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.
For installation and learning resources, refer to the Ruby resources 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
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.
require 'minitest/autorun'
require_relative 'collatz_conjecture'
# Common test data version: 1.2.1 d94e348
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) do
CollatzConjecture.steps(0)
end
end
def test_negative_value_is_an_error
skip
assert_raises(ArgumentError) do
CollatzConjecture.steps(-15)
end
end
end
class CollatzConjecture
def self.steps(n)
raise ArgumentError if n < 1
return 0 if n == 1
return steps(n / 2) + 1 if n.even?
return steps(n * 3 + 1) + 1 if n.odd?
end
end
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