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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(n÷2, steps+1)
    else
        collatz_steps(3n+1, steps+1)
    end
end

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