solvable {cubing}

Solved and Solvability Tests for Cube Objects

Description

Determine if a cube is solved or solvable, and calculate the sign of the corner and edge permutations.

Usage

is.solved(aCube, split = FALSE, co = TRUE, eo = TRUE)
is.solvable(aCube, split = FALSE)
parity(aCube)

Arguments

aCube

Any cube object.

split

Split output into logical vector? See Details.

co

If FALSE, ignore corner orientation.

eo

If FALSE, ignore edge orientation.

Details

The cubieCube and stickerCube objects contain Rubik's cubes that can be physically constructed from properly stickered cubies, but they are not necessarily solvable. These functions test for solved and solvable cubes. The parity function gives the permuation sign (+1 for even and -1 for odd) for the corner and edge permuations. For a cube to be solvable, the two signs must be the same.

For is.solved, a logical value for each separate permutation and orientation component will be given if split is TRUE.

For is.solvable, logical values corresponding to permuatation parity, edge orientation and corner orientation will be given if split is TRUE. The cube is only solvable if all three values are TRUE. The edge and corner orientation values correspond to the fact that if all but one edge (or corner) orientation is known, then the orientation of the final edge (or corner) must be fixed for the cube to be solvable. More precisely, the sum of the edge orientation vector must be even, and the sum of the corner orientation vector must be divisible by three.

Value

A logical value or vector for is.solved and is.solvable. A named integer vector of length two for parity.

See Also

==.cube, randCube, solver

Examples

aCube <- randCube()
is.solvable(aCube)
aCube <- randCube(solvable = FALSE)
is.solvable(aCube)