knights_tour 0.0.5 (latest)

A Polyomino is a puzzle piece composed of a number equally sized grid-squares. Depending on the number of squares they can go by different names.

5 squares: 5-omino or pentomino
2 squares: 2-omino or domino

We represent polyominos as a Set of points with an x and y coordinate.

Typically puzzles and games involving polyominos have physical puzzle pieces that can be flipped over and rotated. The pieces can also be placed down on the puzzle board at different locations.

This means that to decide whether two sets of points represent the same Polyomino puzzle piece, we need to consider them equivalent under these transformations:

rotate 90, 180 or 270 degrees
flipped around (mirroring along the vertical or horizontal axis)
translated

type t

An unplaced polyomino puzzle piece. It is characterized by a normalized PointSet, making it invariant to any combination 90 degree rotation, mirroring, and translation.

val name : t -> char

Gets the 'name' of a polyomino. The name is unique for polyomino of a the same order (i.e. if two polyominos have the same order and the same name, it means they are the same polyomino)

val compare : t -> t -> int

Compares two polymoninos to see if they represent the same shape; invariant to rotation, mirroring and translation

val order : t -> int

The number of squares in a polyomino is called its 'order'.

val points : t -> PointSet.t

Gets the canonical PointSet that characterizes this Polyomino

val variants : t -> PointSet.t List.t

Gets all variants of a given Polyomino. A variant is simlar shape obtained by applying rotation and mirroring transformations (but no translation). I.e. it is a specific orientation of Polyomino that has not yet been placed on a specific location of the board.

val to_string : t -> string

Create a 'string-image' of the polyomino

val of_order : int -> t list

Obtain all unique polymino of order n

val pp_poly : Format.formatter -> t -> unit

Print string image of polyomino to a formatter

val pin_symmetry : t list -> t list

Find the first polyomino that is completely assymetric and remove all but one of its variants. This is a 'hack' that allows eliminating equivalent symmetric solutions from a puzzle.

val randomize : t list -> t list

Randomize the order of puzzle pieces and their variants. This can make running puzzle solvers more interesting as it then tends to produce different solutions each time you run it.

val save : out_channel -> t list -> unit

Writes a list of polyominos and all their variants in a textual format that is human readable; but can also be used to restore that same list of pieces and variants by loading the file later.

val save_fmt : Format.formatter -> t list -> unit

Like save but writes the data to Format.formatter instead of a out_channel

val load : in_channel -> t list

Reads a list of polyominos and all their variants from a file that was previously written using save

val load_lines : Knights_tour.Lines.t -> t list

Reads a list of polyominos and all their variants from sequence of lines, as previously written using save

package knights_tour