魔方 Thistlethwaite 算法，检查良好的边缘

Question

I'm trying to build a rubik's cube solver in C using the Thistlethwaite algorithm.

I'm storing a cube as an array of 6 uint64_t integers (Faces).
Each of this faces stores 8 colors as one byte.
This structure let's me easily rotate faces using bit manipulation but I wonder if I should use something else that would be more appropriate for the Thistlethwaite algorithm.

The issue I'm having is checking if a cube is contained in the sub group G1 <L, R, F, B, U2,D2> From what I understand, a cube that has correctly orientated edges is contained in this subgroup. (see https://www.jaapsch.net/puzzles/thistle.htm )

The paper at the end of the page clearly indicates how to check if an edge is good or not but I could not find a way to implement it.

The question I have is: How to check in code if an edge is correctly oriented given a scrambled cube ?

Answer 1

According to the article, page 1:

Getting into G1

An edge piece is BAD if in taking it home an odd number of quarter-turns of U and D faces is needed; otherwise it is GOOD

A different way of putting this: if you can manage to bring an edge home without ever using a U or D turn (so only turning the L, F, R and B faces), then an edge is good , otherwise it is bad .

So let's say you have a scrambled cube and are looking at one particular edge piece. Identify the position where it should end up (obviously based on the centre pieces). Let's say that one of the two colours of this edge is red. Then identify where the current place of that red face is in the following image:

Do the same for the place where that red side should end up.

If both places have the same colour (yellow or blue) in the above image, then the edge is good . If they have different colours in the above image, then the edge is bad .

You can easily see that if you had taken the other colour side of the edge in question (the not-red one), you would arrive at the same conclusion with this method.

Up to you to translate this to your data structure.