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maclov1n's solution

to Collatz Conjecture in the Julia Track

Published at Oct 01 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

Returns the number of steps required to arrive at
1 following the steps described by the Collatz conjecture.
"""
function collatz_steps(n::Integer)
	n <= 0 && throw(DomainError("$n <= 0"))
	
	function next_collatz(m::Integer)
		return iseven(m) ? div(m, 2) : 3 * m + 1
	end
	
	remainder = n
	steps = 0
	while steps < 10^6
		isone(remainder) && return steps
		remainder = next_collatz(remainder)
		steps += 1
	end
	throw(OverflowError("cannot converge"))
end

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