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Neftali's solution

to Sieve in the Delphi Pascal Track

Published at Dec 23 2020 · 0 comments
Instructions
Test suite
Solution

Use the Sieve of Eratosthenes to find all the primes from 2 up to a given number.

The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e. not prime) the multiples of each prime, starting with the multiples of 2. It does not use any division or remainder operation.

Create your range, starting at two and continuing up to and including the given limit. (i.e. [2, limit])

The algorithm consists of repeating the following over and over:

• take the next available unmarked number in your list (it is prime)
• mark all the multiples of that number (they are not prime)

Repeat until you have processed each number in your range.

When the algorithm terminates, all the numbers in the list that have not been marked are prime.

The wikipedia article has a useful graphic that explains the algorithm: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Notice that this is a very specific algorithm, and the tests don't check that you've implemented the algorithm, only that you've come up with the correct list of primes. A good first test is to check that you do not use division or remainder operations (div, /, mod or % depending on the language).

Testing

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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

Sieve of Eratosthenes at Wikipedia http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you may request help from a mentor.

uSieveTests.pas

``````unit uSieveTests;

interface
uses
DUnitX.TestFramework, uSieve;

const
CanonicalVersion = '1.1.0.1';

type

[TestFixture]
TSieveTest = class(TObject)
private
procedure CompareArrays(Array1, Array2: TArray<integer>);
public
[Test]
//    [Ignore('Comment the "[Ignore]" statement to run the test')]
procedure no_primes_under_two;

[Test]
[Ignore]
procedure find_first_prime;

[Test]
[Ignore]
procedure find_primes_up_to_10;

[Test]
[Ignore]
procedure limit_is_prime;

[Test]
[Ignore]
procedure find_primes_up_to_1000;
end;

implementation

uses
System.SysUtils;

procedure TSieveTest.CompareArrays(Array1, Array2: TArray<integer>);
var
i: integer;
begin
Assert.AreEqual(Length(Array1), Length(Array2), ' - Array lengths must be equal');
for i := Low(Array1) to High(Array1) do
Assert.AreEqual(Array1[i], Array2[i], format('Expecting element %d to = %d, Actual = %d',
[i, Array1[i], Array2[i]]));
end;

procedure TSieveTest.find_first_prime;
begin
CompareArrays([2], TSieve.Primes(2));
end;

procedure TSieveTest.find_primes_up_to_10;
begin
CompareArrays([2, 3, 5, 7], TSieve.Primes(10));
end;

procedure TSieveTest.find_primes_up_to_1000;
begin
CompareArrays([
2,   3,   5,   7,  11,  13,  17,  19,  23,  29,  31,  37,  41,  43,
47,  53,  59,  61,  67,  71,  73,  79,  83,  89,  97, 101, 103, 107,
109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181,
191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433,
439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521,
523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613,
617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809,
811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887,
907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997], TSieve.Primes(1000));
end;

procedure TSieveTest.limit_is_prime;
begin
CompareArrays([2, 3, 5, 7, 11, 13], TSieve.Primes(13));
end;

procedure TSieveTest.no_primes_under_two;
begin
CompareArrays([], TSieve.Primes(1));
end;

initialization
TDUnitX.RegisterTestFixture(TSieveTest);
end.``````
``````unit uSieve;

interface

uses
System.Generics.Collections;

type
TSieve = class
FNumber, FFirst:integer;
FPrimes:TArray<integer>;

// Create the initial arrayh
function ArrayInicial: TArray<integer>;
// detect is the process need to be stopped  (Power(index, 2)>ArrayTop )
function EndProcess:boolean;
// Mark multiples of a position
procedure MarcarMultiplos;
// detect if a position is marked  (Marked if value of position is NEGATIVE )
function IsMarked(const ANumber:integer):boolean;
// next Step of bucle
procedure NextStep;
// Array to return, without marked positions
function ArrayFinal: TArray<integer>;
public
constructor Create(const ANumber: integer);
class function Primes(const ANumber:integer):TArray<integer>;
end;

const
MARKED = -1;

implementation

uses
System.SysUtils, Math;

function TSieve.ArrayFinal: TArray<integer>;
var
i, j:integer;
begin
Result := [];
j := 1;
for i := 0 to (Length(FPrimes)-1) do begin
if not IsMarked(FPrimes[i]) then begin
SetLength(Result, j);
Result[j-1] := FPrimes[i];
Inc(j);
end;
end;
end;

function TSieve.ArrayInicial: TArray<integer>;
var
i:integer;
begin
SetLength(Result, FNumber-1);
for i := 1 to (FNumber-1) do
Result[i-1] := i+1;
end;

constructor TSieve.Create(const ANumber: integer);
begin
inherited Create;
FNumber := ANumber;
FFirst := 0;
FPrimes := ArrayInicial;
end;

function TSieve.EndProcess: boolean;
begin
Result := True;
if Length(FPrimes)>1 then
Result := (Power(FPrimes[FFirst], 2) > FNumber);
end;

function TSieve.IsMarked(const ANumber: integer): boolean;
begin
Result := (ANumber < 0);
end;

procedure TSieve.MarcarMultiplos;
var
i, j:integer;
begin
for i := (FFirst) to FNumber-2 do begin
j := Abs(FPrimes[FFirst] * FPrimes[i]);
if (j <= FNumber) then
if not IsMarked(FPrimes[j-2]) then
FPrimes[j-2] := (FPrimes[j-2] * -1);
end;
end;

procedure TSieve.NextStep;
begin
Inc(FFirst);
end;

class function TSieve.Primes(const ANumber: integer): TArray<integer>;
var
alg:TSieve;
begin
Result := [];
alg := TSieve.Create(ANumber);
try
while not alg.EndProcess do begin
alg.MarcarMultiplos;
alg.NextStep;
end;
Result := alg.ArrayFinal;
finally
FreeAndNil(alg)
end;

end;

end.``````

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