# dgeiger's solution

## 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

In order to run the tests for this track, you will need to install DUnitX. Please see the installation instructions for more information.

If Delphi is properly installed, and `*.dpr` file types have been associated with Delphi, then double clicking the supplied `*.dpr` file will start Delphi and load the exercise/project. `control + F9` is the keyboard shortcut to compile the project or pressing `F9` will compile and run the project.

Alternatively you may opt to start Delphi and load your project via. the `File` drop down menu.

### When Questions Come Up

We monitor the Pascal-Delphi support room on gitter.im to help you with any questions that might arise.

### Submitting Exercises

Note that, when trying to submit an exercise, make sure the exercise file you're submitting is in the `exercism/delphi/<exerciseName>` directory.

For example, if you're submitting `ubob.pas` for the Bob exercise, the submit command would be something like `exercism submit <path_to_exercism_dir>/delphi/bob/ubob.pas`.

## 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 may request help from a mentor.

### 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.');

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.``````