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Free polyominoes enumeration: Difference between revisions
add Scala code
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(0,0) (0,1) (0,2) (1,0) (2,0)
(0,0) (0,1) (0,2) (0,3) (0,4)</pre>
=={{header|Scala}}==
Translation of [[Free_polyominoes_enumeration#Haskell|Haskell]] via [[Free_polyominoes_enumeration#D|D]]
{{works with|Scala|2.12}}
<lang Scala>object Free {
type Point = (Int, Int)
type Polyomino = List[Point]
def rotate90(p: Point): Point = (p._2, -p._1)
def rotate180(p: Point): Point = (-p._1, -p._2)
def rotate270(p: Point): Point = (-p._2, p._1)
def reflect(p: Point): Point = (-p._1, p._2)
def minima(polyomino: Polyomino): Point = {
polyomino.reduce((a,b) => (Math.min(a._1, b._1), Math.min(a._2, b._2)))
}
def translateToOrigin(polyomino: Polyomino): Polyomino = {
val m = minima(polyomino)
polyomino.map(p => (p._1 - m._1, p._2 - m._2))
}
def rotationsAndReflections(polyomino: Polyomino): List[Polyomino] = {
val refPol = polyomino.map(reflect)
List(
polyomino,
polyomino.map(rotate90),
polyomino.map(rotate180),
polyomino.map(rotate270),
refPol,
refPol.map(rotate90), // === pol
refPol.map(rotate180),
refPol.map(rotate270),
)
}
def canonical(polyomino: Polyomino): Polyomino = {
import Ordering.Implicits._
val rot = rotationsAndReflections(polyomino)
val rot1 = rot.map(translateToOrigin)
val rot2 = rot1.map(poly => poly.sorted)
val rots = rot1.take(1).sorted
val rot3 = rot2.min
rotationsAndReflections(polyomino)
.map(translateToOrigin)
.map(poly => poly.sorted).min
}
def contiguous(p: Point): List[Point] = List(
(p._1 - 1, p._2),
(p._1 + 1, p._2),
(p._1, p._2 - 1),
(p._1, p._2 + 1),
)
def newPoints(polyomino: Polyomino): List[Point] = {
polyomino.flatMap(contiguous).filterNot(polyomino.contains(_)).distinct
}
def newPolyominos(polyomino: Polyomino): List[Polyomino] = {
newPoints(polyomino).map(p => canonical(p :: polyomino)).distinct
}
val monomino: Polyomino = List((0, 0))
val monominos: List[Polyomino] = List(monomino)
def rank(n: Int): List[Polyomino] = {
require(n >= 0)
n match {
case 0 => Nil
case 1 => monominos
case _ => rank(n - 1).flatMap(newPolyominos).distinct
}
}
}</lang>
<pre>(0,0) (0,1) (1,1) (1,2) (2,1)
(0,0) (0,1) (0,2) (1,0) (1,1)
(0,0) (0,1) (0,2) (0,3) (1,1)
(0,1) (1,0) (1,1) (1,2) (2,1)
(0,0) (0,1) (0,2) (1,1) (2,1)
(0,0) (0,1) (1,1) (1,2) (2,2)
(0,0) (0,1) (0,2) (1,2) (1,3)
(0,0) (0,1) (1,1) (2,1) (2,2)
(0,0) (0,1) (0,2) (1,0) (1,2)
(0,0) (0,1) (0,2) (0,3) (1,0)
(0,0) (0,1) (0,2) (1,0) (2,0)
(0,0) (0,1) (0,2) (0,3) (0,4)</pre>
=={{header|Kotlin}}==
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