CubicOptimal

After a long time away, I am starting to work on this again. It's final goal is to be an optimal solver, but it's a winding path. I'm doing experimenting, and building out where I like. Expect very dynamic code; I'm changing a lot of things, including class names and project architecture.

The folders

each have a single letter name. Here's what they are and what they contain:

/c contains the basics of the puzzle, including Cube, and Scramble. Of course the goal of the project is to find a Scramble of minimum size. I guess I should mention that I'm following the half-turn metric: 180 degree turns are allowed, but not slice moves.

/h contains heuristics. a heuristic takes in a Cube and returns an estimation of how many moves it will take to solve that cube. All heuristics are complete, meaning that they never overestimate the actual amount of moves. This is a good property for search algorithms.

/s contains search algorithms. They take do the actual work of finding the optimal scramble.

/q contains coordinates. A coordinate is just a different way to chop up a cube mathematically. There are very few rules for what a coordinate can be, but to be useful here are three that the ones I use follow:

1. A coordinate's set of values is closed (graphing them, with moves as edges, one can reach every value from every other value)
2. A coordinate has some defined solved value, and when the coordinate value being solved is necessary (but not sufficient) for the whole cube to be solved.
3. A coordinate could return a vector value, but I prefer integer values. Bonus points if solved is integer 0.

There are also /main and /defunct. main contains two classes, each with a main method. One, Solver, is for developing the optimal solver. The other, Researcher, is for doing experiments. /defunct contains code that at one point I was using, but now don't need. Now that I have this git and am doing proper version control, I probably won't need it for too much longer.

Fair warning, my code contains a lot of comments, and not all of them are exactly professional. I've been making this over 2 years now (starting in high school) I think its funny, and rarely delete comments in case they say something important. Sometimes when code was moved to different classes I moved comments with them, and then they no longer make sense.

Working coordinates and heuristics

The four coordinates most commonly used to describe a cube are orientation and permutation of the corner and edge pieces. CO and EO can't be rotated, however, so rotatable corner orientation and rotatable edge orientation contain added information from the permutation so that the coordinates can be rotated into sym coordinates.

CO: corner orientation
CP: corner permutation
EO: edge orientation
EP: edge permutation
RCO: rotatable corner orientation
REO: rotatable edge orientation
RCP: restricted corner permutation
REP: restricted edge permutation
Kociemba: coordinate used in Kociemba algorithm and Kociemba optimal solver.

PP = Predictive power

Coordinates	Raw	Sym	Raw Size	Sym Size	avg. PP	max PP
CO	Yes	-	2187	-	4.459	6
CP	Yes	Yes	40321	984	4.723	7
EO	Yes	-	2048	-	4.609	7
EP	Too big		479001599
RCO	Yes	Yes	153090	3393	6.430	9
REO	Yes	Yes	70963200	1482170	8.246	11
RCP	Yes	Yes	70
REP	Yes	Yes	34650
UDSlice	Yes	No	495
Kociemba	Not even close	No	2217093120

** avg. PP is for raw if available, else sym

See more in Coordinates Heuristics.md

Current version: 0.3.1

Tentative plan for versions:

0.2.1: Complete structure of how packages c, s, h, and q interact.

0.3.0: Restructure Cube class with permutations. Rotations x48 work.

0.3.1: Rotations x96 work.

0.3.2: Restructure coordinate calculations to be faster, including breaking 0 = solved.

0.3.3: Create power and lexicographic heuristics.

0.3.4: Implement SMA* search.

0.4.0: Coordinate class able to receive permutation input and perform operations on it.

0.5.0: Machine learning to generate heuristics.

See to-do.md for an unorganized list of things I plan on doing.

1.0 released when it's able to optimally solve cubes up to length 20. Current ability: 12.