# BooleanCat's solution

## to Collatz Conjecture in the Lua Track

Published at Jan 05 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 the tests

To run the tests, run the command `busted` from within the exercise directory.

## Further information

For more detailed information about the Lua track, including how to get help if you're having trouble, please visit the exercism.io Lua language page.

## 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.lua

``````local conjecture = require('collatz-conjecture')

describe('collatz-conjecture', function()
it('zero steps for one', function()
assert.are.equal(0, conjecture(1))
end)

it('divide if even', function()
assert.are.equal(4, conjecture(16))
end)

it('even and odd steps', function()
assert.are.equal(9, conjecture(12))
end)

it('large number of even and odd steps', function()
assert.are.equal(152, conjecture(1000000))
end)

it('zero is an error', function()
assert.has_error(
function() conjecture(0) end,
'Only positive numbers are allowed'
)
end)

it('negative value is an error', function()
assert.has_error(
function() conjecture(-15) end,
'Only positive numbers are allowed'
)
end)
end)``````
``````return function(n)
assert(n > 0, 'Only positive numbers are allowed')

function collatz(n)
if n == 1 then return 0 end
if n % 2 == 0 then return 1 + collatz(n / 2) end
return 1 + collatz(3 * n + 1)
end

return collatz(n)
end``````