Py222

Py222 is a 2x2x2 Rubik's Cube representation written in Python. It has support for applying individual moves to the puzzle, as well as space-separated algorithm strings specified in WCA notation.

A cube's state is represented as a 24-element numpy array with indices corresponding to the following stickers, and values corresponding to the following face colors:

sticker indices:
       ┌──┬──┐
       │ 0│ 1│
       ├──┼──┤
       │ 2│ 3│
 ┌──┬──┼──┼──┼──┬──┬──┬──┐
 │16│17│ 8│ 9│ 4│ 5│20│21│
 ├──┼──┼──┼──┼──┼──┼──┼──┤
 │18│19│10│11│ 6│ 7│22│23│
 └──┴──┼──┼──┼──┴──┴──┴──┘
       │12│13│
       ├──┼──┤
       │14│15│
       └──┴──┘

face colors:
    ┌──┐
    │ 0│
 ┌──┼──┼──┬──┐
 │ 4│ 2│ 1│ 5│
 └──┼──┼──┴──┘
    │ 3│
    └──┘

The move definitions are written for a sticker representation, but there are functions to normalize the state's stickers relative to a fixed DLB corner, and convert it into a fixed-corner piece orientation and permutation (OP) representation. There are also various functions that can hash the fixed-corner OP representation state into unique integer indices.

Also included is a sample IDA* solver (solver.py).

Dependencies

• numpy

Usage

  import py222

  # get solved state
  s = py222.initState()
  py222.printCube(s)

      ┌──┬──┐
      │ 0│ 0│
      ├──┼──┤
      │ 0│ 0│
┌──┬──┼──┼──┼──┬──┬──┬──┐
│ 4│ 4│ 2│ 2│ 1│ 1│ 5│ 5│
├──┼──┼──┼──┼──┼──┼──┼──┤
│ 4│ 4│ 2│ 2│ 1│ 1│ 5│ 5│
└──┴──┼──┼──┼──┴──┴──┴──┘
      │ 3│ 3│
      ├──┼──┤
      │ 3│ 3│
      └──┴──┘

  # do some moves
  s = py222.doAlgStr(s, "x y R U' R' U' F2 U' R U R' U F2")
  py222.printCube(s)

      ┌──┬──┐
      │ 2│ 2│
      ├──┼──┤
      │ 2│ 2│
┌──┬──┼──┼──┼──┬──┬──┬──┐
│ 0│ 3│ 1│ 4│ 3│ 0│ 4│ 1│
├──┼──┼──┼──┼──┼──┼──┼──┤
│ 3│ 3│ 1│ 1│ 0│ 0│ 4│ 4│
└──┴──┼──┼──┼──┴──┴──┴──┘
      │ 5│ 5│
      ├──┼──┤
      │ 5│ 5│
      └──┴──┘

  # normalize stickers relative to DLB
  s = py222.normFC(s)
  py222.printCube(s)

      ┌──┬──┐
      │ 0│ 0│
      ├──┼──┤
      │ 0│ 0│
┌──┬──┼──┼──┼──┬──┬──┬──┐
│ 1│ 4│ 2│ 5│ 4│ 1│ 5│ 2│
├──┼──┼──┼──┼──┼──┼──┼──┤
│ 4│ 4│ 2│ 2│ 1│ 1│ 5│ 5│
└──┴──┼──┼──┼──┴──┴──┴──┘
      │ 3│ 3│
      ├──┼──┤
      │ 3│ 3│
      └──┴──┘

Solver Usage

import py222
import solver

# get solved state
s = py222.initState()

# apply some scramble
s = py222.doAlgStr(s, "R U2 R2 F2 R' F2 R F R")

# solve cube
solver.solveCube(s)

      ┌──┬──┐
      │ 2│ 3│
      ├──┼──┤
      │ 1│ 0│
┌──┬──┼──┼──┼──┬──┬──┬──┐
│ 1│ 3│ 5│ 4│ 2│ 2│ 4│ 3│
├──┼──┼──┼──┼──┼──┼──┼──┤
│ 4│ 2│ 0│ 0│ 4│ 1│ 0│ 5│
└──┴──┼──┼──┼──┴──┴──┴──┘
      │ 1│ 5│
      ├──┼──┤
      │ 3│ 5│
      └──┴──┘
normalizing stickers...
generating pruning tables...
searching...
depth 1
depth 2
depth 3
depth 4
depth 5
depth 6
depth 7
depth 8
F R2 F' R U2 R2 F' R 
F R2 F' R' F R2 U2 R'