Rubik's Cube Simulator - Command Line Interface

About

I made this short and simple Rubik's Cube simulator for the 2x2, 3x3, 4x4, 5x5 and 6x6 puzzles back in Grade 10 during a school term break. This project was an exercise in the fundamentals of OOP and making use of classes in Python 3, featuring the use of inheritance and polymorphism. To use the program you will need to have colorama installed along with the Python stdlib.

Functionality

When the program first starts up, a menu will ask for which cube to interact with; for example entering cube3 yields the 3x3 cube.

In the main screen of the program, a Rubik's Cube made in ASCII art (and colored using the colorama module) is displayed. Enter the command ? (or equivalently help) to give a full list of commands.

The program is able to perform the following actions:

Main command	Aliases	Required Arguments	Optional Arguments	Action Performed
?	help	N/A	N/A	Shows the help message.
scramble	scr	N/A	{move} (positive int)	Scrambles the cube with {move} moves. If {move} is not provided then a suitable random number of moves is performed.
{cube notation}	N/A	N/A	N/A	Performs the turns dictated by {cube notation}. For example entering U F' R2 does those three moves on the cube. Specifications on how to format {cube notation} are given in the help message.
solve	N/A	N/A	N/A	Yields an instructional procedure and explanation on how to solve the cube from the current state, returning it to a solved state in the process. Only supported for the 2x2 (Ortega method) and the 3x3 (Beginner's method with 4-step LL)
reset	rst	N/A	N/A	Resets the cube's state to the default solved state (white on the top, green in front)
turnTime	N/A	{ms} {non-negative int)	N/A	Sets how long each move takes to visually perform to {ms} milliseconds when using scramble/scr
change	N/A	N/A	N/A	Takes the user back to the cube selection menu where a different cube can be chosen to interact with. The state of all cubes are saved even after switching cubes.
exit	end	N/A	N/A	Exits the program (cube states are NOT stored).

Implementation Note - Rotating Faces

The $N \times N$ cube's state is stored as a 2D array; a list of 6 face arrays each with $N^2$ entries. Each face array's indexing corresponds with the order of the colored tiles on each face as left-to-right, top-to-bottom.

Example of how the indices of a face array [0,1,2,3,4,5,6,7,8] correspond to the positions of the tiles on the face (for a 3x3 cube).

Typically, the method to rotate a square matrix $A\in M_{N\times N}$ clockwise by $90^{\circ}$ is to take the transpose then reverse the rows;

$$A \longmapsto A^{\top} = \left( x_{0\leq i,j \leq N-1}\right) \longmapsto \left( x_{i,N-j-1}\right)$$

However implementations of this method would be difficult for the 1D array datatype which I chose previously. Instead, I created an algorithm to generate mappings from the indices of an unrotated to where those indices map to upon clockwise or anticlockwise rotation by $90^{\circ}$. For example, I found the indices rotation maps for the 2x2 are

$$[0,1,2,3] \longmapsto [2,0,1,3] \quad \text{(clockwise map)} \qquad\qquad [0,1,2,3] \longmapsto [1,3,0,2] \quad \text{(anticlockwise map)}$$

Specifically, the algorithm generates these maps during the initialization of the cube object, and the methods which rotate faces utilize these maps.