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Published at Jan 15 2020
·
2 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.

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

- 12
- 6
- 3
- 10
- 5
- 16
- 8
- 4
- 2
- 1

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

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

drop down menu.

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

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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`

.

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

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

```
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(AValue:integer):Integer;
implementation
// SOLUTION: Recursive call
function collatzSteps(AValue:integer):Integer;
begin
// Numbers <= 0 not allowed
if (AValue <= 0) then
raise EIllegalNumber.Create('error: Only positive numbers are allowed');
// for 1 => 0 steps
if (AValue = 1) then begin
Result := 0;
Exit;
end;
// Others numbers (use recursive call) and increment the number of steps returned
if Odd(AValue) then
Result := collatzSteps((Avalue * 3) + 1) + 1
else
Result := collatzSteps(AValue div 2) + 1;
end;
end.
```

Using a WHILE structure

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## Community comments

This is very clean solution. How could it guard against potential stack overflow issues if there are too many steps to get

`AValue`

down to 1?Hi Ray. For too large numbers I (many steps) think the solution using WHILE would be better.