Published at Feb 13 2019
·
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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.

Starting with n = 12, the steps would be as follows:

- 12
- 6
- 3
- 10
- 5
- 16
- 8
- 4
- 2
- 1

Resulting in 9 steps. So for input n = 12, the return value would be 9.

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

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`

.

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 "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
```

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.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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