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to Sieve in the Delphi Pascal Track

Published at Sep 01 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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When Questions Come Up

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Submitting Exercises

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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
    public
      constructor Create;

      class function Primes(Limit: Integer): TArray<Integer>;

  end;

implementation

{ TSieve }

constructor TSieve.Create;
begin

end;

class function TSieve.Primes(Limit: Integer): TArray<Integer>;
var
  PrimeList: TList<Integer>;
  Primes: Integer;
  Index: Integer;
  PrimeArray: TArray<Integer>;
  Number: Integer;
begin
  // Create a list of integers
  PrimeList := TList<Integer>.Create;

  // Add the integers from 2 to Limit into the list
  for Index := 2 to Limit do
    PrimeList.Add(Index);

  // Create an integer array for the primes found and set it large enough to
  // hold all of them, since TArray<T> doesn't have a Delete().
  PrimeArray := TArray<Integer>.Create(0);
  SetLength(PrimeArray, Limit - 1);

  // We have no primes found yet, so set the count to 0
  Primes := 0;

  // While there are still numbers to test ...
  while PrimeList.Count > 0 do
    begin
      // Get the next number to text
      Number := PrimeList[0];

      // and remove it from the list.
      PrimeList.Delete(0);

      // Add the number to the array of primes
      PrimeArray[Primes] := Number;

      // Check the multiples equal or lower to the limit, and there are still
      // numbers in the list of numbers to check.
      while (Number <= Limit) and (PrimeList.Count > 0) do
        begin
          // Get the index of the number, if it's in the list
          Index := PrimeList.IndexOf(Number);

          // It's in the list if the index is non-negative
          if Index <> -1 then
            // It's in the list, so remove it
            PrimeList.Delete(Index);

          // Move to the next multiple of Number
          Number := Number + PrimeArray[Primes];
        end;

      // Increment the prime count
      Inc(Primes);
    end;

  // Set PrimeArray to be the proper length
  SetLength(PrimeArray, Primes);

  // Return the PrimeArray
  Result := PrimeArray;
end;

end.

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