package knights_tour

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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 Stdlib.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 : Stdlib.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.

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