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.

Starting with n = 12, the steps would be as follows:

- 12
- 6
- 3
- 10
- 5
- 16
- 8
- 4
- 2
- 1

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

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

```
(ns collatz-conjecture-test
(:require [clojure.test :refer [deftest is testing]]
[collatz-conjecture :refer [collatz]]))
(deftest steps-for-1
(testing "zero steps for one"
(is (= 0 (collatz 1)))))
(deftest steps-for-16
(testing "divide if even"
(is (= 4 (collatz 16)))))
(deftest steps-for-12
(testing "even and odd steps"
(is (= 9 (collatz 12)))))
(deftest steps-for-1000000
(testing "Large number of even and odd steps"
(is (= 152 (collatz 1000000)))))
(deftest steps-for-0
(testing "zero is an error"
(is (thrown? IllegalArgumentException
(collatz 0)))))
(deftest steps-for-negative
(testing "negative value is an error"
(is (thrown? IllegalArgumentException
(collatz -15)))))
```

```
(ns collatz-conjecture)
(defn collatz
([n]
(when (< n 1) (throw (IllegalArgumentException.)))
(collatz n 0))
([n a]
(case n
1 a
(recur
(if (even? n) (/ n 2) (inc (* n 3)))
(inc a)))))
```

A huge amount can be learnt from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that I could read more about to develop my understanding?