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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

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

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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

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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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