How to calculate optimal solutions of parts of the cube with color neutrality?

[MistArts]

So basically, I want to see how to calculate the optimal solutions (or the most move it takes) to solve one part of a cube like 2x2x2, 1x2x2, 1x1x2, 2x2x3, 2x2x3 + 1x2x2, and F2L...with color neutrality. Does anyone know of a program that does that?

 

[StachuK1992]

cube explorer would kinda work...but i get what you're getting at...
I don't know, honestly...

 

[fanwuq]

I assume you know about Johannes's optimal 2x2x2 block solver, but it's not color neutral. To deal with that, you can use Cube explorer to generate an rotated scramble.

 

[MistArts]

I assume you know about Johannes's optimal 2x2x2 block solver, but it's not color neutral. To deal with that, you can use Cube explorer to generate an rotated scramble.

But I need to generate like 24 scrambles for one case...

 

[fanwuq]

I assume you know about Johannes's optimal 2x2x2 block solver, but it's not color neutral. To deal with that, you can use Cube explorer to generate an rotated scramble.

But I need to generate like 24 scrambles for one case...

Wouldn't that be 8? one for each corner?
24 for 2x2x3.

 

[MistArts]

I assume you know about Johannes's optimal 2x2x2 block solver, but it's not color neutral. To deal with that, you can use Cube explorer to generate an rotated scramble.

But I need to generate like 24 scrambles for one case...

Wouldn't that be 8? one for each corner?
24 for 2x2x3.

My mistake...I'm still looking for something else that does all this.

 

[Swordsman Kirby]

The problem is that for God's Algorithm for these subsets you're mentioning is that you have to check literally every position. Luckily for Lars, he only had edges to deal with.

If you're only looking at specific scrambles, Johannes wrote one for cross, 2x2x2 and 1x2x2 extension.

 

[cuBerBruce]

I assume you know about Johannes's optimal 2x2x2 block solver, but it's not color neutral. To deal with that, you can use Cube explorer to generate an rotated scramble.

But I need to generate like 24 scrambles for one case...

Wouldn't that be 8? one for each corner?
24 for 2x2x3.

There are only 12 possible 2x2x3 blocks, but F2L minus 1 C/E slot (presuming that's what MistArts meant by the ambiguous "2x2x3 + 1x2x2") has 24 possibilities.

If you're only looking at specific scrambles, Johannes wrote one for cross, 2x2x2 and 1x2x2 extension.

Of course the program Johannes wrote does the 1x2x2 extension optimally, but not the entire "2x2x2 + 1x2x2 extension" optimally. It does solve all possible 2x2x2 blocks, so it does allow you to determine the best "block-neutral" 2x2x2-block solve for a scramble.

As to the original question:

You could use ACube to do any of the type of blocks you mention.

Suppose you have the scramble: U L F' R' U2 B' L' F D R2 B. This scramble would be input to ACube as:

-DR -UB UL -UR -DF BL -BR -FL FR UF DB DL +DLB ULF -DFL +DBR +UBL -DRF +UFR +URB

If you want solve just the 2x2x2 block in the ULB corner, just change all the items that represent cubies that aren't in that block to "@?". So you would enter the string:

@? -UB UL @? @? BL @? @? @? @? @? @? @? @? @? @? +UBL @? @? @?

Of course, you would need to solve all such possible blocks, and determine which one is optimal. It would obviously be nice to automate the process of generating the input strings, and also automatically determine what the shortest solution is for any of the blocks. Otherwise, this wouldn't be very practical for solving a large number of scrambles (assuming you want to get an approximation of the actual distribution of "block-neutral" solution lengths).

By the way, it has been determined that 11 face turns is the worst-case block-neutral optimal solution for 2x2x3.