 # paulfioravanti's solution

## to Collatz Conjecture in the Elixir Track

Published at Jun 29 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.

## Running tests

Execute the tests with:

``````\$ mix test
``````

### Pending tests

In the test suites, all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by commenting out the relevant `@tag :pending` with a `#` symbol.

For example:

``````# @tag :pending
test "shouting" do
assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
end
``````

Or, you can enable all the tests by commenting out the `ExUnit.configure` line in the test suite.

``````# ExUnit.configure exclude: :pending, trace: true
``````

If you're stuck on something, it may help to look at some of the available resources out there where answers might be found.

## 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.exs

``````defmodule CollatzConjectureTest do
use ExUnit.Case

test "zero steps for one" do
assert CollatzConjecture.calc(1) == 0
end

@tag :pending
test "zero is an error" do
assert_raise FunctionClauseError, fn -> CollatzConjecture.calc(0) end
end

@tag :pending
test "divide if even" do
assert CollatzConjecture.calc(16) == 4
end

@tag :pending
test "even and odd steps" do
assert CollatzConjecture.calc(12) == 9
end

@tag :pending
test "Large number of even and odd steps" do
assert CollatzConjecture.calc(1_000_000) == 152
end

@tag :pending
assert CollatzConjecture.calc(21) == 7
end

@tag :pending
test "more steps than starting number" do
assert CollatzConjecture.calc(7) == 16
end

@tag :pending
test "negative value is an error " do
assert_raise FunctionClauseError, fn -> CollatzConjecture.calc(-15) end
end

@tag :pending
test "string as input value is an error " do
assert_raise FunctionClauseError, fn -> CollatzConjecture.calc("fubar") end
end
end``````

### test_helper.exs

``````ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)``````
``````defmodule CollatzConjecture do
@initial_steps 0
@terminating_number 1

require Integer

defguardp positive_integer?(input) when is_integer(input) and input > 0

@doc """
calc/1 takes an integer and returns the number of steps required to get the
number to 1 when following the rules:
- if number is odd, multiply with 3 and add 1
- if number is even, divide by 2
"""
@spec calc(input :: pos_integer()) :: non_neg_integer()
def calc(input) when positive_integer?(input), do: calc(input, @initial_steps)
defp calc(@terminating_number, steps), do: steps

defp calc(input, steps) when Integer.is_even(input) do
input
|> n_div_two()
|> calc(steps + 1)
end

defp calc(input, steps) do
input
|> three_n_plus_one()
|> calc(steps + 1)
end

defp n_div_two(n), do: div(n, 2)
defp three_n_plus_one(n), do: 3 * n + 1
end``````