IN SCALA COULD YOU COMPLETE THE FUNCTIONS: is_legal, legal_moves, count_tours, enum_tours, first, first_tour. // 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 COMPLETE THE FUNCTIONS: is_legal, legal_moves, count_tours, enum_tours, first, first_tour. // 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() } } */

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Related questions

Question

IN SCALA COULD YOU COMPLETE THE FUNCTIONS: is_legal, legal_moves, count_tours, enum_tours, first, first_tour.

// 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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