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to Perfect Numbers in the Delphi Pascal Track

Published at Sep 02 2020 · 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.

Testing

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Source

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

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uPerfectNumbersTests.pas

unit uPerfectNumbersTests;

interface
uses
  DUnitX.TestFramework;

const
  CanonicalVersion = '1.1.0.1';

type

  [TestFixture]
  PerfectNumbersTest = class(TObject)
  public
    [Test]
//    [Ignore('Comment the "[Ignore]" statement to run the test')]
    procedure Smallest_perfect_number_is_classified_correctly;

    [Test]
    [Ignore]
    procedure Medium_perfect_number_is_classified_correctly;

    [Test]
    [Ignore]
    procedure Large_perfect_number_is_classified_correctly;

    [Test]
    [Ignore]
    procedure Smallest_abundant_number_is_classified_correctly;

    [Test]
    [Ignore]
    procedure Medium_abundant_number_is_classified_correctly;

    [Test]
    [Ignore]
    procedure Large_abundant_number_is_classified_correctly;

    [Test]
    [Ignore]
    procedure Smallest_prime_deficient_number_is_classified_correctly;

    [Test]
    [Ignore]
    procedure Smallest_non_prime_deficient_number_is_classified_correctly;

    [Test]
    [Ignore]
    procedure Medium_deficient_number_is_classified_correctly;

    [Test]
    [Ignore]
    procedure Large_deficient_number_is_classified_correctly;

    [Test]
    [Ignore]
    procedure Edge_case_no_factors_other_than_itself_is_classified_correctly;

    [Test]
    [Ignore]
    procedure Zero_is_rejected_not_a_natural_number;

    [Test]
    [Ignore]
    procedure Negative_integer_is_rejected_not_a_natural_number;
  end;

implementation
uses uPerfectNumbers;

procedure PerfectNumbersTest.Smallest_prime_deficient_number_is_classified_correctly;
begin
  Assert.AreEqual(Deficient, PerfectNumber.Classify(2));
end;

procedure PerfectNumbersTest.Smallest_non_prime_deficient_number_is_classified_correctly;
begin
  Assert.AreEqual(Deficient, PerfectNumber.Classify(4));
end;

procedure PerfectNumbersTest.Medium_deficient_number_is_classified_correctly;
begin
  Assert.AreEqual(Deficient, PerfectNumber.Classify(32));
end;

procedure PerfectNumbersTest.Large_deficient_number_is_classified_correctly;
begin
  Assert.AreEqual(Deficient, PerfectNumber.Classify(33550337));
end;

procedure PerfectNumbersTest.Edge_case_no_factors_other_than_itself_is_classified_correctly;
begin
  Assert.AreEqual(Deficient, PerfectNumber.Classify(1));
end;

procedure PerfectNumbersTest.Smallest_perfect_number_is_classified_correctly;
begin
  Assert.AreEqual(Perfect, PerfectNumber.Classify(6));
end;

procedure PerfectNumbersTest.Medium_perfect_number_is_classified_correctly;
begin
  Assert.AreEqual(Perfect, PerfectNumber.Classify(28));
end;

procedure PerfectNumbersTest.Large_perfect_number_is_classified_correctly;
begin
  Assert.AreEqual(Perfect, PerfectNumber.Classify(33550336));
end;

procedure PerfectNumbersTest.Smallest_abundant_number_is_classified_correctly;
begin
  Assert.AreEqual(Abundant, PerfectNumber.Classify(12));
end;

procedure PerfectNumbersTest.Medium_abundant_number_is_classified_correctly;
begin
  Assert.AreEqual(Abundant, PerfectNumber.Classify(30));
end;

procedure PerfectNumbersTest.Large_abundant_number_is_classified_correctly;
begin
  Assert.AreEqual(Abundant, PerfectNumber.Classify(33550335));
end;

procedure PerfectNumbersTest.Zero_is_rejected_not_a_natural_number;
var MyProc: TTestLocalMethod;
begin
  MyProc := procedure
            begin
              PerfectNumber.Classify(0);
            end;

  assert.WillRaiseWithMessage(MyProc, ENotNaturalNumber, 'Classification is only possible for natural numbers.');
end;

procedure PerfectNumbersTest.Negative_integer_is_rejected_not_a_natural_number;
var MyProc: TTestLocalMethod;
begin
  MyProc := procedure
            begin
              PerfectNumber.Classify(-1);
            end;

  assert.WillRaiseWithMessage(MyProc, ENotNaturalNumber, 'Classification is only possible for natural numbers.');
end;

initialization
  TDUnitX.RegisterTestFixture(PerfectNumbersTest);
end.
unit uPerfectNumbers;

interface

uses
  System.SysUtils;

type
  TAliquot = (Perfect, Abundant, Deficient);

  ENotNaturalNumber = class(Exception);

  PerfectNumber = class
    private

    public
      class function Classify(Number: Integer): TAliquot;

  end;

implementation

{ TPerfectNumber }

function Even(Number: Integer): Boolean;
begin
  Result := (Number div 2) = 0;
end;

class function PerfectNumber.Classify(Number: Integer): TAliquot;
var
  Index: Integer;
  Sum: Integer;
begin
  // Aliquot numbers must be natural numbers, so throw an exception it
  // the number is non-positive
  if Number < 1 then
    raise ENotNaturalNumber.Create('Classification is only possible for natural numbers.');

  // Start with a zero sum
  Sum := 0;

  // Scan through the integers from 1 to Number - 1 looking for factors
  for Index := 1 to  Number - 1 do
    // Is this number a factor
    if (Number mod Index) = 0 then
      // Yes, add it to the sum
      Sum := Sum + Index;

  // If the sum of the factors is the same as the number to test,
  if Sum = Number then
    // it's a perfect aliquot,
    Result := Perfect
  else
    // if the sum of the factors is greater than the number to test,
    if Sum > Number then
      // it's an abundant aliquot.
      Result := Abundant
    else
      // Otherwise, it's deficient.
      Result := Deficient;
end;

end.

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