Data Structures and Algorithms Winter Semester

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1 Page 0 German University in Cairo December 26, 2015 Media Engineering and Technology Faculty Prof. Dr. Slim Abdennadher Dr. Wael Abouelsadaat Data Structures and Algorithms Winter Semester Final Exam Bar Code Instructions: Read carefully before proceeding. 1) Please tick your major Major MET IET Mechatronics BI 2) Duration of the exam: 3 hours (180 minutes). 3) No books or other aids are permitted for this test. 4) This exam booklet contains 15 pages, including this one. Three extra sheets of scratch paper are attached and have to be kept attached. Note that if one or more pages are missing, you will lose their points. Thus, you must check that your exam booklet is complete. 5) Write your solutions in the space provided. If you need more space, write on the back of the sheet containing the problem or on the three extra sheets and make an arrow indicating that. Scratch sheets will not be graded unless an arrow on the problem page indicates that the solution extends to the scratch sheets. 6) When you are told that time is up, stop working on the test. Good Luck! Don t write anything below ;-) Exercise Possible Marks Final Marks

2 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 1 Exercise 1 ( =12 Marks) a) Which sorting algorithm does run fastest when the data is already almost sorted? Choose only one. Justify your answer. 1. Bubble Sort 2. Selection Sort 3. Insertion Sort Insertion Sort, as it will only shift the first i elements when it encounters an item that is out of place. In case of almost sorted arrays, there are not many items that are out of place. b) What does the following postfix expression evaluate to? (Note: % is the modulus operator, not a percentage symbol) Do not transform it to infix notation. Justify your answer by using the appropriate data structure * % / 8 Using Stacks or BTrees (By drawing the steps of the solution) c) Draw all possible binary trees that have the following preorder traversal. Preorder: A B C A A A / / \ \ B B C B / / C C A A \ / B B \ \ C C

3 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 2 d) What is the smallest number of nodes that can be found in a binary search tree tree of height 4 (Note: root is at level zero)? Justify your answer by drawing the tree. 5 Nodes. For example: 0 \ 1 \ 2 \ 3 \ 4 e) Draw a binary tree consisting of 3 nodes such that the preorder and inorder traversals are the same. A \ B \ C f) Draw all possible binary search trees for three keys 1, 2, and / / 2 1 / \ / \ \ \ 2 3 \ / 3 2

4 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 3 Exercise 2 (10 Marks) Write an external method processqueue that simulates a manufacturing line. The method is given a queue of assembly items and an array of stacks. The method should continuously dequeue items from the queue until it is empty. After dequeing an item from the queue, it inspects the dequeued item to determine which stack it will go to. If a target stack is full, the method should enqueue the item back into the queue until the stack has a space again. The definition of class item (that will be inserted in the queue and stacks) is given below. public class AssemblyItem{ public int TargetStack; Stack ADT public class Stack { public Stack(int s); public void push(object k); public Object pop(); public int size(); public boolean isempty(); public boolean isfull(); Queue ADT public class Queue { public Queue(int s); public void enqueue(object k); public Object dequeue(); public int size(); public boolean isempty(); public boolean isfull();

5 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 4 The definition of the method is given below public class AssemblyLine{ public void processqueue( Queue queue, Stack[] StackArr ){ while(!queue.isempty()){ AssemblyItem item =(AssemblyItem) queue.dequeue(); int target = item.targetstack; if(stackarr[target].isfull()) queue.enqueue(item); else stackarr[target].push(item);

6 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 5 Exercise 3 (15 Marks) Write a method called deletetwosmallest that takes a singly linked list and deletes the two nodes that are next to each other in the list and have the smallest combined sum. After this deletion, a node with the smallest combined sum should be inserted at the end of the list. For example, if we have the following list: 1 -> 4 -> -10 -> 6 -> -5 the smallest combined sum of consecutive nodes is -6 which corresponds to = -6. So, after this operation the list would be: 1 -> 6 -> -5 -> -6 For full credit, your solution should NOT use the keyword new. Note: Remember to account for the cases where there are less than 2 elements in the list and when there are exactly two elements in the list. You are only allowed to use the following classes. You should not assume that there are any methods in these classes. public class Node { int data; Node next; public class SinglyLinkedList { Node First; public void deletetwosmallest() { p u b l i c c l a s s N o d e L i s t S o l u t i o n { p u b l i c v oid d e l e t e T w o S m a l l e s t ( ) { / / check l i s t has l e s s t h a n two e l e m e n t s i f ( f i r s t == n u l l f i r s t. n e x t == n u l l ) r e t u r n ; / / check l i s t has e x a c t l y two e l e m e n t s i f ( f i r s t. n e x t. n e x t == n u l l ) { f i r s t. d a t a = f i r s t. d a t a + f i r s t. n e x t. d a t a ; f i r s t. n e x t = n u l l ; r e t u r n ; / / s e a r c h f o r t h e min sum Node c u r r e n t = f i r s t ; Node p r e v i o u s = f i r s t ; Node b e f o r e S m a l l e s t = f i r s t ; i n t mindiff = f i r s t. d a t a + f i r s t. n e x t. d a t a ; w h i l e ( c u r r e n t. n e x t!= n u l l ) { i f ( c u r r e n t. d a t a + c u r r e n t. n e x t. d a t a < mindiff ) {

7 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 6 b e f o r e S m a l l e s t = p r e v i o u s ; mindiff = c u r r e n t. d a t a + c u r r e n t. n e x t. d a t a ; p r e v i o u s = c u r r e n t ; c u r r e n t = c u r r e n t. n e x t ; i f ( b e f o r e S m a l l e s t == f i r s t ) { f i r s t = f i r s t. n e x t ; e l s e { b e f o r e S m a l l e s t. n e x t = b e f o r e S m a l l e s t. n e x t. n e x t ; / / s h i f t i n g t h e d a t a of Nodes and s e t t i n g t h e l a s t node t o m i n D i f f e r e n b e f o r e S m a l l e s t = b e f o r e S m a l l e s t. n e x t ; w h i l e ( b e f o r e S m a l l e s t. n e x t!= n u l l ) { b e f o r e S m a l l e s t. d a t a = b e f o r e S m a l l e s t. n e x t. d a t a ; b e f o r e S m a l l e s t = b e f o r e S m a l l e s t. n e x t ; b e f o r e S m a l l e s t. d a t a = mindiff ; / / Another S o l u t i o n p u b l i c v oid d e l e t e T w o S m a l l e s t 2 ( ) { / / check l i s t has l e s s t h a n two e l e m e n t s i f ( f i r s t == n u l l f i r s t. n e x t == n u l l ) r e t u r n ; / / check l i s t has e x a c t l y two e l e m e n t s i f ( f i r s t. n e x t. n e x t == n u l l ) { f i r s t. d a t a += ( f i r s t. n e x t. d a t a ) ; f i r s t. n e x t = n u l l ; r e t u r n ; / / i n i t i a l i z e v a r i a b l e s i n t smallestsum = f i r s t. d a t a + f i r s t. n e x t. d a t a ; i n t s m a l l e s t I n d e x = 0 ; i n t c u r I n d e x = 0 ; Node c = f i r s t ; / / s e a r c h f o r min sum w h i l e ( c. n e x t!= n u l l ) { i n t cursum =c. d a t a + c. n e x t. d a t a ; i f ( cursum < smallestsum ) { smallestsum = cursum ; s m a l l e s t I n d e x = c u r I n d e x ; c = c. n e x t ; c u r I n d e x ++; / / loop t o c o r r e c t p o s i t i o n c u r I n d e x = 0 ; c = f i r s t ; w h i l e ( c u r I n d e x < s m a l l e s t I n d e x 1) { c = c. n e x t ;

8 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 7 c u r I n d e x ++; / / d e l e t e e l e m e n t s and r e u s e one of nodes Node i n s e r t L a s t = c. n e x t ; i f ( c == f i r s t ) f i r s t = f i r s t. n e x t. n e x t ; e l s e c. n e x t = c. n e x t. n e x t. n e x t ; i n s e r t L a s t. d a t a = smallestsum ; i n s e r t L a s t. n e x t = n u l l ; / / i n s e r t l a s t c = f i r s t ; w h i l e ( c. n e x t!= n u l l ) c = c. n e x t ; c. n e x t = i n s e r t L a s t ;

9 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 8 Exercise 4 Given the following tree and assume the root is at level 0 (5+8=13 Marks) 14 / \ / \ 7 11 / \ / \ / \ / / a) Circle all the true statements about the tree above: 1. The tree is a binary tree. 2. The tree is a binary search tree. 3. The tree is balanced. 4. The tree has a height of The node 30 is at depth 2. The correct statements are 1, 3 and 5. b) For the above tree, Label the following tree traversals as preorder, inorder, postorder, or invalid. (Invalid signifies that one or more sequences are improper traversals of the tree.) PreOrder Invalid InOrder PostOrder

10 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 9 Exercise 5 (4+10=14 Marks) A search tree data structure is similar to a binary search tree except that it keeps two values and three references in a node. The values are called left value and right value. The children are called left, middle and right. The invariants for this data structure are children to the left are smaller than the left value in the node. children in the middle are between the left value and the right value in the node. children to the right are greater than the right value in the node. Following is an example of a tree: a) Write the definition of class Link (aka Node) that could be used with the above description. b) Write a recursive search method that takes an integer as a target parameter and returns the node the target exists in or null. Specify the best case time complexity and the worst case time complexity given a nonempty tree. p u b l i c c l a s s Node { i n t v1 ; i n t v2 ; Node l e f t ; Node middle ; Node r i g h t ; p u b l i c Node ( i n t v1, i n t v2 ) { t h i s. v1 = v1 ; t h i s. v2 = v2 ; c l a s s Tree { Node r o o t ; p u b l i c Tree ( ) { r o o t = n u l l ; p u b l i c Node s e a r c h ( i n t v ) {

11 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 10 r e t u r n s e a r c h ( r o o t, v ) ; p u b l i c Node s e a r c h ( Node n, i n t v ) { i f ( n == n u l l ) r e t u r n n u l l ; e l s e i f ( n. v1 == v n. v2 == v ) r e t u r n n ; e l s e i f ( v > n. v2 ) r e t u r n s e a r c h ( n. r i g h t, v ) ; e l s e i f ( v < n. v1 ) r e t u r n s e a r c h ( n. l e f t, v ) ; e l s e r e t u r n s e a r c h ( n. middle, v ) ; / / b e s t c a s e i s O( 1 ) / / w o r s t c a s e i s O( n )

12 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 11 Exercise 6 Assume the following keys: ( =16 Marks) 28, 47, 20, 36, 23, 25, 19, 22, 7, 54 have been inserted in that same sequence order (28 first, 54 last) in a hash table of size 11. Fill in the hash table with the above values using each of the following collision handling strategies. Assume the hash function used is: a) Linear Probing f(key) = key%11 b) Quadratic Probing c) Chaining

13 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 12 d) Double hashing using the secondary hash function: g(key) = key%7 If the secondary function fails (collision happens), linear probing is used with the first hash function.

14 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 13

15 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 14 Exercise 7 This question is very popular on programming interviews. (10 Marks) Given an array of integers, you would like to print the elements and the count of their duplications in O(n) if we assume a uniform distribution of the integers, no collision occurs. For example, if the array consists of [11,14,11,5,12,14,11,30,5,5,12,5] the algorithm should output the following, assuming we are using a hashtable of size 10, and the hash function is : 30 occurs 1 time(s) 11 occurs 3 time(s) 12 occurs 2 time(s) 14 occurs 2 times(s) 5 occurs 4 time(s) f(key) = key%10 Write in Java the algorithm to perform this operation using Hashtables to ensure an O(n) time complexity. Hint: You can use two hashtables. Consider this interface of the Hashtable: public class Hashtable{ int [] array; int size; public Hashtable (int s){ array = new int[s]; size = s; void put (int key, int value){ // maps the specified key to the specified value in this hashtable void remove (int key){ // removes the key (and its corresponding value) from this hashtable. //This method does nothing if the key is not in the hashtable. int get (int key){ //returns the value to which the specified key is mapped. int hashcode (int key){ //returns the hashcode of the specified key using the function key%tablesize. boolean contains(int value) { // tests if some key maps into the specified value in this hashtable. //This method return true if and only if some key maps to the value argument //in this hashtable, false otherwise.

16 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 15 public void duplicatescount(int [] a){ p u b l i c c l a s s Q7 { p u b l i c s t a t i c v oid d u p l i c a t e s C o u n t ( i n t [ ] a ) { H a s h t a b l e numbers = new H a s h t a b l e ( a. l e n g t h ) ; H a s h t a b l e o c c u r r e n c e s = new H a s h t a b l e ( a. l e n g t h ) ; f o r ( i n t i = 0 ; i < a. l e n g t h ; i ++) { i n t key = numbers. hashcode ( a [ i ] ) ; i n t c o u n t = o c c u r r e n c e s. g e t ( key ) ; o c c u r r e n c e s. p u t ( key, c o u n t + 1 ) ; numbers. p u t ( key, a [ i ] ) ; f o r ( i n t i = 0 ; i < numbers. s i z e ; i ++) { i f ( o c c u r r e n c e s. a r r a y [ i ] > 0) System. o u t. p r i n t l n ( numbers. a r r a y [ i ] + " o c c u r s " + o c c u r r e n c e s. a r r a y [ i ] + " time ( s ) " ) ;

17 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 16 Scratch paper

18 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 17 Scratch paper

19 Data Structures and Algorithms, Final Exam, December 26, 2015 Page 18 Scratch paper

CSEN202: Introduction to Computer Programming Spring Semester 2014 Final Exam

Page 0 German University in Cairo June 14, 2014 Media Engineering and Technology Faculty Prof. Dr. Slim Abdennadher CSEN202: Introduction to Computer Programming Spring Semester 2014 Final Exam Bar Code