--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/knight1.scala Wed Nov 02 13:22:40 2016 +0000
@@ -0,0 +1,76 @@
+import scala.util._
+
+class Computation[A,B](value: A, function: A => B) {
+ lazy val result = function(value)
+}
+
+
+def print_board(n: Int)(steps: List[(Int, Int)]): Unit = {
+ println
+ for (i <- 0 until n) {
+ for (j <- 0 until n) {
+ print(f"${steps.indexOf((i, j))}%3.0f ")
+ }
+ println
+ }
+}
+
+def add_pair(x: (Int, Int))(y: (Int, Int)) =
+ (x._1 + y._1, x._2 + y._2)
+
+def is_legal(n: Int)(x: (Int, Int)) =
+ 0 <= x._1 && 0 <= x._2 && x._1 < n && x._2 < n
+
+def moves(n: Int)(steps: List[(Int, Int)])(x: (Int, Int)): List[(Int, Int)] = {
+ List((1, 2),(2, 1),(2, -1),(1, -2),
+ (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)).filter(is_legal(n)).filterNot(steps.contains(_))
+}
+
+def ordered_moves(n: Int)(steps: List[(Int, Int)])(x : (Int, Int)): List[(Int, Int)] =
+ moves(n)(steps)(x).sortBy(moves(n)(steps)(_).length)
+
+moves(8)(Nil)(1,3)
+ordered_moves(8)(Nil)(1,3)
+ordered_moves(8)(List((2, 4), (2, 6)))(1,3)
+
+def first[A, B](xs: List[A], f: A => Set[B]): Set[B] = xs match {
+ case Nil => Set()
+ case x::xs => {
+ val result = f(x)
+ if (result == Set()) first(xs, f) else result
+ }
+}
+
+// non-circular tour
+def tour(n: Int)(steps: List[(Int, Int)]): Option[List[(Int, Int)]] = {
+ if (steps.length == n * n) Some(steps)
+ else
+ { val list = moves(n)(steps)(steps.head) map (x => new Computation(x, ((x:(Int, Int)) => tour(n)(x::steps))))
+ val found = list.par find (_.result.isDefined)
+ found map (_.result.get)
+ }
+}
+
+val n = 6
+println(s"simple tour: n = $n")
+
+val starts = for (i <- (0 until n).toList;
+ j <- (0 until n).toList) yield new Computation ((i, j), ((x:(Int, Int)) => tour(n)(x::Nil)))
+
+val found = starts.par find (_.result.isDefined)
+print_board(n)((found map (_.result.get)).get)
+
+//for measuring time
+def time_needed[T](i: Int, code: => T) = {
+ val start = System.nanoTime()
+ for (j <- 1 to i) code
+ val end = System.nanoTime()
+ (end - start)/(i * 1.0e9)
+}
+
+//for (i <- 1 to 20) {
+// println(i + ": " + "%.5f".format(time_needed(2, matches(EVIL1(i), "a" * i))))
+//}
+
+
+
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/knight2.scala Wed Nov 02 13:22:40 2016 +0000
@@ -0,0 +1,43 @@
+import scala.util._
+
+def print_board(n: Int)(steps: List[(Int, Int)]): Unit = {
+ for (i <- 0 until n) {
+ for (j <- 0 until n) {
+ print(f"${steps.indexOf((i, j))}%3.0f ")
+ }
+ println
+ }
+ //readLine()
+ System.exit(0)
+}
+
+def add_pair(x: (Int, Int))(y: (Int, Int)) =
+ (x._1 + y._1, x._2 + y._2)
+
+def is_legal(n: Int)(x: (Int, Int)) =
+ 0 <= x._1 && 0 <= x._2 && x._1 < n && x._2 < n
+
+def moves(n: Int)(x: (Int, Int)): List[(Int, Int)] = {
+ List((1, 2),(2, 1),(2, -1),(1, -2),
+ (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)).filter(is_legal(n))
+}
+
+def ordered_moves(n: Int)(steps: List[(Int, Int)])(x : (Int, Int)): List[(Int, Int)] =
+ moves(n)(x).sortBy((x: (Int, Int)) => moves(n)(x).filterNot(steps.contains(_)).length)
+
+moves(8)(1,3)
+ordered_moves(8)(Nil)(1,3)
+ordered_moves(8)(List((2, 4), (2, 6)))(1,3)
+
+// non-circle tour parallel
+def tour(n: Int)(steps: List[(Int, Int)]): Unit = {
+ if (steps.length == n * n)
+ print_board(n)(steps)
+ else
+ for (x <- moves(n)(steps.head); if (!steps.contains(x))) tour(n)(x :: steps)
+}
+
+val n = 8
+println(s"simple tour: n = $n")
+
+for (i <- 0 until n; j <- 0 until n) tour(n)(List((i, j)))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/knight3.scala Wed Nov 02 13:22:40 2016 +0000
@@ -0,0 +1,45 @@
+import scala.util._
+
+def print_board(n: Int)(steps: List[(Int, Int)]): Unit = {
+ for (i <- 0 until n) {
+ for (j <- 0 until n) {
+ print(f"${steps.indexOf((i, j))}%3.0f ")
+ }
+ println
+ }
+ //readLine()
+ System.exit(0)
+}
+
+def add_pair(x: (Int, Int))(y: (Int, Int)) =
+ (x._1 + y._1, x._2 + y._2)
+
+def is_legal(n: Int)(x: (Int, Int)) =
+ 0 <= x._1 && 0 <= x._2 && x._1 < n && x._2 < n
+
+def moves(n: Int)(x: (Int, Int)): List[(Int, Int)] = {
+ List((1, 2),(2, 1),(2, -1),(1, -2),
+ (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)).filter(is_legal(n))
+}
+
+def ordered_moves(n: Int)(steps: List[(Int, Int)])(x : (Int, Int)): List[(Int, Int)] =
+ moves(n)(x).sortBy((x: (Int, Int)) => moves(n)(x).filterNot(steps.contains(_)).length)
+
+moves(8)(1,3)
+ordered_moves(8)(Nil)(1,3)
+ordered_moves(8)(List((2, 4), (2, 6)))(1,3)
+
+// non-circle tour parallel
+def tour(n: Int)(steps: List[(Int, Int)]): Unit = {
+ if (steps.length == n * n && moves(n)(steps.head).contains(steps.last))
+ print_board(n)(steps)
+ else
+ for (x <- moves(n)(steps.head).par; if (!steps.contains(x))) tour(n)(x :: steps)
+}
+
+val n = 7
+println(s"circle tour parallel: n = $n")
+
+val starts = for (i <- 0 until n; j <- 0 until n) yield (i, j)
+
+starts.par.foreach((x:(Int, Int)) => tour(n)(List(x)))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/knight4.scala Wed Nov 02 13:22:40 2016 +0000
@@ -0,0 +1,45 @@
+import scala.util._
+
+def print_board(n: Int)(steps: List[(Int, Int)]): Unit = synchronized {
+ for (i <- 0 until n) {
+ for (j <- 0 until n) {
+ print(f"${steps.indexOf((i, j))}%3.0f ")
+ }
+ println
+ }
+ //readLine()
+ System.exit(0)
+}
+
+def add_pair(x: (Int, Int))(y: (Int, Int)) =
+ (x._1 + y._1, x._2 + y._2)
+
+def is_legal(n: Int)(x: (Int, Int)) =
+ 0 <= x._1 && 0 <= x._2 && x._1 < n && x._2 < n
+
+def moves(n: Int)(x: (Int, Int)): List[(Int, Int)] = {
+ List((1, 2),(2, 1),(2, -1),(1, -2),
+ (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)).filter(is_legal(n))
+}
+
+def ordered_moves(n: Int)(steps: List[(Int, Int)])(x : (Int, Int)): List[(Int, Int)] =
+ moves(n)(x).sortBy((x: (Int, Int)) => moves(n)(x).filterNot(steps.contains(_)).length)
+
+moves(8)(1,3)
+ordered_moves(8)(Nil)(1,3)
+ordered_moves(8)(List((2, 4), (2, 6)))(1,3)
+
+// non-circle tour parallel
+def tour(n: Int)(steps: List[(Int, Int)]): Unit = {
+ if (steps.length == n * n && moves(n)(steps.head).contains(steps.last))
+ print_board(n)(steps)
+ else
+ for (x <- ordered_moves(n)(steps)(steps.head).par; if (!steps.contains(x))) tour(n)(x :: steps)
+}
+
+val n = 7
+println(s"circle tour parallel fast: n = $n")
+
+val starts = for (i <- 0 until n; j <- 0 until n) yield (i, j)
+
+starts.par.foreach((x:(Int, Int)) => tour(n)(List(x)))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/knight5.scala Wed Nov 02 13:22:40 2016 +0000
@@ -0,0 +1,45 @@
+import scala.util._
+
+def print_board(n: Int)(steps: List[(Int, Int)]): Unit = synchronized {
+ for (i <- 0 until n) {
+ for (j <- 0 until n) {
+ print(f"${steps.indexOf((i, j))}%3.0f ")
+ }
+ println
+ }
+ //readLine()
+ System.exit(0)
+}
+
+def add_pair(x: (Int, Int))(y: (Int, Int)) =
+ (x._1 + y._1, x._2 + y._2)
+
+def is_legal(n: Int)(x: (Int, Int)) =
+ 0 <= x._1 && 0 <= x._2 && x._1 < n && x._2 < n
+
+def moves(n: Int)(x: (Int, Int)): List[(Int, Int)] = {
+ List((1, 2),(2, 1),(2, -1),(1, -2),
+ (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)).filter(is_legal(n))
+}
+
+def ordered_moves(n: Int)(steps: List[(Int, Int)])(x : (Int, Int)): List[(Int, Int)] =
+ moves(n)(x).sortBy((x: (Int, Int)) => moves(n)(x).filterNot(steps.contains(_)).length)
+
+moves(8)(1,3)
+ordered_moves(8)(Nil)(1,3)
+ordered_moves(8)(List((2, 4), (2, 6)))(1,3)
+
+// non-circle tour parallel
+def tour(n: Int)(steps: List[(Int, Int)]): Unit = {
+ if (steps.length == n * n) // && moves(n)(steps.head).contains(steps.last))
+ print_board(n)(steps)
+ else
+ for (x <- ordered_moves(n)(steps)(steps.head); if (!steps.contains(x))) tour(n)(x :: steps)
+}
+
+val n = 21
+println(s"circle tour parallel fast: n = $n")
+
+val starts = for (i <- 0 until n; j <- 0 until n) yield (i, j)
+
+starts.par.foreach((x:(Int, Int)) => tour(n)(List(x)))
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/re.scala Wed Nov 02 13:22:40 2016 +0000
@@ -0,0 +1,104 @@
+
+abstract class Rexp
+case object ZERO extends Rexp
+case object ONE extends Rexp
+case class CHAR(c: Char) extends Rexp
+case class ALT(r1: Rexp, r2: Rexp) extends Rexp
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp
+case class STAR(r: Rexp) extends Rexp
+case class NTIMES(r: Rexp, n: Int) extends Rexp
+case class UPNTIMES(r: Rexp, n: Int) extends Rexp
+
+// nullable function: tests whether the regular
+// expression can recognise the empty string
+def nullable (r: Rexp) : Boolean = r match {
+ case ZERO => false
+ case ONE => true
+ case CHAR(_) => false
+ case ALT(r1, r2) => nullable(r1) || nullable(r2)
+ case SEQ(r1, r2) => nullable(r1) && nullable(r2)
+ case STAR(_) => true
+ case NTIMES(r, i) => if (i == 0) true else nullable(r)
+ case UPNTIMES(r: Rexp, n: Int) => true
+}
+
+// derivative of a regular expression w.r.t. a character
+def der (c: Char, r: Rexp) : Rexp = r match {
+ case ZERO => ZERO
+ case ONE => ZERO
+ case CHAR(d) => if (c == d) ONE else ZERO
+ case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
+ case SEQ(r1, r2) =>
+ if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
+ else SEQ(der(c, r1), r2)
+ case STAR(r1) => SEQ(der(c, r1), STAR(r1))
+ case NTIMES(r1, i) =>
+ if (i == 0) ZERO else
+ if (nullable(r1)) SEQ(der(c, r1), UPNTIMES(r1, i - 1))
+ else SEQ(der(c, r1), NTIMES(r1, i - 1))
+ case UPNTIMES(r1, i) =>
+ if (i == 0) ZERO
+ else SEQ(der(c, r1), UPNTIMES(r1, i - 1))
+}
+
+def simp(r: Rexp) : Rexp = r match {
+ case ALT(r1, r2) => (simp(r1), simp(r2)) match {
+ case (ZERO, r2s) => r2s
+ case (r1s, ZERO) => r1s
+ case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s)
+ }
+ case SEQ(r1, r2) => (simp(r1), simp(r2)) match {
+ case (ZERO, _) => ZERO
+ case (_, ZERO) => ZERO
+ case (ONE, r2s) => r2s
+ case (r1s, ONE) => r1s
+ case (r1s, r2s) => SEQ(r1s, r2s)
+ }
+ case r => r
+}
+
+
+// derivative w.r.t. a string (iterates der)
+def ders (s: List[Char], r: Rexp) : Rexp = s match {
+ case Nil => r
+ case c::s => ders(s, simp(der(c, r)))
+}
+
+
+// main matcher function
+def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
+
+//one or zero
+def OPT(r: Rexp) = ALT(r, ONE)
+
+//evil regular expressions
+def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
+val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+
+
+def time_needed[T](i: Int, code: => T) = {
+ val start = System.nanoTime()
+ for (j <- 1 to i) code
+ val end = System.nanoTime()
+ (end - start)/(i * 1.0e9)
+}
+
+
+//test: (a?{n}) (a{n})
+for (i <- 1 to 8001 by 1000) {
+ println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
+}
+
+for (i <- 1 to 8001 by 1000) {
+ println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
+}
+
+//test: (a*)* b
+for (i <- 1 to 7000001 by 500000) {
+ println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
+}
+
+for (i <- 1 to 7000001 by 500000) {
+ println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
+}
+