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Published at Sep 01 2020
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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
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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