The exercises are defined so that it is hard to get a first-class mark.
1st - 35 marks and above.
upper second - 30-34 marks.
lower second - 25-29 marks.
third - 20-24 marks.
fail - 0-19 marks.
The module mark will be the sum of the marks on both class tests. All questions have equal weight.
-
The test must be completed on Jupyter Lab.
-
Run
git pull
on Jupyter Lab to make sure you have the latest version of the course repository. -
Do not modify either the file
Types.hs
or the fileClassTest1-Template.hs
. -
Copy the file
ClassTest1-Template.hs
to a new file calledClassTest1.hs
and write your solutions inClassTest1.hs
.Don't change the header of this file, including the module declaration, and, moreover, don't change the type signature of any of the given functions for you to complete.
If you do make changes, then we will not be able to mark your submission and hence it will receive zero marks!
-
Solve the exercises below in the file
ClassTest1.hs
.
- If your submission doesn't compile or fails to pass the presubmit script on Jupyter Lab, it will get zero marks.
- Run the presubmit script provided to you on your submission from Jupyter by
running
./presubmit.sh ClassTest1
in the terminal (in the same folder as your submission). - This will check that your submission is in the correct format.
- If it is, submit on Canvas.
- Otherwise fix and repeat the presubmission procedure.
Plagiarism will not be tolerated. Copying and contract cheating have led to full loss of marks, and even module or degree failure, in the past.
You will need to sign a declaration on Canvas, before submission, that you understand the rules and are abiding by them, in order for your submission to qualify.
- Each question has some Background Material, an Implementation Task and possibly some Examples.
- Read this material first, then implement the requested function.
- The corresponding type appears in the file
ClassTest1-Template.hs
(to be copied by you). - Replace the default function implementation of
undefined
with your own function.
- This is an open book test.
- You may consult your own notes, the course materials, any of the recommended books or Hoogle.
- Feel free to write helper functions whenever convenient.
- If you do write any helper function, make sure its name does not clash with
any of the functions in the
Types.hs
file. - All the exercises may be solved without importing additional modules. Do not import any modules, as it may interfere with the marking.
- The official submission deadline is 2pm.
- If you are provided extra time, then your submission deadline is that given to you by the Welfare office.
We say that a byte (a sequence of 8 bits) has even parity if the number of 1
s
is even.
Write a function
checkParity :: String -> Bool
checkParity = undefined
which takes as input a string of bits and checks that
- the string size is a multiple of 8, and
- each byte in the string has even parity.
The function should return True
if both conditions are met, and False
otherwise.
We are representing bits here by the characters 0
and 1
. You may
assume that the input strings contain only 0
s and 1
s.
ghci> checkParity "01010101"
True
The above example has length 8 (a multiple of 8) and 4 ones (an even number).
ghci> checkParity "0111011101110110"
False
In the above example, the second byte has 5 ones.
ghci> checkParity "0101011"
False
The above example has only 7 bits (which is not a multiple of 8).
A substitution cipher is an old method of encryption, in which the cipher takes a string and a key that is as long as the alphabet that the message uses. In our case, the message will be expressed using the English alphabet so our cipher key will be a string of length 26. This represents a mapping of each letter of the alphabet to a different letter.
For example, the key "LYKBDOCAWITNVRHJXPUMZSGEQF"
maps 'A'
to 'L'
,
'B'
to 'Y'
, 'C'
to 'K'
and so on.
Write a function
substitution :: String -> String -> String
substitution plaintext key = undefined
which takes a plaintext string (that might contain punctuation and spaces) and an uppercase key and returns the ciphertext.
Note the following:
- The capitalisation of the characters in the plaintext must be preserved by your implementation.
- The encryption should apply only to the letters (i.e. the alphabetic
characters) and punctuation and spaces should be ignored. For this purpose,
you can use the
isLetter :: Char -> Bool
function coming fromData.Char
to test if a given character is a letter. - You may wish to use the function
which converts a character to an index in the key. This function can be found in
charLabel :: Char -> Int charLabel char = ord (toUpper char) - ord 'A'
Types.hs
and will be imported for you automatically.
key1 :: String
key1 = "LYKBDOCAWITNVRHJXPUMZSGEQF"
key2 :: String
key2 = "UDMZIQKLNJOSVETCYPBXAWRGHF"
plaintext1 :: String
plaintext1 = "The Quick Brown Fox Jumped Over The Lazy Dog"
plaintext2 :: String
plaintext2 = "Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum."
ghci> substitution plaintext1 key1
"Mad Xzwkt Yphgr Ohe Izvjdb Hsdp Mad Nlfq Bhc"
ghci> substitution plaintext1 key2
"Xli Yanmo Dptre Qtg Javciz Twip Xli Sufh Ztk"
ghci> substitution plaintext2 key1
"Nhpdv wjuzv bhnhp uwm lvdm, khrudkmdmzp lbwjwukwrc dnwm, udb bh dwzuvhb mdvjhp wrkwbwbzrm zm nlyhpd dm bhnhpd vlcrl lnwxzl. Zm drwv lb vwrwv sdrwlv, xzwu rhumpzb dedpkwmlmwhr znnlvkh nlyhpwu rwuw zm lnwxzwj de dl khvvhbh khrudxzlm. Bzwu lzmd wpzpd bhnhp wr pdjpdadrbdpwm wr shnzjmlmd sdnwm duud kwnnzv bhnhpd dz ozcwlm rznnl jlpwlmzp. Dekdjmdzp uwrm hkkldklm kzjwblmlm rhr jphwbdrm, uzrm wr kznjl xzw hoowkwl bdudpzrm vhnnwm lrwv wb dum nlyhpzv."
Note: these examples are provided in Types.hs
so you can run your function on
them to test that it works correctly on them.
A famous theorem about prime numbers (called Chebyshev's Theorem) asserts that
for any number n
, there always exists a prime number p
such that n < p < 2n
. That is, there is always a prime number between n
and 2n
.
Write a function
largestPrimeBetween :: Int -> Int
largestPrimeBetween = undefined
which returns the largest prime between n
and 2n
.
ghci> largestPrimeBetween 4
7
ghci> largestPrimeBetween 10
19
In number theory, a strong prime is a prime number that is greater than the average of the nearest prime above and below. In other words, it is closer to the succeeding prime than it is to the preceding one.
For example, 17 is the seventh prime: the sixth and eighth primes, 13 and 19, add up to 32, and half of that is 16; 17 is greater than 16, so 17 is a strong prime.
Write a function
strongPrimes :: Int -> [Int]
strongPrimes n = undefined
which takes as input the integer n
and prints the first n
strong prime
numbers.
ghci> strongPrimes 25
[11,17,29,37,41,59,67,71,79,97,101,107,127,137,149,163,179,191,197,223,227,239,251,269,277]
Consider the following data type of directions
data Direction = MoveLeft
| MoveRight
| MoveUp
| MoveDown
deriving (Eq, Show)
Let us define the type Command
to consist of a pair of a Direction
and an
Int
.
type Command = (Direction, Int)
Given a coordinate pair (x, y)
, the execution of a command consists in
incrementing the corresponding coordinate.
So for example, executing (MoveLeft, 10)
on the pair (5, 5)
should result in
(-5, 5)
. (We use the mathematical indexing: "right" means increasing the x
coordinate and "up" means increasing the y coordinate).
Write a function which, given an initial position (x, y)
, computes the final
position after the execution of a list of commands.
executeCommands :: [Command] -> (Int , Int) -> (Int , Int)
executeCommands = undefined
ghci> executeCommands [(MoveRight,10),(MoveLeft,5),(MoveUp,20)] (0,0)
(5,20)
ATMs need to use an algorithm to compute, given an amount, the number of currency notes needed to dispense the money requested by the customer. In this question, you will implement such an algorithm in Haskell.
Implement a Haskell function atmChange
:
atmChange :: Int -> [Int] -> [(Int, Int)]
atmChange = undefined
which takes an amount and a list of denominations in ascending order (such as
[10, 20, 50, 100]
) and returns a list of pairs of denominations and number of
notes to be dispensed (with the fewest number of notes).
ghci> atmChange 2180 [10, 50, 100, 500]
[(500,4),(100,1),(50,1),(10,3)]
In the above example, the user has asked for £2180 with allowed denominations of 10, 50, 100, and 500. The algorithm computes that the ATM will need to dispense 4 bills of 500, 1 bill of 100, 1 bill of 50 and 3 bills of 10.
Note that 2180 = 4 x 500 + 1 x 100 + 1 x 50 + 3 x 10
Some more examples follow.
ghci> atmChange 3270 [10, 50, 100, 500]
[(500,6),(100,2),(50,1),(10,2)]
ghci> atmChange 3270 [10, 50, 100, 200, 500]
[(500,6),(200,1),(100,0),(50,1),(10,2)]
ghci> atmChange 3275 [1, 20, 50, 100, 500, 1000]
[(1000,3),(500,0),(100,2),(50,1),(20,1),(1,5)]