University of KwaZulu-Natal Pietermaritzburg Campus Examinations

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1 University of KwaZulu-Natal Pietermaritzburg Campus Examinations Data Structures COMP201 Date: November Examiners: Hugh Murrell and Satya Baboolal time limit: 3 hours max marks: 100 This paper consists of eight questions. There are also two Java classes attached. Make sure that you have all the questions and attachments. Candidates may attempt all questions.

2 Data Structures (COMP201) 1 Question 1 (Array) Study the wave sequence shown below. Each term in the sequence is generated by summing the previous term and the term at the same height but immediately to the left (for example: 70 = ) etc Construct a java method, wavesequence, that takes an integer, n, as input and returns an array of integers that contains the first n terms of the wave sequence. For example wavesequence(10) should return: { 1, 1, 1, 2, 3, 5, 6, 11, 14, 25 [12] Question 2 (LinkedList) Study the class LinkedList (attached) and then answer the following questions: (a) Write down a code fragment that will create a linked list called squares whose structure is indicated by the following diagram: head > 4 --> 9 --> 16 --> > --- > --- > --- > --- > -->null

3 Data Structures (COMP201) 2 (b) Write down a code fragment that will create a linked list called fours whose structure is indicated by the following diagram: head > 8 --> 12 --> 16 --> > --- > --- > --- > --- > -->null (c) Construct a new method, member(int k), for the LinkedList class that will return a boolean variable that indicates whether or not the integer, k, is a member of the linked list. For example: squares.member(9) should return true. [6] (d) Write one sentence in English that describes the purpose of the following mystery method in a LinkedList setting. public LinkedList mystery(linkedlist that){ LinkedList L1 = that.myclone(); LinkedList L2 = this.myclone(); if (L1.count == 0) return L1; else {int i = L1.removeFront(); LinkedList L3 = L2.mystery(L1); if (L2.member(i)){L3.addFront(i); return L3; (e) Write down the contents of the LinkedList returned after the execution of the statement: squares.mystery(fours).

4 Data Structures (COMP201) 3 Question 3 (Stack) (a) Define the methods, push, pop and peek that could appear in the ADT for Stack. [4] (b) Suppose that a stack, s, is created by pushing the integers 1, 2 and 3 onto an empty stack in that order: _ 3 s = 2 1 /// Sketch the structure of s after the following code is executed: s.pop() s.push(s.peek()) s.pop() (c) Convert the following infix expression to a postfix expression and then explain how to evaluate such a postfix expression using a stack. ( ) / * ( 4-1 ) [6]

5 Data Structures (COMP201) 4 Question 4 (Tree) (a) Study the class BinarySearchTree attached and then write down Java statements to construct the BinarySearchTree, bst, shown below: (b) Construct a Java method, height(), that will return the length of the longest branch of a BinarySearchTree. In the example above bst.height() should return 4. [4] (c) Explain why the example tree above is a balanced binary search tree. (d) Draw the tree that results after the statement bst.insert(6) is executed in accordance with the BinarySearchTree code attached to this paper. (e) Explain why the new tree generated in part (d) above is now an unbalanced tree and show how to balance it by means of a rotation operation. [4] Question 5 (Queue) (a) Write down the ADT for Queue. [4] (b) Explain how to use a Queue to perform a breadth first search of a binary tree. [6]

6 Data Structures (COMP201) 5 Question 6 (Heap) (a) Draw the heap represented by the following array: {, 85, 70, 80, 50, 40, 75, 30, 20, 10, 35 (b) Show what the array would look like after the value 76 is added to the heap. [3] (c) Now show what the array would look like if the value 85 is removed from the heap produced in (b). [3] (d) How would you use a heap to sort an array of n numbers that are in no particular order? (e) Derive the complexity of your HeapSort algorithm in terms of n. [4] Question 7 (HashMap) You have been asked to perform an analysis of a day s trading on the JSE. You have been supplied with an ascii text file containing one day s worth of stock trading transaction. Each line in the file contains one colon separated transaction record with three fields: STOCK_NAME:SHARES_TRADED:PRICE_PER_SHARE for example AMPLATS:1500:25.35 which states that in this transaction, 1500 shares of AMPLATS were sold at R25.35 per share. Explain (in English) how to make use of the built-in Java classes, Tokenizer and HashMap to count the day s transactions and provide the following analysis: How many different companies traded on the day? How many AMPLATS shares were traded on the day? What was the total value of AMPLATS shares traded on the day? What were the 20 top stocks (in terms of total Rand value) traded on the day? [12]

7 Data Structures (COMP201) 6 Question 8 (HuffmanCode) Construct a Huffman code for the 50-character string: "fee fie fo fum i smell the blood of an english man" where the apostrophes are not part of the string. Report on the number of bits used when this string is compressed with your code. [12]

8 Data Structures (COMP201) 7 Attachment (LinkedList) public class LinkedList { Node head; int count; private static class Node { int cargo; Node next; public Node () { cargo = 0; next = null; public Node (int c, Node n) { this.cargo = c; this.next = n; public String tostring(){ return cargo + ""; public LinkedList (){ head = null; count = 0; public void print(){ Node current = head; System.out.print("("); while (current!= null) { System.out.print(current); if (current.next!= null) System.out.print(","); current = current.next; System.out.print(")"); System.out.println(" # " + count);

9 Data Structures (COMP201) 8 public void addfront(int i){ Node n = new Node(i,null); addfront(n); private void addfront(node n){ n.next = head; head = n; count++; public int removefront(){ Node t = head; head = head.next; count--; return t.cargo; public void reverse(){ if (head == null head.next == null) return; Node second = head.next; Node third = second.next; head.next = null; while(third!= null) { second.next = head; head = second; second = third; third = third.next; ; second.next=head; head = second; public LinkedList myclone(){ LinkedList cl = new LinkedList(); Node p = head; while (p!= null){ Node n = new Node(p.cargo,null); cl.addfront(n); p = p.next; cl.reverse(); return cl;

10 Data Structures (COMP201) 9 Attachment (BinarySearchTree) public class BinarySearchTree { // Root node pointer. Will be null for an empty tree. private Node root; /** --Node-- The binary tree is built using this nested node class. Each node stores one data element of type int. Each node has left and right sub-tree pointer which may be null. */ private static class Node { Node left; Node right; int data; Node(int newdata) { left = null; right = null; data = newdata; public String tostring(){ return data+" "; /** Creates an empty binary tree -- a null root pointer. */ public void BinarySearchTree() { root = null; /** Inserts the given data into the binary tree. Uses a recursive helper. */ public void insert(int data) { root = insert(root, data);

11 Data Structures (COMP201) 10 /** Recursive insert -- given a node pointer, recur down and insert the given data into the tree. Returns the new node pointer (the standard way to communicate a changed pointer back to the caller). */ private Node insert(node node, int data) { if (node==null) { node = new Node(data); else { if (data < node.data) { node.left = insert(node.left, data); else if (data > node.data){ node.right = insert(node.right, data); return(node); // in any case, return the new pointer to the caller