Final Announcement
Most probably, the grade distribution of the final questions will be something like:
-
%30: Classes in Java, Python, Javascript. Additionally, look at function argument topics (default argument values, variable length of arguments) since you’ll need those to merge multiple Java functions (constructors) with the same name into just one function in Python and Javascript.
-
%50: Haskell.
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%20-30: Questions from Midterm that were not very well solved/understood. You can find the questions and some of the code here. Especially take a look at questions 3 (closures), 4 (reduce function) and 5 (call by value/reference).
Final Examples
Classes
- Example codes may be provided later (or may be not :)…
Q: (Template) Give the equivalent of the following class definition which is in language A, in languages B and C.
Haskell
- List Comprehensions (link to book chapter)
Q: Solve question 2 given in our first lab exercise by using list comprehensions.
Q: Give the values of the following expressions:
exp1 = [x+y | x <- [3..6], y <- drop x [10,13..30]]
exp2 = [x+y | x <- [3..6], y <- drop x [10,13..30]]
-- to be used in exp3
letters = ['A'..'E']
nums = [1..5]
--
f letter num = [ (letters !! (i-1), nums !! (j-1))
| i <- nums, j <- nums,
abs(x-i) == abs(y-j),
(x,y) /= (i,j)
]
where
x = case letter of
'A' -> 1
'B' -> 2
'C' -> 3
'D' -> 4
'E' -> 5
_ -> error "wrong arg"
y = if num >= 1 && num <= 5 then num else error "wrong arg"
--
exp3 = f 'B' 2- Syntax in functions (link to book chapter)
Q: Give the output of each application of function
patrQ. If there would be an error, state that as well.
-- Patterns in function
-- Function definition
patrQ [] (y:ys) = ys ++ [y]
patrQ (x:xs) (y:[]) = [x] ++ y:xs
patrQ (x:[]) (y:ys) = [y] ++ ys ++ [x]
patrQ (x1:x2:xs) (y1:y2:[]) = x2:y2:y1:x1:xs
patrQ xs (y:ys) = [head ys] ++ y:tail xs
patrQ xs _ = xs ++ xs
-- Applications
patrQ "ABCDE" "12"
patrQ "ABCDE" "1234"
patrQ "A" "123"
patrQ "A" "1"
patrQ "ABC" "1"
patrQ "ABCDEF" "12"
patrQ "AB" "12"
patrQ "AB" "123"
patrQ "" ""
patrQ "" "123"
patrQ "ABC" ""Q: Give 7 different calls of function
guardQwhere each call will produce a different value (“Answer1” through “Answer7”). Don’t forget to specify which call produces which value.
-- Guards, if and case expressions
guardQ x y
| x < y = if even x then "Answer1"
else (if odd y then "Answer2" else "Answer3")
| x > y = case x+y of
10 -> "Answer4"
15 -> "Answer5"
_ -> "Answer6"
| otherwise = "Answer7"- Polymorphism and Type Inference (link to book chapter)
Q: For each of the following functions give its type signature. Don’t forget to include type constraints like
Num t => ...orOrd a => ....
t1 x y = (y, x, y)
t2 x y = (y, x, if x == y then x else y)
t3 x y = (y, x - 1, if x == y then x else y)
t4 x y = (y, x - 1.5, if x == y then x else y)
t5 x y = (y, x, if x < y then x else y)
t6 x y = x ++ y
t7 x y = x ++ y ++ "XYZ"
t8 x y = (x, y ++ "XYZ")
t9 x y = (x ++ tail y, y ++ "XYZ")
t10 x y = x ++ y ++ [(head y - 2.5)]
t11 (x:xs) (y:ys) = xs ++ ys
t12 (x:xs) (y:ys) = xs ++ y
t13 (x:xs) (y:ys) = take x ys
t14 (x:xs) (y:ys) = take (x-y) ys
t15 (x:xs) (y:ys) = (take x ys) ++ "ABC"
t16 (x:xs) (y:ys) (z:zs)= (take x ys) ++ zs
t17 (x:xs) (y:ys) (z:zs)= (take x ys) ++ z
t18 (x:xs) (y:ys) (z:zs)= (take x ys) ++ z ++ [head z - x]Higher Order Functions in Haskell (link to book chapter)
Q: What will be the value of
result_expressions below:
c x y z = 3*x + 5*y - z
c1 = c 10
c2 = c 3 3
result1 = c1 2 4
result2 = c2 4
result3 = map (c 4 3) [1,4,9]
result4 = map (\x -> c x 10 5) [1,4,9]
result5 = map (\f -> f 10) (map (\ (x,y) -> c x y) (zip [1,2,10] [4,5,4]))Haskell and other languages
Q: Implement the quicksort algorithm in Python, Javascript, and Java as close to as its Haskell definition below (see the related book section if you don’t get how it works):
quicksort :: (Ord a) => [a] -> [a]
quicksort [] = []
quicksort (x:xs) =
let smallerSorted = quicksort [a | a <- xs, a <= x]
biggerSorted = quicksort [a | a <- xs, a > x]
in smallerSorted ++ [x] ++ biggerSorted