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to Collatz Conjecture in the Delphi Pascal Track

Published at Sep 03 2020 · 0 comments
Instructions
Test suite
Solution

The Collatz Conjecture or 3x+1 problem can be summarized as follows:

Take any positive integer n. If n is even, divide n by 2 to get n / 2. If n is odd, multiply n by 3 and add 1 to get 3n + 1. Repeat the process indefinitely. The conjecture states that no matter which number you start with, you will always reach 1 eventually.

Given a number n, return the number of steps required to reach 1.

Examples

Starting with n = 12, the steps would be as follows:

  1. 12
  2. 6
  3. 3
  4. 10
  5. 5
  6. 16
  7. 8
  8. 4
  9. 2
  10. 1

Resulting in 9 steps. So for input n = 12, the return value would be 9.

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

An unsolved problem in mathematics named after mathematician Lothar Collatz https://en.wikipedia.org/wiki/3x_%2B_1_problem

Submitting Incomplete Solutions

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uCollatzconjectureTests.pas

unit uCollatzconjectureTests;

interface
uses
  DUnitX.TestFramework;

const
  CanonicalVersion = '1.2.0.1';

type
  [TestFixture]
  CollatzconjectureTest = class(TObject)
  public
    [Testcase('Zero steps for one', '1, 0')]
//    [Ignore('Comment the "[Ignore]" statement to run the test')]
    procedure Zero_steps_for_one(const aNumber: integer; const aExpected: integer);

    [Testcase('Divide if even','16, 4')]
    [Ignore]
    procedure Divide_if_even(const aNumber: integer; const aExpected: integer);

    [Testcase('Even and odd steps','12, 9')]
    [Ignore]
    procedure Even_and_odd_steps(const aNumber: integer; const aExpected: integer);

    [Testcase('Large number of even and odd steps', '1000000, 152')]
    [Ignore]
    procedure Large_number_of_even_and_odd_steps(const aNumber: integer; const aExpected: integer);

    [Testcase('Zero is an error', '0,error: Only positive numbers are allowed')]
    [Ignore]
    procedure Zero_is_an_error(const aNumber: integer; const aExpected: string);

    [Testcase('Negative value is an error', '-15,error: Only positive numbers are allowed')]
    [Ignore]
    procedure Negative_value_is_an_error(const aNumber: integer; const aExpected: string);
  end;

implementation
uses uCollatzconjecture;

procedure CollatzconjectureTest.Zero_steps_for_one(const aNumber: integer; const aExpected: integer);
begin
  Assert.AreEqual(aExpected, collatzSteps(aNumber));
end;

procedure CollatzconjectureTest.Divide_if_even(const aNumber: integer; const aExpected: integer);
begin
  Assert.AreEqual(aExpected, collatzSteps(aNumber));
end;

procedure CollatzconjectureTest.Even_and_odd_steps(const aNumber: integer; const aExpected: integer);
begin
  Assert.AreEqual(aExpected, collatzSteps(aNumber));
end;

procedure CollatzconjectureTest.Large_number_of_even_and_odd_steps(const aNumber: integer; const aExpected: integer);
begin
  Assert.AreEqual(aExpected, collatzSteps(aNumber));
end;

procedure CollatzconjectureTest.Zero_is_an_error(const aNumber: integer; const aExpected: string);
var MyProc: TTestLocalMethod;
begin
  MyProc := procedure
            begin
              collatzSteps(aNumber);
            end;

  Assert.WillRaiseWithMessage(MyProc, EIllegalNumber, aExpected);
end;

procedure CollatzconjectureTest.Negative_value_is_an_error(const aNumber: integer; const aExpected: string);
var MyProc: TTestLocalMethod;
begin
  MyProc := procedure
            begin
              collatzSteps(aNumber);
            end;

  Assert.WillRaiseWithMessage(MyProc, EIllegalNumber, aExpected);
end;

initialization
  TDUnitX.RegisterTestFixture(CollatzconjectureTest);
end.
unit uCollatzconjecture;

interface

uses
  System.SysUtils;
type
  EIllegalNumber = Class(Exception);

function collatzSteps(aNumber : Integer) : Integer;


implementation

{ TCollatzconjecture }

function collatzSteps(aNumber: Integer): Integer;
var
  lRemainder : Integer;
  lSteps : Integer;
begin
  lSteps := 0;
  if aNumber = 1 then
    Result := 0
  else
  begin
  if aNumber > 0 then
  begin
    if Odd(aNumber) then
    begin
      lRemainder := aNumber*3 +1;
      lSteps := lSteps +1;
    end
    else
    begin
      lRemainder := aNumber div 2;
      lSteps := lSteps +1;
    end;
  end
  else raise EIllegalNumber.Create('error: Only positive numbers are allowed');

  end;
  while (lRemainder > 1) and not (aNumber = 1) do
  begin
    if Odd(lRemainder) then
    begin
      lRemainder := lRemainder*3 +1;
      lSteps := lSteps +1;
    end
    else
    begin
      lRemainder := lRemainder div 2;
      lSteps := lSteps +1;
    end;
    if lRemainder = 1 then
      Result := lSteps;
  end;

end;

end.

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