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to Collatz Conjecture in the Clojure Track

Published at Jul 13 2018 · 0 comments
Test suite

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:

  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.


An unsolved problem in mathematics named after mathematician Lothar Collatz https://en.wikipedia.org/wiki/3x_%2B_1_problem

Submitting Incomplete Solutions

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(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
   (when (< n 1) (throw (IllegalArgumentException.)))
   (collatz n 0))
  ([n a]
   (case n
     1 a
       (if (even? n) (/ n 2) (inc (* n 3)))
       (inc a)))))

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