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:
Resulting in 9 steps. So for input n = 12, the return value would be 9.
Execute the tests with:
$ mix test
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
# @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
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
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 end @tag :pending test "zero is an error" do assert_raise FunctionClauseError, fn -> CollatzConjecture.calc(0) end end @tag :pending test "divide if even" do assert CollatzConjecture.calc(16) == 4 end @tag :pending test "even and odd steps" do assert CollatzConjecture.calc(12) == 9 end @tag :pending test "Large number of even and odd steps" do assert CollatzConjecture.calc(1_000_000) == 152 end @tag :pending test "start with odd step" do assert CollatzConjecture.calc(21) == 7 end @tag :pending test "more steps than starting number" do assert CollatzConjecture.calc(7) == 16 end @tag :pending test "negative value is an error " do assert_raise FunctionClauseError, fn -> CollatzConjecture.calc(-15) end end @tag :pending test "string as input value is an error " do assert_raise FunctionClauseError, fn -> CollatzConjecture.calc("fubar") end end end
ExUnit.start() 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 input |> n_div_two() |> calc(steps + 1) end defp calc(input, steps) do input |> three_n_plus_one() |> calc(steps + 1) end defp n_div_two(n), do: div(n, 2) defp three_n_plus_one(n), do: 3 * n + 1 end
A huge amount can be learned from reading other people’s 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.