The University of Nottingham

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1 The University of Nottingham SCHOOL OF COMPUTER SCIENCE A LEVEL 1 MODULE, SPRING SEMESTER PROGRAMMING PARADIGMS Time allowed: TWO hours THIRTY minutes Candidates may complete the front cover of their answer book and sign their desk card but must NOT write anything else until the start of the examination period is announced. Answer ALL FOUR QUESTIONS Dictionaries are not allowed with one exception. Those whose first language is not English may use a standard translation dictionary to translate between that language and English provided that neither language is the subject of this examination. Subject specific translation dictionaries are not permitted. No electronic devices capable of storing and retrieving text, including electronic dictionaries, may be used. DO NOT turn your examination paper over until instructed to do so ADDITIONAL MATERIAL: Haskell standard prelude

2 2 1. Haskell/FP: Types and recursion a) Fill in the missing parts? in the following definitions to make them type correct. It does not matter what they do as long as they are type correct: e1 ::? e1 = [True,False,True] e2 ::? e2 = (1,2,3) e3 :: a -> (a,a,a) e3? =? e4 :: [a] -> [a] -> [a] e4 xs ys =? e5 :: Int -> (Int -> Int) e5 = \x ->? b) Write down the most general types for the following functions: one x = [x] two x = (x,x) three xs = xs ++ xs ++ xs first x y = x inc x = x+1 c) Define the following library functions using recursion. Each is defined in the attached standard prelude, but not directly using recursion. (10 marks) sum :: [Int] -> Int length :: [a] -> Int reverse :: [a] -> [a] map :: (a -> b) -> [a] -> [b] replicate :: Int -> a -> [a] d) Using the definition fac 0 = 1 fac n = n * fac (n-1) show how the expression fac 3 is evaluated.

3 3 2. Haskell/FP: Recursion and sorting a) Complete the missing parts? in the following definition for a recursive function that inserts an integer into the correct position in a sorted list. For example, insert 3 [1,2,4,5] should return [1,2,3,4,5]. insert :: Int -> [Int] -> [Int] insert x [] =? insert x (y:ys) = if x <= y then? else? b) Show how your definition evaluates insert 3 [1,2,4,5]. c) Using insert, define a recursive function isort :: [Int] -> [Int] that implements the insertion sort algorithm, in which the empty list is already sorted, and any non-empty list is sorted by inserting the head of the list into the result of recursively sorting the tail of the list. d) Show how your definition evaluates isort [3,2,1]. There is no need to show how each application of the function insert is evaluated. e) Using list comprehensions, define functions smaller :: Int -> [Int] -> [Int] larger :: Int -> [Int] -> [Int] that return the numbers in a list that are strictly smaller and larger than a given number, e.g. smaller 3 [2,4,1,5] should return [2,1]. (2 marks) f) Using smaller and larger, complete the missing parts? in the following definition for a recursive function that implements the quicksort algorithm. You may assume that the argument list contains no duplicates. qsort :: [Int] -> [Int] qsort [] =? qsort (x:xs) = qsort? ++? ++ qsort? g) Draw a tree diagram to explain how qsort [3,2,4,1,5] evaluates. There is no need to show how each application of smaller and larger are evaluated, and you may assume that qsort [x] = [x] for any number x.

4 4 3. Java/OO: Interfaces and Lambda Expressions Consider the following MyVector class: public class MyVector protected Integer[] internalarray; public MyVector( int initialsize ) internalarray = new Integer[initialSize]; public void resize( int newsize ) if ( newsize!= internalarray.length ) Integer[] newarray = new Integer[newSize]; for (int i=0; i < Math.min(newSize,internalArray.length); i++) newarray[i] = internalarray[i]; internalarray = newarray; public Integer get( int index ) if ( index < internalarray.length ) return internalarray[index]; return null; // Unknown public static void main(string[] args) MyVector vec = new MyVector(5); for ( int i = 0 ; i < 20 ; i++ ) vec.set(i, i*i ); // This calls set() see part a // vec could be used here, e.g. in parts e and g for ( int i = 0 ; i < 20 ; i++ ) System.out.println( "Element" + i + "=" + vec.get(i) ); a) Provide the implementation for a method set() which will take two parameters, an (int) index and an Integer value, which will set the array element at the specified index to the specified value. Implement your method so that it will automatically grow the array if an attempt is made to set a value beyond the end of the array (please note the resize() method). A correct set() method would ensure that the main() method above would output the first 20 square numbers.

5 5 b) Implement an interface called Operation, with one method called apply, which will take a single parameter value (of type int) and return a value of type int. c) Create a class called OpDouble which implements the interface Operation, and has an apply() method which returns a value which is double the value of the parameter provided. d) Provide the implementation of a new method in the MyVector class, called applytoall(), which will take a single parameter (of type Operation, from part b) and will call the apply() method of the supplied Operation for every element in the array, setting the new value of the element to be the value returned by apply(). e) Provide a single line of code which will call the function applytoall() from part d) using a new object of your OpDouble type, to double the value of all elements in the array. (2 marks) f) Explain what Lambda expressions are in Java and why these are useful. g) Provide an example of the use of a Lambda expression in Java by giving a single line of code which when executed will halve the values of all items in the MyVector vec. (You may use the answers to parts a-d of this question.)

6 6 4. Java/OO: Understanding code, sub-classing and class diagrams Consider the Java code for the InfTree class on the next page which implements an infinite tree. a) What is the output if the following code is executed? (9 marks) InfTree mytree = new InfTree(1); System.out.println( "Head = " + mytree.val() ); System.out.println( "l() = " + mytree.l().val() ); System.out.println( "r() = " + mytree.r().val() ); InfTree current = mytree; for ( int i = 0 ; i < 6 ; i++ ) System.out.println("Left branches, level " + i + "=" + current.val()); current = current.l(); // Go to next left sub-tree current = mytree; for ( int i = 0 ; i < 6 ; i++ ) System.out.println("Right branches, level " + i + "=" + current.val()); current = current.r(); // Go to next right sub-tree b) Provide the code for a sub-class of the InfTree class which will change the behaviour so that each left tree node multiplies the value of the parent by 2 rather than adding 1. Explain clearly why you need a constructor for this class. You may find it useful to consider the factory design pattern. (8 marks) c) Draw a simplified class diagram showing the InfTree class and your new class, with all relationships, attributes and operations. Provide a key which clearly shows the notation which you used in your diagram. (8 marks)

7 7 public class InfTree // Assume that tree node contains the left sub-tree protected InfTree left; // Assume that tree node contains the right sub-tree protected InfTree right; // Assume that tree node uses its parent tree protected InfTree parent; // Each tree node has an integer value protected int value; public InfTree( int value ) parent = this; // Root is its own parent this.value = value; public int val() // get value in tree node return value; public InfTree l() // get left subtree // generate next node if it does not exist if ( left == null ) genleft(); return left; public void genleft() left = new InfTree( val() +1 ); left.parent = this; public InfTree r() // get right subtree // generate next node if it does not exist if ( right == null ) genright(); return right; public void genright() right = new InfTree( val() + p().val() ); right.parent = this; public InfTree p() // get parent tree return parent; End