# 4d47's solution

## to Collatz Conjecture in the Clojure Track

Published at Jul 13 2018 · 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

## Submitting Incomplete Solutions

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

### collatz_conjecture_test.clj

``````(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? Throwable
(collatz 0)))))

(deftest steps-for-negative
(testing "negative value is an error"
(is (thrown? Throwable
(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)))))``````