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dgeiger's solution

to Nth Prime in the Delphi Pascal Track

Published at Sep 06 2020 · 0 comments
Instructions
Test suite
Solution

Given a number n, determine what the nth prime is.

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

If your language provides methods in the standard library to deal with prime numbers, pretend they don't exist and implement them yourself.

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

A variation on Problem 7 at Project Euler http://projecteuler.net/problem=7

Submitting Incomplete Solutions

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

uNthPrimeTests.pas

unit uNthPrimeTests;

interface

uses
  DUnitX.TestFramework;

const
  CanonicalVersion = '2.1.0.1';

type
  [TestFixture]
  TNthPrimeTest = class(TObject) 
  public
    [Test]
//    [Ignore('Comment the "[Ignore]" statement to run the test')]
    procedure there_is_no_zeroth_prime;

    [Test]
    [Ignore]
    procedure first_prime;

    [Test]
    [Ignore]
    procedure second_prime;

    [Test]
    [Ignore]
    procedure sixth_prime;

    [Test]
    [Ignore]
    procedure big_prime;
  end;

implementation

uses
  System.SysUtils, uNthPrime;


procedure TNthPrimeTest.first_prime;
begin
  Assert.AreEqual(2, NthPrime(1));
end;

procedure TNthPrimeTest.second_prime;
begin
  Assert.AreEqual(3, NthPrime(2));
end;

procedure TNthPrimeTest.sixth_prime;
begin
  Assert.AreEqual(13, NthPrime(6));
end;

procedure TNthPrimeTest.big_prime;
begin
  Assert.AreEqual(104743, NthPrime(10001));
end;

procedure TNthPrimeTest.there_is_no_zeroth_prime;
begin
  Assert.WillRaiseWithMessage(procedure begin NthPrime(0); end , EArgumentOutOfRangeException, 'there is no zeroth prime');
end;

initialization
  TDUnitX.RegisterTestFixture(TNthPrimeTest);
end.
unit uNthPrime;

interface

uses
  System.Math, System.SysUtils;

type
  EArgumentOutOfRangeException = class(Exception);

function NthPrime(Number: Integer): Integer;

implementation

function Sieve(Candidate: Integer): Boolean;
var
  Factor: Integer;
begin
  // Since primes are rare, default to non-prime
  Result := False;

  // A prime number must be a positive integer greater than one. If the
  // candidate number doesn't meet this criterion, leave early.
  if Candidate < 2 then
    exit;

  // If Candidate is two, we can short cut here, since two is the first prime,
  // and is also the only even prime.
  if Candidate = 2 then
    begin
      Result := True;

      exit;
    end;

  // Three is the first odd prime, so we start there
  Factor := 3;

  // We only need to check 3..Sqrt(Candidate). As part of this we need to
  // for Candidate to be a real number for Sqrt().
  while Factor <= Trunc(Sqrt(Candidate * 1.0)) do
    begin
      // Is this factor a prime factor?
      if Candidate mod Factor = 0 then
        // This factor is a factor for Candidate, so Candidate isn't prime.
        Exit;

      // Try the next possible factor
      Inc(Factor, 2);
    end;

  // If we got this far, Candidate is prime
  Result := True;
end;

function NthPrime(Number: Integer): Integer;
var
  Count: Integer;
  Current: Integer;
begin
  // The count of primes must be a positive integer.
  if Number < 1 then
    raise EArgumentOutOfRangeException.Create('there is no zeroth prime');

  // We handle the first prime differently than all others. The first prime is
  // two, which is also the only even prime.
  if Number = 1 then
    begin
      Result := 2;

      Exit;
    end;

  // We already know the first prime, so we set the count to one. This is done
  // to simplify the code in the loop.
  Count := 1;

  // Set the current candidate to start at one
  Current := 1;

  // We need to keep looping until we find the correct prime
  while Count < Number do
    begin
      // Since we know all remaining primes are odd, we move to the
      // next odd candidate
      Inc(Current, 2);

      // Is the current candidate prime?
      if Sieve(Current) then
        // Yes - increment the count of primes
        Inc(Count);
    end;

  // We found the correct prime, so return it
  Result := Current;
end;

end.

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