Module 01 Project

Introduction

In this PA you will write a few Ruby methods to practice Ruby syntax and explore the standard Ruby classes.

Project starter files: p1.zip

Requirements

factors(n) — must return an Array of all the factors of n, in order and without duplicates. The result must be [] if n < 1. For examples, factors(1) == [1] and factors(12) == [1,2,3,4,6,12].

primes(n) — must return an Array of all prime numbers less than or equal to n, in order and without duplicates. primes must return [] if n < 2. For examples, primes(10) == [2,3,5,7].

prime_factors(n) — must return an Array of all prime factors of n, in order and without duplicates. prime_factors must return [] if n < 2. For examples, prime_factors(1) == [] and prime_factors(12) == [2,3].

perfects(n) — must return an Array of all perfect numbers less than or equal to n, in order and without duplicates. A perfect number is one whose factors sum to twice the number. For example, perfects(10) == [6] (because the factors of 6 are 1, 2, 3, and 6, and these sum to 12).

pythagoreans(n) — must return an Array of Arrays of Pythagorean triples whose elements are all less than or equal to n, in order without duplicates, and such that each triple is ordered. A Pythagorean triple is three positive integers (x, y, z) such that x² + y² = z². For example, pythagoreans(15) == [[3,4,5], [5,12,13], [6,8,10], [9,12,15]].

The Integer iterator upto() is quite useful in solving these problems. Alternatively, you can use Ranges. The Array select method is also useful.

Some test routines are included in test.rb. However, your submission will be graded based on additional tests not provided to you, so you should write your own test cases as well.

For this assignment, you may NOT use any classes or methods that are not in the Ruby Core. If you are unsure about a particular class or method, you can consult the documentation.

Submission

Your program must contain implementations of the five methods described above. You must name your Ruby script file p1.rb. You must put your name in a comment at the top of the file. As usual, decompose your methods to make them more readable, use good names, indent properly (indentation is conventionally two spaces in Ruby), and so on. You will partly be graded on the readability of your code but mostly on whether it works.

Submit ONLY r1.rb to the appropriate assignment on Canvas by the deadline.