 # murdho's solution

## to Collatz Conjecture in the Crystal Track

Published at Feb 13 2019 · 0 comments
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.

## Setup

Follow the setup instructions for Crystal here:

http://exercism.io/languages/crystal

More help installing can be found here:

http://crystal-lang.org/docs/installation/index.html

## Making the Test Suit Pass

Execute the tests with:

``````\$ crystal spec
``````

In each test suite all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by changing `pending` to `it`.

## 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_spec.cr

``````require "spec"
require "../src/*"

describe "CollatzConjecture" do
it "zero steps for one" do
CollatzConjecture.steps(1).should eq(0)
end

pending "divide if even" do
CollatzConjecture.steps(16).should eq(4)
end

pending "even and odd steps" do
CollatzConjecture.steps(12).should eq(9)
end

pending "large number of even and odd steps" do
CollatzConjecture.steps(1000000).should eq(152)
end

pending "zero is an error" do
expect_raises(ArgumentError) do
CollatzConjecture.steps(0)
end
end

pending "negative value is an error" do
expect_raises(ArgumentError) do
CollatzConjecture.steps(-15)
end
end
end``````
``````class CollatzConjecture
def self.steps(n)
raise ArgumentError.new("n has to be positive") if n <= 0

_steps(n, 0)
end

private def self._steps(n, count)
return count if n == 1

if n.even?
_steps(n / 2, count + 1)
else
_steps(n * 3 + 1, count + 1)
end
end
end``````