ðŸŽ‰ Exercism Research is now launched. Help Exercism, help science and have some fun at research.exercism.io ðŸŽ‰

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).

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

If Delphi is properly installed, and `*.dpr`

file types have been associated with Delphi, then double clicking the supplied `*.dpr`

file will start Delphi and load the exercise/project. `control + F9`

is the keyboard shortcut to compile the project or pressing `F9`

will compile and run the project.

Alternatively you may opt to start Delphi and load your project via. the `File`

drop down menu.

We monitor the Pascal-Delphi support room on gitter.im to help you with any questions that might arise.

Note that, when trying to submit an exercise, make sure the exercise file you're submitting is in the `exercism/delphi/<exerciseName>`

directory.

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`

.

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

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

```
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.
```

A huge amount can be learned from reading other peopleâ€™s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

Level up your programming skills with 3,450 exercises across 52 languages, and insightful discussion with our volunteer team of welcoming mentors.
Exercism is
**100% free forever**.

## Community comments