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# cmcaine's solution

## to Collatz Conjecture in the Julia Track

Published at Sep 28 2020 · 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.

## Source

An unsolved problem in mathematics named after mathematician Lothar Collatz https://en.wikipedia.org/wiki/3x_%2B_1_problem

## Version compatibility

This exercise has been tested on Julia versions >=1.0.

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

### runtests.jl

``````# canonical data version: 1.2.1

using Test

include("collatz-conjecture.jl")

# canonical data
@testset "Canonical data" begin
@test collatz_steps(1) == 0
@test collatz_steps(16) == 4
@test collatz_steps(12) == 9
@test collatz_steps(1000000) == 152
@test_throws DomainError collatz_steps(0)
@test_throws DomainError collatz_steps(-15)
end``````
``````"""
collatz_steps(n)

The number of steps taken to reach one(n) following the 3n+1 conjecture process.
"""
function collatz_steps(n, steps=0)
if n < one(n)
throw(DomainError(n, "must be a positive integer"))
end
return if isone(n)
steps
elseif iseven(n)
collatz_steps(nÃ·2, steps+1)
else
collatz_steps(3n+1, steps+1)
end
end``````