Computer Science 1 Bh

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1 UNIVERSITY OF EDINBURGH course CS0077 COLLEGE OF SCIENCE AND ENGINEERING SCHOOL OF INFORMATICS Computer Science 1 Bh Resit Examination Specimen Solutions Date: Friday 6th September 2002 Time: 09:30 11:00 (one and a half hours) Place: Adam House Room: Ground Floor Board of examiners Chair: D.K. Arvind External Examiner: R. Dyckhoff Notes about Specimen Solutions 1. These specimen solutions are issued for guidance only, to help as a revision aid. They do not represent a complete picture of how the exam was marked; they are specimen solutions, not a marking guide. 2. The solutions typically present one answer from a set of possible answers. Often, answers which have alternative wording or different technical details are equally acceptable. 3. If you have any questions concerning these solutions, please contact the course organiser. Please note that the course organiser will not be able to answer questions about the marking of the exam.

2 Question 1 (a) Consider the following fragment of the Java class hierarchy, showing some of the collections classes. Object AbstractCollection AbstractList AbstractSet ArrayList Vector HashSet TreeSet i. The class AbstractCollection is part of the java.util package. Show the first line of the AbstractCollection.java file which must be used to declare this. [1 mark] package java.util; ii. The class AbstractSet implements the interface Set, and is public. Show the first line of Java code which used to define the class AbstractSet. public abstract class AbstractSet extends AbstractCollection implements Set

3 iii. Explain briefly what it means to say that an abstract class like AbstractSet cannot be instantiated. Show a line of code in your answer which attempts to do this, but does not compile. An abstract class has one or more methods which are declared abstract, which means that they are given no implementation (method body). Because of this, no object of an abstract class can be created, so for example the code AbstractSet s = new AbstractSet(); would not compile (even though AbstractSet provides a nullary constructor). [ Question continues on next page ]

4 (b) Consider the following Java code: class A { int g() { return 5; int f(int i) { return 2*i + g(); class B extends A { int f(int i) { return -(super.f(i)); class C extends B { int g() { return 2; class TestExtends { public static void main(string[] args) { A obj1 = new A(); B obj2 = new B(); C obj3 = new C(); A obj4 = (A)new C(); System.out.println(obj1.f(1)); System.out.println(obj1.f(2)); System.out.println(obj2.f(3)); System.out.println(obj3.f(4)); System.out.println(obj4.f(5)); Show the output when the main method of TestExtends is executed. [5 marks]

5 Question 2 For each code fragment below, place a tick in the left-hand box if the code throws an exception which escapes to the surrounding code, and a cross otherwise. In the cases that throw an exception, provide the name of the class of the exception thrown in the right-hand box. If no exception is thrown to the surrounding code, leave the right-hand box empty. (a) String s = null; int length = s.length(); throws an class of NullPointerException (b) int[] a = new int[10]; int i = a.length; while (--i > 0) { a[i] = 10-i; throws an class of (c) Object o1, o2 = null; boolean b = o1.equals(o2); throws an class of NullPointerException (d) int k = 0; try { int i = 1/k; catch (Error e) { throws an class of ArithmeticException

6 (e) try { throw new RuntimeException(); finally { System.out.println("Hello"); throws an class of RuntimeException

7 Question 3 (a) Programmers targetting the Java Virtual Machine typically write their programs in Java and compile them to Java byte code using a Java compiler. However, since Java byte code is itself another programming language why do programmers not program in it directly, thereby bypassing the compilation process entirely? [3 marks] Any of the following points could be made: 1. Java is a high-level language whereas Java byte code is a low-level language. (a) Java has a while loop whereas Java byte code only has goto. Java has conditionals with two limbs whereas byte code has jumps with fall-through. (b) Java has nested classes whereas Java byte code does not. 2. Java programs are typically shorter than their byte code equivalents and hence easier to develop and debug. 3. Java byte code would still need to be assembled into class files so compilation is not entirely bypassed. No assembler is provided in the Java Development Kit. (b) Consider the following Java method to calculate factorials of numbers. public class Fac { public static final int fac (int n) { if (n == 0) return 1; else return n * fac (n-1); Provide the equivalent Java byte code method which would be produced by a Java compiler. Recall that a static method is invoked with the invokestatic instruction and that isub denotes integer subtraction and that imul denotes integer multiplication. [7 marks]

8 Method int fac(int) 0 iload 0 if n 1 ifne 6 is zero [1] 4 iconst 1 then 5 ireturn return 1 [1] 6 iload 0 else store n [1] 7 iload 0 and compute 8 iconst 1 the value of 9 isub (n minus 1) [1] 10 invokestatic #2 <Method int fac(int)> factorial [1] 13 imul multiply these two values [1] 14 ireturn and return this as the result [1]

9 Question 4 (a) Control flow in Java byte code programs is determined by unconditional jumps (goto) and conditional jumps (such as if icmplt). Which constructs in the Java programming language produce jump instructions in the byte code program which is output by the Java compiler? Any (two) of the following: if, while, for, do, break, continue, && and. None of the following: switch, try, catch, finally, ++, & and. (b) The following Java byte code method was produced by a Java compiler. Give a method written in Java source code which could have produced this output. [8 marks] Method int loops(int) 0 iconst 0 1 istore 1 2 goto 24 5 iconst 0 6 istore 2 7 goto iinc iinc iload 2 17 iconst 5 18 if icmplt iinc iload 1 25 iconst 3 26 if icmplt 5 29 iload 0 30 ireturn

10 class ForLoops { public static int loops(int n) { // n is variable 0 for (int i = 0 ; i < 3 ; i++) { // Lines 0 to 26 // i is variable 1 for (int j = 0 ; j < 5 ; j++) { // Lines 5 to 18 // j is variable 2 n += 2; // Line 10 return n; // Lines 29 and 30

11 Question 5 Consider the following scheduling problem problem: We are given a number of activities to schedule into the day. An activity can vary in duration from 20 to 240 minutes. We are also given a number of timetable slots into which the activities must be scheduled. A slot specifies a time of day and duration of the slot in minutes. Our goal is to find an allocation of activities to slots such that the amount of wasted time at the end of slots that have activites allocated to them is minimized. We can allocate two or more activities to a slot provided the total time for the activites does not exceed the length of the slot. (a) One proposal to solve this problem is the greedy approach where we allocate activities to slots by choosing the longest unallocated activity and allocating it to a slot that leaves least wasted time at the end of the slot (i.e. is the closest fit available for the activity.) Can you find a set of activities and slots that causes this method to fail to find an optimal solution for the problem? [4 marks] Activities: 40, 20. Slots: (13:00-14:00) (14:00-14:40) (b) In this section you are asked to provide an outline of an approach to solving this problem that will find an optimal allocation for your example constructed in Part (a). Do not attempt to make your approach efficient, please try to provide a solution that works even though it may be extremely inefficient. i. Provide a sketch of a solution method that will solve the scheduling problem. [4 marks] If we have n activities and m slots just consider all ways of choosing p slots, where p n, from m and consider all possible allocations of the n activities to the slots. ii. Provide a, reasonably accurate, estimate of the running time of the program for n activities and m slots. The m choose n term dominates - 2 marks if they say something like this one mark for anything sensible involving factorials

12 Question 6 Consider the following brief description of part of the activity of the Informatics Teaching Office (ITO): The ITO records for each degree programme the classes that should be taken to satisfy the programme, the students taking each class, the lecturer for the class, the members of the class and their marks. An analyst has begun to build a class model for this system and has identified: Degree Programme, Class, Student, Lecturer and Marks as class names to be used in building the class model. (a) Explain what is meant by an association and how associations are used to make a more elaborate class model. Illustrate your answer by identifying some associations between the classes identified in the question. [3 marks] Associations are relationships between classes. For example, programmes comprise classes; lecturers teach courses. (b) Explain how you might go about validating a class model. Use the example above to illustrate your answer. [3 marks] One would use CRC (classes, responsibilities, collaborations) cards to record the requirements on the individual classes in the model. For example if the Degree Programme class is responsible for recording progress in the programme we should be able to check that the responsibilities of the classes that collaborate with the degree programme class are sufficient to ensure we can record progress in the programme. (c) The ITO is responsible for checking that each student is enrolled on classes that match their degree programme. Demonstrate that, using the identified associations, the ITO can carry out this responsibility. You may identify additional associations if necessary. The student class must have appropriate associations with the programme, and the list of classes taken. Programme has the responsibility to record the classes relevant to a programme so the ITO can check the classes taken by any student are correct. (d) What is meant by refactoring in object-oriented design? Explain its role in the design process. Refactoring involves rewriting the code to eliminate structurally undesirable features of the code while retaining the same functionality. It is is used to clean up code periodically after new functionality has been developed.

13 Question 7 (a) In informal terms, what is Java s notion of a graphics context? [3 marks] It supplies methods to perform simple graphical operations on a display with a twodimensional coordinate system. (b) What is the class of a graphics context object? [1 mark] Graphics. (c) Assuming the existence of methods randa() and randb() which return random integers in the range 0 to 500, and 0 to 255 respectively, write a paint method that will repeatedly draw lines with random-chosen colours between pairs of randomly-chosen points in a grid. [6 marks] public void paint (Graphics g) { while (true) { g.setcolor (new Color(randb(), randb(), randb())); g.drawline (randa(), randa(), randa(), randa());

14 Question 8 (a) Explain the roles of (i) the datapath, and (ii) the control unit, of a processor in a von Neumann machine. [4 marks] Datapath combines data values and performs simple operations on them. Control unit manages the movement of data around the processor and the actions performed. (b) What is the von Neumann bottleneck? Words representing instructions or data are sent one-by-one between the processor and the memory. (c) Describe two ways in which internal parallelism is incorporated within present-day processors, while still preserving the external sequential nature of the von Neumann model. [4 marks] Pipelining within the fetch-execute cycle, using two or more stages. Superscalar processors with instruction reordering and speculative execution of instructions.

15 Question 9 For parts (a), (b) and (c), use chains of logical equivalences. Whenever possible, name the rule or rules being used at each step. (a) Show the equivalence P (Q R) (P Q) R is true. P (Q R) P ( Q R) characterisation ( P Q) R associativity (P Q) R DeMorgans law (P Q) R characterisation (b) Show that (P (P Q)) Q is a tautology. (P (P Q)) Q (P ( P Q)) Q characterisation ( P ( P Q)) Q DeMorgans law ( ( P Q) ( P Q) associativity, commutativity t excluded middle (c) Put ((B C) A) into DNF (Disjunctive Normal Form). ((B C) A) (B C) A of characterisation (B C) A cancellation (B A) (C A) distributivity, over

16 (d) Use a semantic tree to show that the propositional formula (P Q) P is not a tautology. Explicitly state a counter-example truth assignment suggested by the tree. f: (P Q) P t: P Q f: P f: P t: Q t: P t: P Counter-example truth-assignment is {P t, Q t. Marking: 2 marks for correct rule applications 1 mark for closing contradictory path 1 mark for correctly reading off counter-example from tree. [4 marks]

17 Question 10 (a) Consider the static Java method for computing a geometric sum 1 + r + r r n. public static int geomsum(float r, int n) { if (n == 0) return 1; else return Math.pow(r,n) + geomsum(r, n-1); where Math.pow(r, n) computes r n. Show by induction on n that n : N. geomsum(r, n) = r(n+1) 1 r 1 where N is the non-negative integers {0, 1, 2,.... For simplicity, assume there is no difference between Java floating-point arithmetic and arithmetic on real numbers. i. How does the base case argument go? The base case is: geomsum(a, 0) = r1 1 r 1 Both sides are obviously equal to 1. ii. For the step case, what is the inductive hypothesis and what is the statement to be shown? [1 mark] The inductive hypothesis is: and is to be shown, where k 0. geomsum(r, k) = rk+1 1 r 1 geomsum(r, k + 1) = rk+2 1 r 1 iii. What s the proof of the step case? geomsum(r, k + 1) = Math.pow(r, k + 1) + geomsum(r, k) by definition of geomsum = r k+1 + rk+1 1 by I.H. and def. of Math.pow r 1 by arithmetic = rk+2 1 r 1

18 (b) Complete the the requires (precondition), ensures (postcondition) and loop invariant assertions for the following Java method which evaluates the integer value of a boolean array arr: //@ requires //@ arr!= null; [1 mark] //@ ensures //@ \result = //@ (\sum int k; 0<=k & k<arr.length; arr[k]? intpow(2,k) : 0); static boolean intval(int i; int[] arr) { int val = 0; //@ loop_invariant //@ val = //@ (\sum int k; 0<=k & k<j; arr[k]? intpow(2,k) : 0); for (int j = 0; j!= arr.length; j++) { if (arr[j]) val = val + intpow(2,j); return val; Assume that a method static int intpow(int a, int b) {... for computing a b is defined elsewhere in the same class. Recall, a loop invariant assertion concerns the state of the program just before each evaluation of the loop termination test. Write your assertions using the extended Java-like syntax illustrated in class, or, if you prefer, more logic-like or mathematical syntax.