2024 Review B

1. Write an implementation of mapMaybe, which keeps the “Just” results and throws away the “Nothing” results.

        ex1 = mapMaybe chop4 ["dog", "goldmedal", "fish"]
        check1 = (ex1 == ["medal"])
   
        chop4 :: String -> Maybe String
        chop4 s  | length s <= 4  = Nothing
                 | otherwise      = Just (drop 4 s)
   

2. Stone age functions use pattern matching and recursion, but not list comprehensions or any of the “fancy” machinery. Where possible, they even avoid guards and if statements.

   Write a Stone Age implementation of reverse. Try to avoid using the ++ operator. Stone age definitely means you should not use init or last. (Instead of re-implementing all of the tools you want to use, look for a simpler way using a helper function.)

3. The class definition for Semigroup looks like this:

    class Semigroup c where
        (<>) :: c -> c -> c
   

   Make the following into an instance of semigroup with addition in the first component and multiplication in the second.

    data WorkerL w = WorkerR w w
        deriving (Show, Eq)
   

   Actually you can only do this with a numerical type for w. Add that into your work if you know how.

4. (gcfl) One classic Advent of Code problem is to multiply the first and last numbers hidden in a string of “garbage”. For example, given the ex3 below, the numbers are 123, 45, 678 and 9, so the answer would be 123*9, which is 1107.

    ex3 = "garbage123xyz45truck678dark9day"
    check3 = (gcfl ex3 == 123 * 9)
   

   Write gcfl :: String -> Integer.

5. What is the type signature, including common typeclasses, for each of these?

   1. last

   2. sum

   3. replicate

   4. Average, as defined below.

       average xs = (sum xs) / (fromIntegral len)
           where len = length xs
      

   5. Revjoin:

       revjoin xs ys = (xs ++ [last xs / last ys] ++ ys)
      

6. Write the data definition for:

7. a School, which is just like a String

8. a Studious, including hrs for a decimal number of hours studied, sch for the school they attend, and fd for their main field of interest.

9. (schrs) Write a signature and the function to find the total number of hours the students at each school study. The output should be a list of (School, Double).