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to Sieve in the Delphi Pascal Track

Published at May 25 2019 · 0 comments
Instructions
Test suite
Solution

Note:

This exercise has changed since this solution was written.

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

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

uSieveTest.pas

unit uSieveTest;

interface
uses
  DUnitX.TestFramework, uSieve;

const
  CanonicalVersion = '1.1.0';

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

type
  TSieve = class
    class function Primes(limit: Integer): TArray<Integer>;
  end;

implementation

uses
  System.Sysutils,
  System.Generics.Collections;

{ TSieve }

class function TSieve.Primes(Limit: Integer): TArray<Integer>;
var
  Numbers: TList<Integer>;
  Current: Integer;

  procedure FillNumbers;
  begin
    Numbers := TList<Integer>.Create;
    for var i := 2 to Limit do
      Numbers.Add(i);
  end;

  procedure RemoveNonprimes;
  begin
    var NonPrime := Current + Current;
    while NonPrime <= Limit do
    begin
      Numbers.Remove(NonPrime);
      NonPrime := NonPrime + Current;
    end;
  end;

begin
  if Limit < 2 then Exit;
  FillNumbers;
  repeat
    Current := Numbers.First;
    Result := Result + [Current];
    Numbers.Remove(Current);
    RemoveNonprimes;
  until Numbers.Count = 0;
  Numbers.DisposeOf;
end;

end.

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