# HG changeset patch # User Christian Urban # Date 1542907232 0 # Node ID bc131735c9408346040972d7a5619d779c47495f # Parent f968188d4a9bfd490ad97afe65ee5fcba81f04f8 update diff -r f968188d4a9b -r bc131735c940 templates3/knight1.scala --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/templates3/knight1.scala Thu Nov 22 17:20:32 2018 +0000 @@ -0,0 +1,107 @@ +// Part 1 about finding Knight's tours +//===================================== + +// If you need any auxiliary function, feel free to +// implement it, but do not make any changes to the +// templates below. Also have a look whether the functions +// at the end are of any help. + + + +type Pos = (Int, Int) // a position on a chessboard +type Path = List[Pos] // a path...a list of positions + +//(1) Complete the function that tests whether the position x +// is inside the board and not yet element in the path. + +//def is_legal(dim: Int, path: Path, x: Pos) : Boolean = ... + + + +//(2) Complete the function that calculates for a position x +// all legal onward moves that are not already in the path. +// The moves should be ordered in a "clockwise" manner. + + +//def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = ... + + +//some test cases +// +//assert(legal_moves(8, Nil, (2,2)) == +// List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4))) +//assert(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6))) +//assert(legal_moves(8, List((4,1), (1,0)), (2,2)) == +// List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4))) +//assert(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6))) + + +//(3) Complete the two recursive functions below. +// They exhaustively search for knight's tours starting from the +// given path. The first function counts all possible tours, +// and the second collects all tours in a list of paths. + +//def count_tours(dim: Int, path: Path) : Int = ... + +//def enum_tours(dim: Int, path: Path) : List[Path] = ... + + +//(5) Implement a first-function that finds the first +// element, say x, in the list xs where f is not None. +// In that case Return f(x), otherwise None. If possible, +// calculate f(x) only once. + +//def first(xs: List[Pos], f: Pos => Option[Path]) : Option[Path] = ... + + +// test cases +//def foo(x: (Int, Int)) = if (x._1 > 3) Some(List(x)) else None +// +//first(List((1, 0),(2, 0),(3, 0),(4, 0)), foo) // Some(List((4,0))) +//first(List((1, 0),(2, 0),(3, 0)), foo) // None + + + + +//(6) Implement a function that uses the first-function from (5) for +// trying out onward moves, and searches recursively for a +// knight tour on a dim * dim-board. + + +//def first_tour(dim: Int, path: Path) : Option[Path] = ... + + + + + + +/* Helper functions + + +// for measuring time +def time_needed[T](code: => T) : T = { + val start = System.nanoTime() + val result = code + val end = System.nanoTime() + println(f"Time needed: ${(end - start) / 1.0e9}%3.3f secs.") + result +} + +// can be called for example with +// time_needed(count_tours(dim, List((0, 0)))) +// in order to print out the time that is needed for +// running count_tours + +// for printing a board +def print_board(dim: Int, path: Path): Unit = { + println + for (i <- 0 until dim) { + for (j <- 0 until dim) { + print(f"${path.reverse.indexOf((j, dim - i - 1))}%3.0f ") + } + println + } +} + + +*/ diff -r f968188d4a9b -r bc131735c940 templates3/knight2.scala --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/templates3/knight2.scala Thu Nov 22 17:20:32 2018 +0000 @@ -0,0 +1,36 @@ +// Part 2 about finding a single tour for a board using the Warnsdorf Rule +//========================================================================= + +// !!! Copy any function you need from file knight1.scala !!! +// +// If you need any auxiliary function, feel free to +// implement it, but do not make any changes to the +// templates below. + +type Pos = (Int, Int) // a position on a chessboard +type Path = List[Pos] // a path...a list of positions + + +//(6) Complete the function that calculates a list of onward +// moves like in (2) but orders them according to Warnsdorf’s +// rule. That means moves with the fewest legal onward moves +// should come first. + + +//def ordered_moves(dim: Int, path: Path, x: Pos) : List[Pos] = .. + + +//(7) Complete the function that searches for a single *closed* +// tour using the ordered_moves function from (6). This +// function will be tested on a 6 x 6 board. + + +//def first_closed_tour_heuristic(dim: Int, path: Path) : Option[Path] = ... + + +//(8) Same as (7) but searches for *non-closed* tours. This +// version of the function will be called with dimensions of +// up to 30 * 30. + +//def first_tour_heuristic(dim: Int, path: Path) : Option[Path] = ... + diff -r f968188d4a9b -r bc131735c940 templates3/knight3.scala --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/templates3/knight3.scala Thu Nov 22 17:20:32 2018 +0000 @@ -0,0 +1,24 @@ +// Finding a single tour on a "mega" board +//========================================= + + +// !!! Copy any function you need from file knight1.scala !!! +// !!! or knight2.scala !!! +// +// If you need any auxiliary function, feel free to +// implement it, but do not make any changes to the +// templates below. + + +type Pos = (Int, Int) // a position on a chessboard +type Path = List[Pos] // a path...a list of positions + +//(9) Implement a function that searches for a +// you have to be careful to write a tail-recursive version as this +// function will be called with dimensions of up to 70 * 70 +// and starting field (0, 0). It has to produce a solution within +// 30 seconds. + + +//def tour_on_mega_board(dim: Int, path: Path) : Option[Path] = ... +