Chapter 4: Excercises

This page contains a set of excercises for the corresponding chapter.
Read the task description, copy the code template if present and solve it in your Eclipse.
If you are stuck, you can show the solution for this task. Be careful not to spoil the solution for yourself unnecessarily.

Contents

1. GCD and LCM
2. Linear Function
3. Polygons
4. Chessboard

GCD and LCM

1. Implement a function gcd, which returns the greatest common divisor of two parameters.
   Feel free to reuse the previous solution from chapter 2, just wrapt it up in a function.
2. Implement a function lcm, which returns the least common multiple of two parameters.

   

3. Test your implementation.

Just as an example: gcd(15, 21) = 3, lcm(15, 21) = 105.

Show solution

program gcdlcm import IO operation gcd(parameter a : integer, parameter b : integer) : integer loop if a = b then return b endif if a < b then b := b - a else a := a - b endif endloop endoperation operation lcm(parameter a : integer, parameter b : integer) : integer return a * b div gcd(a, b) endoperation main IO.writeInteger(gcd(15, 21)) IO.writeLine() IO.writeInteger(lcm(15, 21)) endmain

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Linear Function

1. Implement the linear function f(x) = 0.5*x + 1.
2. Declare a composition Point, which stores x and y coordinates.
   Create a list of points and fill it with five points using the function f(x) with x ∈ [1, 2, 3, 4, 5].
3. Implement a procedure drawLine(...) which accepts a list of points as a parameter and draws a line according to this list.
   Be aware, that you have to translate point coordinates into pixel coordinates before drawing.
   You can use the Turtle.moveTo(x, y) operation.



program linearFunction import Mathematics import Turtle import IO import Lists // IMPLEMENT YOUR SOLUTION HERE // END OF IMPLEMENTATION main Turtle.showCoordinateSystem(true) Turtle.setThickness(2) variable i : integer loop if i = 5 then exit endif IO.writeRational(f(i)) IO.writeLine() i := i + 1 endloop // IMPLEMENT YOUR SOLUTION HERE // END OF IMPLEMENTATION endmain

Show solution

program linearFunction import Mathematics import Turtle import IO import Lists type Point : composition attribute x : rational attribute y : rational endtype operation f(parameter x : rational) : rational return 0.5 * x + 1.0 endoperation operation drawLine(parameter punkte : list<Point>) Turtle.showCoordinateSystem(true) Turtle.setPosition(punkte[0].x * 100, punkte[0].y * 100) variable i : integer i := 1 loop if i = Lists.lengthOf(punkte) then exit endif Turtle.moveTo(punkte[i].x * 100, punkte[i].y * 100) i := i + 1 endloop endoperation main Turtle.showCoordinateSystem(true) Turtle.setThickness(2) variable i : integer loop if i = 5 then exit endif IO.writeRational(f(i)) IO.writeLine() i := i + 1 endloop i := 0 variable points : list<Point> loop if i = 5 then exit endif variable point : Point point.x := i point.y := f(i) points := Lists.append(points, point) i := i + 1 endloop drawLine(points) endmain

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Polygons

Implement the procedures draw(...) and move(...) to get the following image:



You can use the following operations:

• Turtle.startFilledPolygon(color : Turtle.Colors) - initiates drawing a colored polygon.
• Turtle.endFilledPolygon() - finishes drawing a colored polygon.
• Turtle.penUp() - stops drawing while the cursor is moving.
• Turtle.penDown() - starts drawing again, when Turtle.penUp() was previously called.

program turtlePolygons import Turtle // TODO: implement draw(...) // TODO: implement move(...) main Turtle.setDirection(90) Turtle.showCoordinateSystem(true) Turtle.setFrameSize(300,200) Turtle.setPosition(50, 150) Turtle.setThickness(2) draw(4, 60, Turtle.Colors.RED) move(65) draw(3, 45, Turtle.Colors.GREEN) move(50) draw(6, 45, Turtle.Colors.BLUE) Turtle.showCursor(false) endmain

Show solution

program turtlePolygons import Turtle operation draw(parameter n : integer, parameter l : integer, parameter color : Turtle.Colors) Turtle.startFilledPolygon(color) variable a : integer loop if a = n then exit endif Turtle.forward(l) Turtle.left(360.0/n) a := a + 1 endloop Turtle.endFilledPolygon() endoperation operation move(parameter a : integer) Turtle.penUp() Turtle.forward(a) Turtle.penDown() endoperation main Turtle.setDirection(90) Turtle.showCoordinateSystem(true) Turtle.setFrameSize(300,200) Turtle.setPosition(50, 150) Turtle.setThickness(2) draw(4, 60, Turtle.Colors.RED) move(65) draw(3, 45, Turtle.Colors.GREEN) move(50) draw(6, 45, Turtle.Colors.BLUE) Turtle.showCursor(false) endmain

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Chessboard

Move parts of your previous chessboard implementation from chapter 3 into operations:

• The operation initialiseBoard(...) should include the previous initialization semantics.
• The operation printBoard(...) should include the previous printing on the console semantics.
• The operation drawBoard(...) must draw the chessboard using Turtle.
  You can increase the drawing speed using Turtle.setAnimationSpeed(Turtle.Speed.FAST).



program turtleChessboard import Turtle import IO import Strings import Lists type PieceType : enumeration PAWN, ROOK, KNIGHT, BISHOP, QUEEN, KING endtype type Color : enumeration BLACK, WHITE endtype type Piece : composition attribute pieceType : PieceType attribute color : Color endtype type Field : composition attribute color : Color attribute number : integer attribute character : string attribute piece : Piece endtype // TODO: implement initialiseBoard(...) // TODO: implement printBoard(...) // TODO: implement drawBoard(...) main variable chessboard : list<list<Field>> chessboard := initialiseBoard(chessboard) printBoard(chessboard) drawBoard(chessboard) endmain

Show solution

program turtleChessboard import Turtle import IO import Strings import Lists type PieceType : enumeration PAWN, ROOK, KNIGHT, BISHOP, QUEEN, KING endtype type Color : enumeration BLACK, WHITE endtype type Piece : composition attribute pieceType : PieceType attribute color : Color endtype type Field : composition attribute color : Color attribute number : integer attribute character : string attribute piece : Piece endtype operation initialiseBoard(parameter chessboard : list<list<Field>>) : list<list<Field>> chessboard := [8 ** [8 ** Field{}]] variable abc : list<string> abc := ["a", "b", "c", "d", "e", "f", "g", "h"] variable i : integer loop if i = Lists.lengthOf(chessboard) then exit endif variable j : integer loop if j = Lists.lengthOf(chessboard) then exit endif chessboard[i][j].number := 8-i chessboard[i][j].character := abc[j] if (i + j) mod 2 = 1 then chessboard[i][j].color := Color.BLACK else chessboard[i][j].color := Color.WHITE endif j := j + 1 endloop i := i + 1 endloop return chessboard endoperation operation printBoard(parameter chessboard : list<list<Field>>) variable i : integer loop if i = Lists.lengthOf(chessboard) then exit endif IO.writeString(Strings.genericToString(chessboard[i]) & "\n") i := i + 1 endloop endoperation operation drawBoard(parameter chessboard : list<list<Field>>) Turtle.setAnimationSpeed(Turtle.Speed.FAST) Turtle.setDirection(90) variable size : integer size := 8 variable i : integer loop if i = Lists.lengthOf(chessboard) then exit endif variable j : integer loop if j = Lists.lengthOf(chessboard) then exit endif Turtle.setPosition(i*20+100, j*20+100) if chessboard[i][j].color = Color.BLACK then Turtle.startFilledPolygon(Turtle.Colors.BLACK) variable temp : integer loop if temp = 4 then exit endif Turtle.forward(20) Turtle.right(90) temp := temp + 1 endloop Turtle.endFilledPolygon() endif j := j + 1 endloop i := i + 1 endloop Turtle.setPosition(100, 100) variable temp : integer loop if temp = 4 then exit endif Turtle.forward(size*20) Turtle.right(90) temp := temp + 1 endloop Turtle.showCursor(false) endoperation main variable chessboard : list<list<Field>> chessboard := initialiseBoard(chessboard) printBoard(chessboard) drawBoard(chessboard) endmain

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