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dgeiger's solution

to Collatz Conjecture in the Delphi Pascal Track

Published at Aug 31 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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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

function Even(aNumber: Integer): Boolean;
begin
  // We'll make this a function for simplicity
  Result := (aNumber mod 2) = 0;
end;

function collatzSteps(aNumber: Integer): Integer;
begin
  // By definition, aNumber must be a positive integer, so if aNumber isn't
  // a positive integer we need to raise out custom error
  if aNumber < 1 then
    raise EIllegalNumber.Create('error: Only positive numbers are allowed');

  // If aNumber is one, we're finished and can stop recursing
  if aNumber = 1 then
    begin
      // Return zero, since we aren't doing any more steps
      Result := 0;

      // Exit the function
      Exit;
    end;

  // We created an Even() function for simplicity, so we'll use it here
  if Even(aNumber) then
    // Add one to the number of steps for aNumber/2
    Result := collatzSteps(aNumber div 2) + 1
  else
    // Add one to the number of steps for (aNumber*3)+1
    Result := collatzSteps((aNumber * 3) + 1) + 1;
end;

end.

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