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1 Philadelphia University Faculty of Engineering Student Name: Student Number: Dept. of Computer Engineering Final Exam, First Semester: 201/2018 Course Title: Data Structures and lgorithms Date: 1/2/2018 Course No: (630224) Time llowed: 2 hour Lecturer: nis Nazer No. of Pages: Question Q1 Q2 Q3 Q4 Q5 Q6 Q Total Grade Question 1: Choose the correct answer in the following questions: Question (1.5 mark each) (18 marks) nswer 1) The data structure is suitable if many insert/delete operations are used, while the structure is suitable if many random access operations are used. ) rray, Queue B) Stack, Tree C) Hash table, Circular linked list D) Linked list, rray D 2) Given that lgorithm X is O(lg n) and the runtime of the algorithm for n=1,000,000 is 1s. What is the expected approximate runtime if n = 10,000,000? ) 1.532s B) 1.16s C) 10.0s D) 100s B 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 s s s s D ) O(n) B) O(lgn) C) O(n 2 ) D) O(n 3 ) 4) What is the output of the following code segment? LLStack S; LLQueue Q; for ( int c=1; c<=10; c++) S.push(c); c++; Q.enqueue(c); cout << S.topEl() << ", " << Q.topEl() ; ) 9, 2 B) 10, 1 C) 1, 10 D) 1, 5 1/

2 Question 1: Continued... Choose the correct answer in the following questions: Question 5) What is the output of the following code segment LinkedList L; for (int c=1; c<=5; c++) if ( c % 2 == 0 ) L.addToHead(c); L.addToTail(c); while (! L.isEmpty() ) cout << L.deleteFromHead() << ", "; nswer B ) 5, 4, 3, 2, 1, B) 4, 2, 1, 3, 5, C) 5, 1, 3, 2, 4, D) 1, 2, 3, 4, 5, 6) finding the maximum in an unsorted array is: ) O(1) B) O(lg (n)) C) O(n) D) O(n 2 ) C ) Consider 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 : ) 1, 3, 2 B) 1, 2, 3 C) 3, 1, 2 D) 2, 1, 3 8) ssume that N is the number of nodes in a tree, and K is the number of arcs in the tree, the relation between N and K is: ) K = N + 1 B) K = N 1 C) N = K 1 D) There is no relation B 9) 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, 4,, 1, 0, 2, 3 ) 0, 2, 3, 2, 4,, 1, 1, 8, 6 B) 0, 1, 1, 2, 2, 3, 4, 6,, 8 C) 0, 1, 1, 2, 4,, 2, 3, 8, 6 D) None of the choices is correct C 10) ssume you have a sorted array of 1000 elements, what is the maximum number of comparisons that are performed in binary search to find whether the element is in the data or not ) 10 B) 50 C) 1000 D) Cannot be determined 11) What is the worst case scenario for insertion sort algorithm? ) a reversed sorted array B) a sorted array C) a half sorted array D) a random array 12) for an array of size 1000, how many elements are guaranteed to be in their final position after 50 iterations of selection sort? ) 10 B) 500 C) 950 D) None of the choices D 2/

3 Question 2: (5 marks) a) Name the disadvantage of using an array to implement a queue structure (1 mark) rray should pre allocated, so the memory space for the queue should be reserved beforehand. The enqueue() operation in a full stack is O(n) b) Write the member function "addtohead()" for a doubly linked circular list (2 marks) void DDCL::addToHead(int d) DDLNode *p = new DDLNode(d); if ( head == NULL ) tail = p; tail->next = p; tail->prev = p; p->next = tail->next; tail->next->prev = p; p->prev = tail; tail->next = p; c) Given a stack S1, write statements to copy the elements of S1 into an empty stack S2. Note that S1 should stay the same after the copy operation (2 marks) int main() Stack S1, S2, S_tmp; //... S1 is populated... // move elements to S_tmp, stack is reversed while (! S1.isEmpty() ) S_tmp.push( S1.pop() ); // move elements into S1 and S2, stack is reversed (back to original state) while (! S_tmp.isEmpty() ) int d = S_tmp.pop(); S1.push ( d ); S2.push ( d ); return 0; 3/

4 Question 3: The following member function is added to the list: void LinkedList::mystery(int d) Node *n = new Node(d, NULL); Node *q, *p; if ( head == NULL ) head = tail = n; if (head->data > d) n->link = head; head = n; p = q = head; while ( q!= NULL && q->data < d ) p = q; q = q->link; n->link = q; p->link = n; if ( q == NULL ) tail = n; a) What is the output of the following program? (2 marks) Program int main() LinkedList L; int [ ] =, 4, 1, 5 ; for ( int c=0; c < 4 ; c++ ) L.mystery( [c] ); while (! L.isEmpty() ) cout << L.deleteFromHead() << endl; return 0; Output b) What does the function do? (1 mark) it inserts elements in a linked list in sorted order 4/

5 Question 4: a) What is the output of the following program? (1 mark) Program void recfun( int [], int S, int i=0 ) if ( i == S ) recfun(, S, i+1 ); cout << [i] << endl; int main() int [ ] =, 4, 1, 5 ; recfun(, 4); return 0; Output b) Rewrite the recursive function above using a non recursive version of the same function. (2 marks) void nonrecfun( int [], int S, int i=0 ) int n = S-1; while ( n > i ) cout << [n] << endl; i++; Question 5: ssume you want to store the following data in a hash table. The hash function used is f(x) = x % 11. Start filling the table with x=16 16, 5, 11, 2, 38, 18 a) What is the size of the array that should be used to store the hash table? why? (1 mark) The size of the array should be 11, to make sure that all possible hash values are within array bounds b) Write the contents of the array if we use Linear probing for collision resolution (1 mark) index element c) Write the contents of the array if we use quadratic probing for collision resolution (1 mark) index element /

6 Question 6: The following data is inserted in a binary search tree structure, starting from 9 9, 1, 4,, 11, 2, 14, 5 (4 marks) a) Draw the resulting tree structure (1 mark) b) What is the order of the nodes if you perform postorder traversal (1 mark) post order Left, Right, Visit 2, 5,, 4, 14, 11, 1, 9 c) What is the order of the nodes if you perform breadth first traversal (assume left then right) (1 mark) 9, 4, 1, 2,, 11, 5, 14 d) draw the tree structure if you delete the node 9 using the merge algorithm (1 mark) /

7 Question : (4 marks) a) Name two sorting algorithms other than selection, insertion, bubble, comb, merge, or quick sort. (1 mark) heap sort, radix sort, bucket sort, coctail sort, counting sort, shell sort,. b) The code below is part of the merge sort algorithm. template <typename T> void mergesort(t X[], int first, int last) if ( last == first + 1 ) if ( X[first] > X[last] ) swap ( X[first], X[last] ); if ( first < last ) int mid = (first+last)/2; int n1 = mid- first + 1; int n2 = last - mid; mergesort(x,first, mid); mergesort(x, mid+1, last); merge(&x[first], n1, &X[mid+1], n2 ); ssume an array of size 8, what is correct order of function calls if you start with mergesort(x, 0, )? wrong order of function calls correct order of function calls mergesort(x, 2, 3 ) 1) mergesort(x, 0, 3 ) mergesort(x, 0, 1 ) 2) mergesort(x, 0, 1 ) merge(&x[4], 2, &X[6], 2) 3) mergesort(x, 2, 3 ) merge(&x[0], 4, &X[4], 4) 4) merge(&x[0], 2, &X[2], 2) mergesort(x, 6, ) 5) mergesort(x, 4, ) mergesort(x, 4, 5 ) 6) mergesort(x, 4, 5 ) merge(&x[0], 2, &X[2], 2) ) mergesort(x, 6, ) mergesort(x, 0, 3 ) 8) merge(&x[4], 2, &X[6], 2) mergesort(x, 4, ) 9) merge(&x[0], 4, &X[4], 4) GOOD LUCK /