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.
Starting with n = 12, the steps would be as follows:
Resulting in 9 steps. So for input n = 12, the return value would be 9.
An unsolved problem in mathematics named after mathematician Lothar Collatz https://en.wikipedia.org/wiki/3x_%2B_1_problem
This exercise has been tested on Julia versions >=1.0.
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
# 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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