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# SergiiVlasiuk's solution

## to Perfect Numbers in the Scala Track

Published at Aug 17 2019 · 0 comments
Instructions
Test suite
Solution

Determine if a number is perfect, abundant, or deficient based on Nicomachus' (60 - 120 CE) classification scheme for natural numbers.

The Greek mathematician Nicomachus devised a classification scheme for natural numbers, identifying each as belonging uniquely to the categories of perfect, abundant, or deficient based on their aliquot sum. The aliquot sum is defined as the sum of the factors of a number not including the number itself. For example, the aliquot sum of 15 is (1 + 3 + 5) = 9

• Perfect: aliquot sum = number
• 6 is a perfect number because (1 + 2 + 3) = 6
• 28 is a perfect number because (1 + 2 + 4 + 7 + 14) = 28
• Abundant: aliquot sum > number
• 12 is an abundant number because (1 + 2 + 3 + 4 + 6) = 16
• 24 is an abundant number because (1 + 2 + 3 + 4 + 6 + 8 + 12) = 36
• Deficient: aliquot sum < number
• 8 is a deficient number because (1 + 2 + 4) = 7
• Prime numbers are deficient

Implement a way to determine whether a given number is perfect. Depending on your language track, you may also need to implement a way to determine whether a given number is abundant or deficient.

The Scala exercises assume an SBT project scheme. The exercise solution source should be placed within the exercise directory/src/main/scala. The exercise unit tests can be found within the exercise directory/src/test/scala.

To run the tests simply run the command `sbt test` in the exercise directory.

For more detailed info about the Scala track see the help page.

## Source

Taken from Chapter 2 of Functional Thinking by Neal Ford. http://shop.oreilly.com/product/0636920029687.do

## Submitting Incomplete Solutions

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

### PerfectNumbersTest.scala

``````import org.scalatest.{Matchers, FunSuite}

/** @version 1.1.0 */
class PerfectNumbersTest extends FunSuite with Matchers {

test("Smallest perfect number is classified correctly") {
PerfectNumbers.classify(6) should be(Right(NumberType.Perfect))
}

test("Medium perfect number is classified correctly") {
pending
PerfectNumbers.classify(28) should be(Right(NumberType.Perfect))
}

test("Large perfect number is classified correctly") {
pending
PerfectNumbers.classify(33550336) should be(Right(NumberType.Perfect))
}

test("Smallest abundant number is classified correctly") {
pending
PerfectNumbers.classify(12) should be(Right(NumberType.Abundant))
}

test("Medium abundant number is classified correctly") {
pending
PerfectNumbers.classify(30) should be(Right(NumberType.Abundant))
}

test("Large abundant number is classified correctly") {
pending
PerfectNumbers.classify(33550335) should be(Right(NumberType.Abundant))
}

test("Smallest prime deficient number is classified correctly") {
pending
PerfectNumbers.classify(2) should be(Right(NumberType.Deficient))
}

test("Smallest non-prime deficient number is classified correctly") {
pending
PerfectNumbers.classify(4) should be(Right(NumberType.Deficient))
}

test("Medium deficient number is classified correctly") {
pending
PerfectNumbers.classify(32) should be(Right(NumberType.Deficient))
}

test("Large deficient number is classified correctly") {
pending
PerfectNumbers.classify(33550337) should be(Right(NumberType.Deficient))
}

test("Edge case (no factors other than itself) is classified correctly") {
pending
PerfectNumbers.classify(1) should be(Right(NumberType.Deficient))
}

test("Zero is rejected (not a natural number)") {
pending
PerfectNumbers.classify(0) should be(
Left("Classification is only possible for natural numbers."))
}

test("Negative integer is rejected (not a natural number)") {
pending
PerfectNumbers.classify(-1) should be(
Left("Classification is only possible for natural numbers."))
}
}``````
``````import scala.util.Either

object PerfectNumbers {
def classify(number: Int): Either[String, NumberType] = {
if (number <= 0) Left("Classification is only possible for natural numbers.")
else {
println(s"number=\$number factors(number)" + factors(number) + " " + factors(number).sum)
factors(number).sum match {
case p if p == number => Right(NumberType.Perfect)
case a if a > number => Right(NumberType.Abundant)
case _ => Right(NumberType.Deficient)
}
}
}

private def factors(num: Int): IndexedSeq[Int] = (1 to num / 2).filter {
num % _ == 0
}
}

sealed abstract class NumberType

object NumberType {

case object Perfect extends NumberType

case object Abundant extends NumberType

case object Deficient extends NumberType

}``````

### What can you learn from this solution?

A huge amount can be learned from reading other peopleâ€™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?