Problem Set #1: Introductory Exercises

Activity Description

Solve with your team the Clojure exercises described in this problem set. Make sure each function passes all the unit tests.

Create a namespace called introductory. At the begining of the file add the following code in order to declare the namespace and import the required external functions:

(ns introductory
  (:require [clojure.test :refer [deftest is run-tests]])
  (:require [clojure.math.numeric-tower :refer [sqrt]]))

and at the end add:

(run-tests)

All the code you write should go between these two instructions.

1. Write a function called gibibytes->bytes that takes a number of \(\textit{gibibytes}\) and returns its corresponding conversion to bytes.

   Remember that:

   • 1 KiB (kibibyte) = \(2^{10}\) bytes = 1,024 bytes
   • 1 MiB (mebibyte) = \(2^{20}\) bytes = 1,024 kibibytes
   • 1 GiB (gibibyte) = \(2^{30}\) bytes = 1,024 mebibytes

   Unit tests:

   (deftest test-gibibytes->bytes
     (is (= 0 (gibibytes->bytes 0)))
     (is (= 1073741824 (gibibytes->bytes 1)))
     (is (= 5368709120 (gibibytes->bytes 5)))
     (is (= 26415122612224 (gibibytes->bytes 24601))))

2. Write a function called f2c that takes a temperature \(F\) in degrees Fahrenheit and converts it to degrees Celsius. Unit tests:

   (deftest test-f2c
     (is (= 100.0 (f2c 212.0)))
     (is (= 0.0 (f2c 32.0)))
     (is (= -40.0 (f2c -40.0))))

   TIP: If \(F\) is a temperature in degrees Fahrenheit, to convert it to \(C\) degrees Celsius we must use the following formula:

   $$ C = \frac{5 (F - 32)}{9} $$

3. Write a function called sign that takes an integer value \(n\). It returns -1 if \(n\) is negative, 1 if \(n\) is positive greater than zero, or 0 if n is zero. Unit tests:

   (deftest test-sign
     (is (= -1 (sign -5)))
     (is (= 1 (sign 10)))
     (is (= 0 (sign 0))))
   

4. Write a function called roots that returns a vector containing the two possible roots that solve a quadratic equation given its three coefficients (\(a\), \(b\), \(c\)) using the following formula:

   $$ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} $$

   Unit tests:

   (deftest test-roots
     (is (= [-1 -1] (roots 2 4 2)))
     (is (= [0 0] (roots 1 0 0)))
     (is (= [-1/4 -1] (roots 4 5 1))))
   

   TIP: To obtain the square root of a number, use the already imported sqrt function defined in the clojure.math.numeric-tower namespace.

5. The BMI (body mass index) is used to determine if a person's weight and height proportion is adequate. The BMI may be calculated using the following formula:

   $$ \textit{BMI} = \frac{\textit{weight}}{\textit{height}^2} $$

   Where \( \textit{weight} \) should be given in kilograms and \( \textit{height} \) in meters. The following table shows how different BMI ranges are classified:

   BMI range	Description
   BMI < 20	underweight
   20 ≤ BMI < 25	normal
   25 ≤ BMI < 30	obese1
   30 ≤ BMI < 40	obese2
   40 ≤ BMI	obese3

   Write a function called bmi that takes two arguments: weight and height. It should return a symbol that represents the corresponding BMI description computed from its input.

   Unit tests:

   (deftest test-bmi
     (is (= 'underweight (bmi 45 1.7)))
     (is (= 'normal (bmi 55 1.5)))
     (is (= 'obese1 (bmi 76 1.7)))
     (is (= 'obese2 (bmi 81 1.6)))
     (is (= 'obese3 (bmi 120 1.6))))
   

6. Write a function called type-of-triangle that takes as input three numeric values that represent the sides of a triangle and returns a symbol indicating if the triangle is is equilateral, isosceles, or scalene.

   Properties of a triangle

   • A triangle is said to be equilateral if all its sides are equal.
   • A triangle is said to be isosceles if exactly two of its sides are equal.
   • A triangle is said to be scalene if none of its sides are equal.

   Unit tests:

   (deftest test-type-of-triangle
     (is (= 'equilateral (type-of-triangle 3 3 3)))
     (is (= 'equilateral (type-of-triangle 4.2 4.2 4.2)))
     (is (= 'isosceles (type-of-triangle 4 4 3)))
     (is (= 'isosceles (type-of-triangle 4 3 4)))
     (is (= 'isosceles (type-of-triangle 3 4 4)))
     (is (= 'scalene (type-of-triangle 1 2 3)))
     (is (= 'scalene (type-of-triangle 7.1 6.4 9.2))))
   

Deliverables

The program source file must include at the top the authors’ personal information (student ID and name) within comments. For example:

;----------------------------------------------------------
; Problem Set #1: Introductory Exercises
; Date: February 17, 2022.
; Authors:
;          A01770771 Sylvie Laufeydottir
;          A01777771 Loki Laufeyson
;----------------------------------------------------------

Also, each function should include a documentation string (docstring) with a brief description of its behavior. For example:

(defn max2
  "Returns the largest of the two numbers x and y."
  [x y]
  (if (> x y) x y))

Only one team member needs to upload the file.

Due date is Wednesday, February 23.

Evaluation

This activity will be evaluated using the following criteria:

-10	The program doesn't contain within comments the author’s personal information.
-30	A docstring is missing in one or more functions.
10	The program contains syntax errors.
1	The program was plagiarized in whole or in part.
10-100	Depending on the amount of exercises that were solved correctly.