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v2000vova's solution

to Perfect Numbers in the Delphi Pascal Track

Published at Apr 10 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

Submitting Incomplete Solutions

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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
SysUtils,
System.Generics.Collections;

type
ENotNaturalNumber = class(Exception);

type
TClassifyResult = (Deficient, Perfect, Abundant);

type
PerfectNumber = class
class function Classify(aValue : Int64) : TClassifyResult;
end;

implementation

class function PerfectNumber.Classify(aValue : Int64) : TClassifyResult;
var
ModValue, DivValue : Int64;
Number : Int64;
Sum : Int64;

begin
if aValue <= 0 then
raise ENotNaturalNumber.Create('Classification is only possible for natural numbers.');
{}
if aValue = 1 then begin
Result := Deficient;
Exit;
end;
{}
Sum    := 1;
Number := 2;
{}
while Number < Sqrt(aValue) do begin
ModValue := aValue mod Number;
DivValue := aValue div Number;
{}
if ModValue = 0 then begin
Inc(Sum, Number);
if DivValue <> Number then
Inc(Sum, DivValue);
{}
if Sum > aValue then begin
Result := Abundant;
Exit;
end;
end;
Inc(Number);
end;
{}
if Sum > aValue then
Result := Abundant
else if Sum < aValue then
Result := Deficient
else
Result := Perfect;
end;

end.``````

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