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4d47's solution

to Collatz Conjecture in the Erlang Track

Instructions
Test suite
Solution

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.

Examples

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

In order to run the tests, issue the following command from the exercise directory:

For running the tests provided, rebar3 is used as it is the official build and dependency management tool for erlang now. Please refer to the tracks installation instructions on how to do that.

In order to run the tests, you can issue the following command from the exercise directory.

$ rebar3 eunit

Test versioning

Each problem defines a macro TEST_VERSION in the test file and verifies that the solution defines and exports a function test_version returning that same value.

To make tests pass, add the following to your solution:

-export([test_version/0]).

test_version() ->
  1.

The benefit of this is that reviewers can see against which test version an iteration was written if, for example, a previously posted solution does not solve the current problem or passes current tests.

Questions?

For detailed information about the Erlang track, please refer to the help page on the Exercism site. This covers the basic information on setting up the development environment expected by the exercises.

Source

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.

collatz_conjecture_tests.erl

-module(collatz_conjecture_tests).

% This file is automatically generated from the exercises canonical data.

-include_lib("erl_exercism/include/exercism.hrl").
-include_lib("eunit/include/eunit.hrl").


zero_steps_for_one_test() ->
    ?assertMatch(0, collatz_conjecture:steps(1)).

divide_if_even_test() ->
    ?assertMatch(4, collatz_conjecture:steps(16)).

even_and_odd_steps_test() ->
    ?assertMatch(9, collatz_conjecture:steps(12)).

large_number_of_even_and_odd_steps_test() ->
    ?assertMatch(152, collatz_conjecture:steps(1000000)).

zero_is_an_error_test() ->
    ?assertMatch({error,
		  "Only positive numbers are allowed"},
		 collatz_conjecture:steps(0)).

negative_value_is_an_error_test() ->
    ?assertMatch({error,
		  "Only positive numbers are allowed"},
		 collatz_conjecture:steps(-15)).

version_test() ->
    ?assertMatch(2, collatz_conjecture:test_version()).
-module(collatz_conjecture).
-export([steps/1, test_version/0]).
-spec test_version() -> pos_integer().
-spec steps(pos_integer()) -> non_neg_integer().


test_version() ->
    2.

steps(N) when N =< 0 ->
    {error, "Only positive numbers are allowed"};
steps(N) ->
    steps(N, 0).
steps(1, Count) ->
    Count;
steps(N, Count) when N rem 2 == 0 ->
    steps(N div 2, Count + 1);
steps(N, Count) ->
    steps(N * 3 + 1, Count + 1).

What can you learn from this solution?

A huge amount can be learnt 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.

  • What compromises have been made?
  • Are there new concepts here that I could read more about to develop my understanding?