IN SCALA COULD YOU PLEASE COMPLETE THE FUNCTIONS: // If you need any auxiliary functions, feel free to // implement them, but do not make any changes to the // templates below. Also have a look whether the functions // at the end of the file 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 testcases // //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] = ??? //(4) 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] = ??? // testcases // //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 //(5) Implement a function that uses the first-function from (4) 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() } }
IN SCALA COULD YOU PLEASE COMPLETE THE FUNCTIONS:
// If you need any auxiliary functions, feel free to
// implement them, but do not make any changes to the
// templates below. Also have a look whether the functions
// at the end of the file 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 testcases
//
//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] = ???
//(4) 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] = ???
// testcases
//
//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
//(5) Implement a function that uses the first-function from (4) 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()
}
}
*/
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