M180 Data Structures and Algorithms in Java Mock Final Exam version 2

Transcription

1 M180 Data Structures and Algorithms in Java Mock Final Exam version 2 PART 1: ALL QUESTIONS ARE REQUIRED [10 Marks] Question 1: Choose the correct answer: (10 marks, one mark each) 1) Which of the following case does not exist in complexity theory? a) Best case b) Worst case c) Average case d) Null case 2) The first step in sort is to break the array into two parts. a) Selection b) Insertion c) Merge d) Bubble 3) Given an n-element array, an algorithm chooses half of the elements from the array at random and executes an O(n) time calculation for each element. The running time of this algorithm is: a) O(n) b) O(n 2 ) c) O(n n ) 4) To arrange the elements of a binary search tree in ascending order, we do a) Post-order traversal b) In-order traversal c) Pre-order traversal 5) The node that is neither a leaf nor a root is called a) Edge b) Interior Node c) Child Node d) None of above 6) Which of the following expressions is asymptotically the largest? a) b) n log n 3 c) 1000 log n d) n 2 log n 7) To represent hierarchical relationship between elements, which data structure is suitable? a) Array b) Queue c) Tree d) All of above

2 8) When new data are to be inserted into a data structure, but there is no available space; this situation is usually called: a) Overflow b) Underflow c) No Flow 9) In Stacks, the push operation should perform as a condition before inserting a new item. a) if (top>(size-1)) b) if (top<(size-1)) c) if (top<(size)) d) if (top>(size)) 10) Which of the following statements is true about the Queues? a) Inserting a new item is taken place at the rear of the queue b) Enqueue method is used to insert a new item c) Removing items is taken place at the front of the queue d) All of the above PART 2: ALL QUESTIONS ARE REQUIRED [40 Marks] Question 1: (7 marks) What is the worst-case complexity of each of the following two code fragments? 1-A): for (i = 0; i < N; i++) { for (j = 0; j < N; j++) { for (k = 0; k < N; k++) { Number of operations in the nested loop = n 2 Number of operations in the simple loop = n Total number of operations = n 2 + n So, the complexity = O(n 2 ) 1-B): for (i = 0; i < N; i++) { for (j = N; j > i; j--) { The inner loop will be executed ) times which equals i.e. Total number of operations = n 2 + n) So, the complexity = O(n 2 ) ) Question 2: (6 marks) Given the following array of integers which needs to be sorted in ascending order: Determine the number of comparison and swap operations that are performed if the insertion sorting is chosen. Justify your answer. Insertion sort need 4 swaps and 8 comparisons //4 marks for the correct number of swaps & comparisons, and 2 marks for justification. 2/5

3 Question 3: (6 marks) What are the minimum and maximum number of siblings a node in a binary tree can have? What if the node is the root? Binary tree nodes can have 0 or 1 sibling. If the node is the root, it will have no siblings. Question 4: (8 marks) Study the following Java code and determine whether the following statements are true or false. 1 java.util.stack s = new java.util.stack(); 2 System.out.println(s.empty()); 3 for (int i=0; i<5; i++) 4 s.push(new Integer(i*10)); 5 System.out.println(s.peek()); 6 for (int i=0; i<5; i++) 7 s.push(s.pop()); 8 java.util.stack ss = new java.util.stack(); 9 while (!s.empty()) 10 ss.push(s.pop()); 11 System.out.println(ss.pop()); 12 System.out.println(ss.peek()); 13 System.out.println(ss.peek() + " " + s.peek()); Q4-A: The output from line 2 is 0 false, the output is true not 0 Q4-B: The output from line 5 is 40 true Q4-C: The output from line 11 is 0 true Q4-D: The output from line 12 is 10 true Question 5: (4 marks) Draw the state of the stack after invoking each method in the following sequence of methods. Assume that the stack is initially empty push(2), push(1), pop(), push(4), push(5), peek(), pop(), pop() Question 6: (9 marks) Study the following tree and fill up the table below accordingly: 3/5

4 Traversal Order Order in which Nodes are visited In-order 3, 5, 6, 7, 10, 12, 13, 15, 16, 18, 20, 23 Pre-order 15, 5, 3, 12, 10, 6, 7, 13, 16, 20, 18, 23 Post-order 3, 7, 6, 10, 13, 12, 5, 18, 23, 20, 16, 15 PART 3: ALL QUESTIONS ARE REQUIRED [50 marks] Question 1: (10 marks) Show the steps which are carried out when a merge sort algorithm run on the following set of integers to sort them in ascending order (smaller values on the left): Note that in your solution you need to show each step in the sorting process. Refer to a similar example in Meeting 6 (Sorting Algorithms) Question 2: (10 marks) Write a java method count() that takes one argument, an element target. The method should return the number of elements in this LinkedList which are equals() to target. (Hint: the method header is public int count (Object target)) public int count(object target) { int counter = 0; for (ListNode node = first; node!= null; node = node.next) { if (node.data.equals(target)) counter++; return counter; Question 3: (12 marks) Implement the Java method FindNode() that takes a reference to a binary search tree root and an integer x as arguments. The method searches the tree and returns the node which includes the argument x. If no such node, the method returns null. public BinaryNode FindNode(BinaryNode root, int x) { if (root == null) return null; if (x == root.data) return root; if (x < root.data) return FindNode(root.left, x); else return FindNode(root.right, x); Question 4: (18 marks) You are given a Stack class and a Queue class. The following functions are available for use: public class Stack { public boolean empty(){ public void push(int n){ public int pop(){ 4/5

5 public class Queue { public boolean empty(){ public void enqueue(int n){ public int dequeue(){ Q4-A: Write a method reversequeue that takes a queue, myqueue, as an input and reverses the order of elements in myqueue. You are only allowed to use Stack and Queue objects in your method. public static void reversequeue(queue myqueue) { Stack stack = new Stack(); while (!myqueue.empty()) stack.push(myqueue.dequeue()); while (!stack.empty()) myqueue.enqueue(stack.pop()); Q4-B: Write a method atfrontofqueue that takes a queue, myqueue, and an integer x as input and adds x to the head of myqueue. You are only allowed to use Stack and Queue objects in your method. public static void atfrontofqueue(queue myqueue, int x) { Queue tempqueue = new Queue(); while (!myqueue.empty()) tempqueue.enqueue(myqueue.dequeue()); myqueue.enqueue(x); while (!tempqueue.empty()) myqueue.enqueue(tempqueue.dequeue()); 5/5