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abeger's solution

to Collatz Conjecture in the Ruby Track

Published at Nov 18 2020 · 0 comments
Instructions
Test suite
Solution

Note:

This exercise has changed since this solution was written.

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.


For installation and learning resources, refer to the exercism help page.

For running the tests provided, you will need the Minitest gem. Open a terminal window and run the following command to install minitest:

gem install minitest

If you would like color output, you can require 'minitest/pride' in the test file, or note the alternative instruction, below, for running the test file.

Run the tests from the exercise directory using the following command:

ruby collatz_conjecture_test.rb

To include color from the command line:

ruby -r minitest/pride collatz_conjecture_test.rb

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_test.rb

require 'minitest/autorun'
require_relative 'collatz_conjecture'

# Common test data version: 1.1.1 25c4479
class CollatzConjectureTest < Minitest::Test
  def test_zero_steps_for_one
    # skip
    assert_equal 0, CollatzConjecture.steps(1)
  end

  def test_divide_if_even
    skip
    assert_equal 4, CollatzConjecture.steps(16)
  end

  def test_even_and_odd_steps
    skip
    assert_equal 9, CollatzConjecture.steps(12)
  end

  def test_large_number_of_even_and_odd_steps
    skip
    assert_equal 152, CollatzConjecture.steps(1_000_000)
  end

  def test_zero_is_an_error
    skip
    assert_raises(ArgumentError) { CollatzConjecture.steps(0) }
  end

  def test_negative_value_is_an_error
    skip
    assert_raises(ArgumentError) { CollatzConjecture.steps(-15) }
  end

  # Problems in exercism evolve over time, as we find better ways to ask
  # questions.
  # The version number refers to the version of the problem you solved,
  # not your solution.
  #
  # Define a constant named VERSION inside of the top level BookKeeping
  # module, which may be placed near the end of your file.
  #
  # In your file, it will look like this:
  #
  # module BookKeeping
  #   VERSION = 1 # Where the version number matches the one in the test.
  # end
  #
  # If you are curious, read more about constants on RubyDoc:
  # http://ruby-doc.org/docs/ruby-doc-bundle/UsersGuide/rg/constants.html

  def test_bookkeeping
    skip
    assert_equal 1, BookKeeping::VERSION
  end
end
module CollatzConjecture
  def self.steps(start_num)
    raise ArgumentError unless valid?(start_num)
    num = start_num
    steps = 0
    while num != 1
      steps += 1
      num = transform(num)
    end
    steps
  end

  def self.transform(num)
    return num / 2 if num.even?
    (num * 3) + 1
  end

  def self.valid?(num)
    num >= 1
  end
end

module BookKeeping
  VERSION = 1
end

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