2) Which data structure is most suitable for search operations? A) Linked List B) Queue C) Hash table D) Sorted array

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1 Philadelphia University Faculty of Engineering Student Name: Student Number: Dept. of omputer Engineering Final Exam, First Semester: 2016/201 ourse Title: Data Structures and Algorithms Date: 31/12/201 ourse No: (63022) Time Allowed: 2 Hours Lecturer: Anis Nazer No. of Pages: Question 1: hoose the correct answer in the following questions Question 1) Which of the following statements is true?. this is a very tricky question, leave it to the end, in case you change your mind:) (I) I love this course (II) I learned a lot of useful information in the course (III) The exam is very hard A) (I) only ) (II) only ) (III) only D) other? (15 marks) Answer 2) Which data structure is most suitable for search operations? A) Linked List ) Queue ) Hash table D) Sorted array 3) The table below shows the run times of an algorithm for some values of n, what is the complexity of the code? n runtime (ms) D A) O(n) ) O(n 2 ) ) O(lg n) D) O(nlg n) ) What is the complexity of the following code assuming fun() is O(n)? for( i=1 ; i < n ; i++ ) for( j=1 ; j <= 1000 ; j=+j ) fun(j) A) O(n) ) O(n 2 ) ) O(nlg n) D) None of the choices 5) Which of the following operations will be O(n) for a doubly linked list implemented using nodes and pointers? A) addtohead() ) deletefromtail() ) isinlist() D) addtotail() 6) A max heap is a tree structure where every node is larger than its children, which of the following is a max heap? A) 2 ) 6 ) 6 D) None of the choices D 2 1/6

2 ) The number of levels in a complete binary tree containing N elements is A) floor(lg(n +1)) ) N ) 2 N D) cannot be determined A 8) Suppose that bubble sort of 100 items has completed 30 iterations of the outermost loop. How many items are now guaranteed to be in their final position (never to be moved again)? A) 0 ) 15 ) 30 D) unknown 9) onsider the average case for the following operations on a data of size n 1. finding the maximum of a sorted array 2. finding the maximum in a queue 3. finding the maximum in a binary search tree The operations from fastest to slowest : A) 3, 1, 2 ) 1, 2, 3 ) 2, 1, 3 D) 1, 3, 2 D 10) In the worst case scenario, sequential search is and binary search is A) O(n 2 ), O(lg n) ) O(n), O(lg n) ) O(lg n), O(n) D) O(n), O(n) 11) Assume the array size is 100 and the used hash function is based on folding, where the key is divided into 3 digit numbers and the numbers are added. What is the hash for the key value ? A) 1269 ) 69 ) 15 D) 8 12) Assuming an array of size 2 k, how many merge operations will be performed using merge sort algorithm? A) 2 k 1 ) k ) (2 k 1 ) 1 D) depends on the data 13) Given the following array, what is the order of elements after two passes of comb sort (i.e h= then h=5) 1, 8, 6, 2,,, 1, 0, 2, 3 A) 0, 2, 3, 2,,, 1, 1, 8, 6 ) 0, 1, 1, 2, 2, 3,, 6,, 8 ) 0, 1, 1, 2,,, 2, 3, 8, 6 D) None of the choices is correct Refer to the following ST tree to answer parts (1) and (15) A 1) The order of visited nodes after performing breadth first traversal is: A) 2, 1, 6,,, 3, 5, 8 ) 2, 1, 6,, 3, 5,, 8 ) 1, 3, 5,, 8,, 6, 2 D) 1, 2, 3,, 5, 6,, 8 15) The order of visited nodes using post order traversal after removing node 6 with merge algorithm A) 1, 3, 5,, 8,, 2 ) 1, 3, 8,, 5,, 2 ) 1, 3,, 8,, 5, 2 D) 1, 2, 3,, 5,, 8 2/6

3 Question 2: (5 marks) Assuming that the types LLQueue and LLStack are implemented as discussed in lectures, what is the output of the following programs? Program class Node public: int data; Node *next; Node( int d=0, Node *p = NULL) data = d; next = p; ; ; Node *t, *p; t = new Node(3); t = new Node(8, t); t = new Node(, t); while ( t!= NULL ) p = t; cout << p >data << endl; t = t >next; delete p; int rec(int n) if ( n < 2 ) return n; return rec(rec(n 1)); cout << rec(5); int rec(int n) if ( n < 2 ) return n; return rec(n 1) + rec(n 2); cout << rec(5); LLQueue m; for (int i=0; i < ; i++) m.enqueue(i); m.enqueue(i+1); m.dequeue(); m.display(); // assume that reverse() reverses the stack LLStack s; for (int i = 1; i <= 8 ; i++) s.push(i*i); output: cout << s.pop() << endl; s.reverse(); s.pop(); s.reverse(); cout << s.pop() << endl; 3/6

4 Question 3: a) Name three applications that use a stack data structure - function call stack - adding big intgeres - delimiter matching - acktracking can be implemented using a stack (13 marks) (1 mark) b) Give a brief definition of the term acktracking and give an example of a problem that can be solved using acktracking acktracking: is an algorithm to solve some problems, where you start by a guess and continue, if you reach a point where there is more than one option, you chose one and continue until you reach a solution. If a solution is not found, you backtrack to the nearest point where you had an option, and chose another valid option (1 mark) c) Write a function that returns a random number between 1 and with the following distribution 2 marks) returned value probability int random() int N = rand() % ; if ( N > 85 ) return ; if ( N > 35 ) return 3; if ( N > 30 ) return 2; return 1; 1 30% 2 5% 3 50% 15% e) Write a recursive member function "count()" for the linkedlist class that returns the number of nodes in the list int LinkedList::count() return count(head); int LinkedList::count(Node *p) if ( p == NULL ) return count(p->link); f) Write a member function "isst()" for the inarytree class that returns true if the tree is a binary search tree bool inarytree::isst() if ( root == NULL ) return false; return isst(root); bool inarytree::isst(node *p) if (p == NULL (p->left == NULL && p->right == NULL) ) return true; bool ST_flag = true; if ( p->left!= NULL ) if ( p->data > p->left->data) ST_flag = isst( p->left ); ST_flag = false; if ( ST_flag && p->right!= NULL ) if ( p->data < p->right->data ) ST_flag = isst ( p->right ); ST_flag = false; return ST_flag; /6

5 g) Write ++ code for a member function insertsorted(int d) for a linked list. The function traverses the list until it finds the correct location, then it inserts a node in that location. // assuming ascending order void LinkedList::insertSorted(int d) if ( head == NULL d < head->data ) addtohead(d); Node *p, *q; p = q = head; while ( p!= NULL && d > p->data ) q = p; p = p->link; if ( p == NULL ) addtotail(d); q->link = new Node(d, p); (3 marks) h) Write a function "join()" that takes two LinkedLists L1 and L2 and returns a linked list L3. The returned list is composed of joining the lists L1 with L2. Note that the function is not a member of the LinkedList class and L1, L2 should not be modified. Assume member functions of LinkedList class are defined LinkedList join( LinkedList L1, LinkedList L2 ) LinkedList tmp; int d; while (! L1.isEmpty() ) d = L1.deleteFromHead(); tmp.addtotail(d); L3.addtoTail(d); while (! tmp.isempty() ) L1.addToTail( tmp.deletefromhead() ) while (! L2.isEmpty() ) d = L2.deleteFromHead(); tmp.addtotail(d); L3.addtoTail(d); while (! tmp.isempty() ) L2.addToTail( tmp.deletefromhead() ) return L3; 5/6

6 Question : ( marks) Assuming you have the following key values, and an array of size, and hash function is h(x) = x % 15, 8, 28, 29, 0, a) Define the following terms double hashing and clustering briefly (in context of the topic of hashing) Double hashing: is a method to resolve collisions in a hash table, where a second hash function is used to find the location of the colliding key lustering: is a problem in hash tables, where colliding key tend to be placed or grouped together, this occurs mainly when linear probing is used to resolve collisions b) What are the contents of the array after adding the keys using linear probing index data (1.5 marks) c) What are the contents of the array after adding the keys using quadratic probing index data (1.5 marks) d) Write a ++ search function based on linear probing. The prototype of the function is as follows: bool search(int table[][2], int key, int size); where table is a 2D array, the first column contains the keys, and the second column contains 0 if the position is available, and 1 if the position is occupied bool search(int table[][2], int key, int size) int i = key % ; int counter = 1; while ( table[i][1]!= 0 && counter <= ) if ( table[i][0] == key ) return true; i = (i + 1) % ; return false; cout << "GOOD LUK :)"; 6/6