Final. Please write (printing clearly) the infonnation requested in the boxes at the top of this page.

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1 ~_/ Family name CSc 115 Summer 2000 (Fundamentalsof ProgrammingII) Given name Final I Student ill.~ ~~SbCIJ ~I' Utll'/t.\lS\1 ~f ~\~10\1\~ ~.().'rjq~~o~~,.," ' ' 'i\ti O~\tI.~ n'ft ap~' "-.:~;. August , " Please write (printing clearly) the infonnation requested in the boxes at the top of this page. This paper has eleven (11) pages including this cover page. Students must count the number of pages in this examination paper before beginning to write, and report any discrepancy immediately to the invigilator. Please write your answers in the spaces provided on this exam paper. Use the backs ofthe pages for rough work-they will not be marked unless you explicitly ask us to. You do not need to comment your code. This is a closed-book examination: no book, no notes, no calculator-no than your brain! sources of infonnation other The marks assigned to each question are indicated in the left margin. Duration: 2 hours Question # % of total Out of Marks 1 31% % % % % % 8 Total 100% 90 Good -..

2 - -. CSc 115 Page 2 1. Give (short) answers to the following questions. There may be more than one correct way to answer each question. (1) a) Which package are the standard Java collection classes and interfaces (e.g. List, LinkedList, SortedSet, etc.) located in? java.util b) Characterizethe differencebetweenexplicitand automaticstoragereclamation. Giveone advantagefor each approach.. explicit: the programmer explicitly deallocates memory 0 advantage: maybe faster, more control. automatic: the runtime system automatically deallocates memory 0 advantage: may be faster, more robust, easier to use c) Giventhe Huffinancodingtree below and assuming that left branches are '0' and right branches are 'I', decode the following bit string back into the original text: SUCCESS (4) d) Write a method to shift all items in an array right by m spots. The last m items in the array should be discarded, and the first m locations in the array should be set to null. Do not allocate any temporary storage. If m > a.length, set all elements of the array to be null. If m < 0, do nothing. public static void shiftright(object[] a, int m) { if (m <= 0) return; for (int i = a.length-m-l; i >= 0; i--)a[i+m] = a[i]; for (int i = 0; i < m && i < a.length;i++)a[i]= null;

3 (2) CSc 115 Page 3 e) Whatare the two rules a binarytreemust satisfyto be considereda heap?. it must be complete. for every node, the children must have lower priority than their parent (2) (2) f) Add 42 to the following heap (represented as an array), assuming that it uses the natural ordering on integers. 8 ~ 30 ~ 14 ] 23 I 42 I 17 [ ~42 [!2] 30 ] 23 I [ g) Remove an element from the following heap (represented as an array), assuming that it uses the natural ordering on integers. 8 ~ 30 ~ 14 ~ 42 [!2] 30~ 14 ~ 8 h) Explainthe processof bottom-uptesting. Use a diagramto illustrateyourdescription. Start testing at the bottom of the dependency graph, in other words the modules that can stand alone and don't need to use any other modules that you're developing. As each modulepasses its tests, you can start testing modules that depend on ones which are already knownto be correct. Continue in this manneruntil you reach your top modules, and the entire application is tested. ~ ~ 8 0

4 (4) CSc 115 Page 4 i) Assuming that A, B, and C are all standard (checked) exception classes (but otherwise not related by inheritance), complete the throws declarations on the methods in the following class. If a method doesn't need a throws declaration, then leave the space empty. public class X { boolean f ( ) throws A { if (Math.random() < 0.5) return true; else throw new A(); void g ( ) throws B throw new B(); { void h(a a) System.out.println(a); { int p() throws B C { try { for (int i=o; i<5; i++) f(); go; ) catch (A a) { h(a) ; throw new C(); j) Circle the correct word choice for each ofthe following programming rules of thumb: Variables should always have the «!iall~/ largest) possible scope. Fields should have as (CIili@>/ much) visibility as ~ossible. Methods should be placed as (low down /~) in the class hierarchy as makes sense. I (1) k) After executing the following code fragment int[] a = {23, 14, 42; int p = 0; int b = a[p++]; what is the value ofb? 23

5 2. Consider the following code fragment: CSc 115 Page 5 public static boolean hasduplicates(object[] a) { for (int i = 0; i < a.length-l; i++) { Object 0 = a[i]; for (int j = i+l; j < a.length; j++) { if (o.equals(a[j]» return true; return false; The method is meant to return true if the objects contained in the array are not all unique. a) There are circumstances in which this method will fail with an exception. Describe the circumstances, the offending statement, and the exact exception that will be thrown. If an element of the array is null,o.equals(a[jdwill fail with a NullPointerException. (2) b) Assuming that n = a.length,what is the average Big-O running time estimate of this method? 0(n2) (7) c) How could you improve the average Big-O running time estimate ofthis method? Describe any abstract data types and algorithms that you would use, but don't write any code. State and justify the expected running time of your improved method. If you have to change the method's signature, you may do so. However, include the new method signature and a justification for the change in your answer. You may not change the method's specification. Rewrite the method to first sort the array usinga fast sorting algorithm (e.g. HeapSort or TreeSort). Once the array is sorted, any duplicate elements will be next to each other. To detect them, we need onlycheck consecutive elements for equality. Since the sorting algorithm is O(n logn) and the linear search is O(n), the improvedmethod'saverage runningtime estimate wouldbe O(n logn). In order to do this, we'd need to be able to order the elements. Hence the method wouldeither need to take an explicit Comparatorargument, or require that each item be Comparable,as so: publicstatic booleanhasduplicates(comparable[]a)

6 3. Use the following interfaces and classes for this question: public interface Comparable { int compareto(object 0); CSc 115 Page 6 class TreeNode { Comparable data; TreeNode leftchild, rightchild; public class BinarySearchTree { private TreeNode root; public boolean add (Comparable item) { II *** IMPLEMENT ME *** public void printsorted() { II *** IMPLEMENT ME *** You willbe implementing some methods of a binary search tree data structure. To be successful, you'll need to know the rules for arranging data in a binary search tree. For all the questions below:. You are not allowed to add fields to any class.. You can define new non-public methods if necessary.. Make sure your methods work correctly on empty trees. (6) a) Implement the printsortedmethod. The method should print out the items in the tree on System.out, one item per line. The items must be printed out in ascending natural order. You may write either a recursive or iterative implementation, as you prefer. publicvoid printsortedo { printinorder(root ); private void printinorder(treenode if (node == null) return; printinorder(node.leftchi Id); System.out.println(node.data); printinorder( node.rightchiid); node){

7 (6) CSc 115 Page 7 b) Complete the following implementation of the add method by filling in the blanks. The method should add the given item to the binary search tree if it's not already there. The method should return true if the item was successfully added, and false if it was already present in the tree. public boolean add (Comparable item) { TreeNode newnode = new TreeNode(); newnode.data = item; if (root == null) { root = newnode ; return true; TreeNode node = root; while (true) { int r = item.compareto(node.data); if (r -==- 0) return false; TreeNode child = r ~ 0? node.leftchild : node.rightchild; if (child == null) { if (r < 0) node.leftchild = newnode; else node.rightchild = newnode; return true; node = child_; (2) c) State any preconditions for the add method, either in English or as Java expressions. item!= null (2) d) What is the average Big-O running time estimate for the add method, if n is the number of nodes in the tree when the method is called? What is the worst-case running time estimate? average: O(log n) worst: O(n)

8 4. The code below is used in the questions on the following page. questions first. II An arbitrary expression that can be evaluated public interface Expression { II Return the value of this expression. int evaluate(); CSc 115 You might want to read the Page 8 II An expression with a constant value public class Constant implements Expression { protected int value; public Constant(int value) {this. value = value; public int evaluate() {return value; II An expression with two operands public abstract class BinaryOperation implements Expression { protected Expression leftop, rightop; II The division operation, divides leftop by rightop public class Division extends BinaryOperation { public int evaluate() { return leftop.evaluate() I rightop.evaluate(); II The subtraction operation public class Subtraction extends BinaryOperation { public int evaluate() { return leftop.evaluate() - rightop.evaluate(); public class TestDriver { public static void main(string[] args) { BinaryOperation a = new Division(); a.leftop = new Constant(7); a.rightop = new Constant(O); BinaryOperation b = new Subtraction(); b.leftop = new Constant(5); b.rightop = a; BinaryOperation c = new Division(); c.leftop = b; c.rightop = new Constant; System.out.println(c.evaluate(»; - -~ ~-

9 ....;;: ~~... (7) CSc 115 Page 9 a) Draw a UML class diagram for the classes and interfaces defined on the previous page. You ('~n ()mit 11'I.o~fon ; T...~l,...:I~~ ;._. ' u.l' '~..1.-~u Expression 11 rightop evaluate(): int 1 leftop L Constant value: int evaluateo: int BinaryOperation Division evaluateo: int Subtraction evaluateo: int (6) b) The expression tree built in the main method is drawn below, What mathematical expression does it correspond to? (Make sure to parenthesize it properly!) (5-7 / 0) / 3 c) Complete the call stack for the program on the previous page. Execution starts in the TestDri ver.main (String [] ) method; this call is filled in for you. Show the call stack at the point in time where the Di videbyzeroexception is thrown by the virtual machine. For each call frame, specify the piece of code being executed by naming the class and method it's defined in. Also draw a reference to the call's receiver (this) in the adjoining diagram. You may not need to fill in all the call frames provided. this: 0 Division.evaluateO this: Subtraction.evaluateO this: Division.evaluateO this: T estdriver.main( String[D