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 Post subject: What defines an algorithm?Posted: Fri Jul 22, 2005 1:19 pm

Joined: Tue Jun 28, 2005 3:11 pm
I know that an algorithm is a sequence of twists. My question is does it count as a different algorithm if you perform an extra twist before you perform the algorithm?

For my example I can use the Fridrich 'T' (R B U'B'U B U B²R'B U B U'B') to solve the last layer corners. By using B' before I use this algorithm I can rotate corners, and then use the pattern as stated above to permute the corners correctly. Would this count as two algorithms, or one?

The reason I am asking this question is because, in a different thread, I saw someone state that four algorithms is the fewest needed to solve the cube. I would think that the single twist would count as a seperate algorithm, but would like others thoughts. If it does not count as a seperate algorithm then it is possible to solve the cube with only 3 algorithms, and I suspect that it could be reduced down to 2. I need at least 3 twists to set up my second algorithm though to solve the cube currently, but I would not be supprised if that could be reduced.

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 Post subject: Re: What defines an algorithm?Posted: Fri Jul 22, 2005 1:43 pm

Joined: Tue Oct 07, 2003 10:00 pm
dblthnk84 wrote:
in a different thread, I saw someone state that four algorithms is the fewest needed to solve the cube.

Can you remind us which thread that was? And the answer is, two algorithms are minimum but it's quite complicated. I once wrote a larger post in the yahoo forum about it, if I can find it again I'll post the link.

Oh, of course only one algorithm is necessary. It all depends on what kind of algorithm we're talking about. The "minimum two" statement was for algorithms being fixed sequences of twists.

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 Post subject: Posted: Fri Jul 22, 2005 2:04 pm

Joined: Tue Jun 28, 2005 3:11 pm
David J wrote:

There are only six corner orientations and three edge orientations which need solving.

If you want a minimum set four algs will suffice, though they may need to be done more than once:

Permute corners R U' L' U R' U' L (U)
Orient corners R U R' U R U2 R' (U2)
Orient edges r U r' U2 r U r'
Permute edges F2 U r U2 r' U F2

It was in the "LL Methods" thread (in the Speedsolving forum).

Thanks for the responce, if you find that post I would really appreciate it. I'm currious as to what the simplest method to solving would be.

Also could I get a ruling on if the extra twist makes a new algorithm?

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 Post subject: Posted: Fri Jul 22, 2005 2:08 pm

Joined: Tue Oct 07, 2003 10:00 pm
Those four weren't meant to be a complete set in a technical/theoretical sense, just in a practical sense. They were meant to be accompanied by U turns (and cube rotations), making it actually five algorithms to be precise.

Yes, if you add a twist then of course you get a different algorithm.

Btw, to solve the cube using only three algorithms is easy:
1. U
2. x
3. y

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 Post subject: Posted: Fri Jul 22, 2005 3:35 pm

Joined: Wed Apr 06, 2005 7:57 pm
http://dictionary.reference.com/search?q=algorithm

It seems to usual refer to a specifc sequence of moves.

You could say that the Fridrich method is one algorithm. It is made up os smaller algos.

3 : Cross, F2L, LL

and you can keep breaking them down.

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 Post subject: Posted: Fri Jul 22, 2005 10:05 pm

Joined: Tue Jan 06, 2004 8:31 pm
Making a F2L cross is not an algorithm, just a series of intuitive moves. I'm pretty sure an algorithm will cycle back to the same position you started from if you apply it multiple times. Try 7 sunes in one giant finger trick.

What about mirrors being different algorithims? I think they are.

_________________
"It's like an alarm clock, WOO WOO" -Bubb Rubb

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 Post subject: Posted: Fri Jul 22, 2005 10:08 pm

Joined: Tue Jun 28, 2005 3:11 pm
But does the process of building the cross involve multiple algorithms that are ignored because they are so simple?

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 Post subject: Posted: Fri Jul 22, 2005 10:25 pm

Joined: Wed Apr 06, 2005 7:57 pm
I would say yes.

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 Post subject: Posted: Sat Jul 23, 2005 12:50 pm

Joined: Tue Jun 28, 2005 3:11 pm
Thanks, that is what I wanted to know.

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 Post subject: Posted: Sat Jul 23, 2005 2:16 pm

Joined: Tue Jan 06, 2004 8:31 pm
If you want to get technical about it you could say U2 is an alg. But why would you want to? Just so you can say that you know 100's of algorithms?

I think when referring to puzzle solving that an alg is a series of moves that accomplish a task that is either too slow or too difficult to do intuitively.

Building a cross intuitively is a piece of cake, memorizing algs would seem to be a waste of time and effort.

That's my 2¢

-mike grimsley

_________________
"It's like an alarm clock, WOO WOO" -Bubb Rubb

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 Post subject: Re: What defines an algorithm?Posted: Tue Aug 09, 2005 11:59 am

Joined: Tue Mar 04, 2003 11:17 am
dblthnk84 wrote:
I know that an algorithm is a sequence of twists. My question is does it count as a different algorithm if you perform an extra twist before you perform the algorithm?

Yes.

There are different definitions of the term algorithm. It does not apply to a single turn. It applies to a series of moves, which repeated, produce the same effect.
A recipe is an algorithm, a method for solving the cube is also an algorithm, but the main way it is used in cubing a the mathematical definition, that is, it is recursive. Recursive means that that after sufficient repititions of an algorithm you will return to the initital state.
For example begin with a solved cube and do R2 B2 R F2 R' B2 R F2 R three times and it returns to the solved state.

To answer your question, there are set up moves which make for different algorithms. For example R2 B2 R F2 R' B2 R F2 R solves one position and creates another. Adding a Back side turn before and after: B R2 B2 R F2 R' B2 R F2 R B' solves and creates two other positions respectively.

Another way to look at your question:
Start with a solved cube, do R U R' U R U2 R' six times and it returns to solved position. Now add U2 at the end: do R U R' U R U2 R' U2 three times and it returns to the solved position.

Regards,

David J

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