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Published at Jul 13 2018
·
1 comment

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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.

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 can see how others have completed the exercise.

```
unit uCollatzconjectureTest;
interface
uses
DUnitX.TestFramework;
const
CanonicalVersion = '1.2.0';
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 = Exception;
function collatzSteps(const aNumber: integer): integer;
implementation
function collatzSteps(const aNumber: integer): integer;
var limit: UInt64;
function convergingToOne(aLimit: UInt64): UInt64;
begin
if Odd(aLimit) then
result := aLimit * 3 + 1
else
result := aLimit div 2 ;
end;
begin
// edge case 1
if (aNumber < 1) then
raise EIllegalNumber.Create('error: Only positive numbers are allowed');
// normal case
result := 0;
limit := aNumber;
while ((limit > 1) or (result > 999)) do
begin
limit := convergingToOne(limit);
Inc(result);
end;
end;
end.
```

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## Community comments

@amoradell that is exactly what I am talking about. I like your function name, it helps me understand how it is driving the loop. Doesn't really tell me what the function is actually doing. I guess I am on the fence about what is more important here? What does the function do for the loop or what is the function doing? If you were to consider the ladder then computeCollatzNumber would be another way to go for naming the function. Thanks for the good work! Keep it up.