pending
  test "more steps than starting number" do
    assert CollatzConjecture.calc(7) == 16

  @tag :pending
  test "negative value is an error " do
    assert_raise FunctionClauseError, fn -> CollatzConjecture.calc(-15) end

  @tag :pending
  test "string as input value is an error " do
    assert_raise FunctionClauseError, fn -> CollatzConjecture.calc("fubar") end


ExUnit.configure(exclude: :pending, trace: true)
defmodule CollatzConjecture do
  @initial_steps 0
  @terminating_number 1

  require Integer

  defguardp positive_integer?(input) when is_integer(input) and input > 0

  @doc """
  calc/1 takes an integer and returns the number of steps required to get the
  number to 1 when following the rules:
    - if number is odd, multiply with 3 and add 1
    - if number is even, divide by 2
  @spec calc(input :: pos_integer()) :: non_neg_integer()
  def calc(input) when positive_integer?(input), do: calc(input, @initial_steps)
  defp calc(@terminating_number, steps), do: steps

  defp calc(input, steps) when Integer.is_even(input) do
    |> n_div_two()
    |> calc(steps + 1)

  defp calc(input, steps) do
    |> three_n_plus_one()
    |> calc(steps + 1)

  defp n_div_two(n), do: div(n, 2)
  defp three_n_plus_one(n), do: 3 * n + 1

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