2024 Haskell Test A

Write your answers on blank sheets of paper. Skip to a new page if you skip a problem, so you can put your answers in order in the final submission.

Abbreviated reference for Code World:

• Point is (Double, Double)
• pictures :: [Picture]->Picture
• circle r, rectangle width height
• solidCircle, solidRectangle, colored, translated x y, scaled x y
• Event : TimePassing 4.2, KeyPress “A”, PointerMovement (x,y), PointerPress (x,y)

1. In your Code World animation, you want to keep track of a Point (pos), a Point for the direction (dir), a list of Points (pts), and a Double (gtime). Write a data definition for Game that allows you to include these elements in separate fields with the accessors given.

2. Your player is supposed to move in the direction dir every 1.0 units of game time. Write a part of the event handler that will update the game struct as time passes. (Update the game time as well!) Use the record update syntax if you know it.

   evth :: Event -> Game -> Game
   evth (TimePassing p)
   

   Example: position is (0,1), direction is (3,4), and 1.0 units of time pass: the position is then (3,5). Position is (10,8), direction is (1,-1), and 3.2 units of time pass: player is then at (13.2,4.8).

3. There are two items we put in most of our deriving clauses. Explain what they do. Briefly!

   1. Eq
   2. Show

4. Make your Game a member of the Ord typeclass by comparing only the gtime and ignoring the rest of the items.

5. Using only your “Stone Age” programming skills, write the replicate function

    myreplicate :: Int -> a -> [a]
   

6. Use foldl to remove duplicates from a list. Write your own fold helper function and complete the function call.

    undup [1,1,1,2,3,2] == [1,2,3]
    undup xs = foldl ...finish me...
   

7. Could this be the signature of a foldl helper function? Explain why not or give an example of how to use it.

    seven :: Int -> [Int] -> Int
   

8. The class definition for Functor f requires a function

    fmap :: (a -> b) -> f a -> f b
   

   Explain why the following definition does not make Int into a functor:

    g x = x*x
    fmap g x = x*x
   

9. In an Advent of Code problem, you are presented with a matrix of unknown dimensions stored in a file f.

    10 30 50 70
    21 43 65 87
    37 74 111 148
   

   Use Matrix as an abbreviation for the type [[Int]].

    type Matrix = [[Int]]
   

   Write the function getMatrix :: String -> Matrix that receives as input the result from readFile and produce a matrix of numbers.

    exInput="10 30 50 70\n21 43 65 87\n37 74 111 148\n"
    getMatrix exInput == [[10,30,50,70],[21,43,65,87],[37,74,111,148]]
   

   Show an example of what any helper function does. Try to keep this straightforward instead of overcomplicating it.

10. Given a matrix of numbers, the function isArith determines if each row is an “arithmetic sequence”. That means that within a given row the numbers increase by the same amount every time you move one column to the right. The amounts being added can be different for different rows.

    In the example above:

    • the first row is created by adding 20 each time, so it is good;
    • the second row is created by adding 22 each time, so is it is good;
    • the third row is created by adding 37, so it is good.

    Since every row is created by adding a constant to the first number, isArith returns true.

    Write isArith :: Matrix -> Bool.

11. The function toSquare :: Matrix -> Matrix adds rows or columns of zeros to make a square matrix. Write toSquare. You may assume the input matrix is a rectangle. Extra credit for handling non-rectangles.

    In the example above, the output of toSquare would be:

    10 30  50  70
    21 43  65  87
    37 74 111 148
     0  0   0   0
    

    Another example would be a 1 column matrix turning into a square matrix:

               10      10  0  0
     toSquare  21  ==  21  0  0
               37      37  0  0
    

12. The function deleteCol :: Int -> Matrix -> Matrix takes in a number k and removes column k from the matrix, beginning the count with column 0.

    Using the example immediately above, deleteCol 1 produces:

           10  50  70
           21  65  87
           37 111 148
            0   0   0
    

13. (matrixBuild) Given a list of Maybe Int, create a matrix by appending each number to the “current row” and going to the next row when you hit Nothing.

    Example:

    matrixBuild [Just 10, Just 50, Just 70, Nothing,
                 Just 21, Just 65, Just 87]
       == [[10,50,70],[21,65,87]]
    

Notes

I did not like matrixBuild as a demonstration of Maybe skills. Look for another way to test that.