NET/JRF-COMPUTER SCIENCE & APPLICATIONS. Time: 01 : 00 Hour Date : M.M. : 50

Transcription

1 1 NET/JRF-COMPUTER SCIENCE & APPLICATIONS UNIT TEST : DATA STRUCTURE Time: 01 : 00 Hour Date : M.M. : 50 INSTRUCTION: Attempt all the 25 questions. Each question carry TWO marks. 1. Consider the following code fragments int i, j, x; read (x); i = 1, j = 1; while (i < 10) j = j*i; i = i+1; if(i = = x) exit; Which of the following is correct at the end of the execution of the program j x 1! i x (a) (b) j 9! i 10 j 9! i 10 j x 1! i x (c) j 10! i 10 j x 1! i x (d) 2. Which of the following expressions evaluate to the largest number? (a) + * 257 (b) 2 + * 5 7 (c) * (d) * 7. What is the recurrence relation for the bit strings of length n that do not contains two consecutive 0 s. (a) Tn Tn 1 2Tn 2 (b) Tn Tn 1 Tn 2 (c) Tn 2Tn 1 Tn 2 (d) Tn 2Tn 1 2Tn 2 4. Let Mn BEAN is a data structure and we want to use Mr. BEAN to generate permutation of an input sequence 1, 2,, 4, 5, 6, 7, 8, 9 in that order. Consider the following statements (I) 2, 1, 4, 5, 7, 6, 9, 8 is a valid permutation if Mr. BEAN is a STACK (II) 1, 2,, 4, 9, 8, 7, 6, 5 is a valid permutation of Mr. BEAN is a Queue Which of the above statement is CORRECT? (a) I only (b) II only (c) both I and II (d) neither I nor II 5. Consider the following statement (I) In an AVL tree with n nodes max number of possible rotation is n 1. (II) If splay tree1 contain as data 1, 2,, 4 and splay tree2 contains data 9, 8, 10, 25, 0 the by joining them resultant splay tree has either 4 or 8 as root. (III) The difference between the external path length and internal path length in an extended binary tree with n internal node is 2n. Which of the above statement is correct (a) I only (b) I, II only (c) I, II, III (d) none of the above

2 2 6. What is the running time of the following code void foo (int n) int i, j, k for (i = 0; i < 10 ; i++) for (j = 0; j < n; j++) for (k = n 2; k < n + 2; k++) printf( KBC ); (a) O(n) (b) O(n 2 ) (c) O(n ) (d) O(nlogn) 7. Let us consider a linked list head above linked list is traversed till end and each key is inserted into an AVL tree. The final AVL tree is traversal in PREORDER and keys are inserted into a stack during the traversal. The key are popped one by one from the stack and printed. What is the correct printed sequence (a) 5, 2, 1,, 15, 11, 25, 50 (b) 50, 25, 11, 15,, 1, 2, 5 (c) 1, 2,, 5, 11, 15, 25, 50 (d) None of these 8. Consider the following method void BBC(int n) if (n > 0) BBC (n 1); print ( %, d, n); BBC (n 1); (a) what is output of BBC() (a) (b) (c) (d) Let T be a non empty strictly B.T. n(t) = number of leaf nodes h(t) = height of T T L = Left subtree of T T R = Right subtree of T and F T 0 if T is a leaf FTL F TR min h TL, htr otherwise Then what is F(T) =? (a) n(t) + h(t) 1 (b) n(t) + h(t) (c) n(t) h(t) 1 (d) n (T) h (T) 10. Let T be a rooted binary tree whose vertices are labelled with symbols a, b, c, d, e, f, g, h, i, j, k. Suppose the in-order (visit left sub-tree, visit root, visit right sub-tree) and post-order (visit left sub-tree, visit right sub-tree, visit root) traversals of T produce the following sequences. in-order: a, b, c, d, e, f, g, h, i, j, k post-order: a, c, b, e, f, h, j, k, i, g, d How many leaves does the tree have? (a) Four. (b) Five (c) Six (d) Cannot be determined uniquely from the given information.

3 11. Let A be a square matrix size n n. Consider the following pseudo code. What is the expected output? C = 100; for i = 1 to n do for j = 1 to n do Temp = A[ i ] [ j ] + C ; A [ i ] [ j ] = A [ j ] [ i ] ; A [ j ] [ i ] = Temp C ; for i = 1 to n do for j = 1 to n do print (A[ i ] [ j ]); (a) The matrix A itself (b) Transpose of the matrix A (c) Adding 100 to the upper diagonal elements and subtracting 100 from lower diagonal elements of A (d) None of these. 12. The following C function takes a simply-linked list as input argument. It modifies the list by moving the last element to the front of the list and returns the modified list. Some part of the code is left blank. typedef struct node int value; struct node *next; Node; Node *move_to_front(node *head) Node *p, *q; if ((head = = NULL: (head->next = = NULL)) return head; q = NULL; p = head; while (p-> next!=null) q=p; p=p->next; return head; Choose the correct alternative to replace the blank line. (a) q = NULL; p->next = head; head = p; (b) q->next = NULL; head = p; p->next = head; (c) head = p; p->next = q; q->next = NULL; (d) q->next = NULL; p->next = head; head = p; 1. A B-Tree used as an index for a large database table has four levels including the root node. If a new key is inserted in this index, then the maximum number of nodes that could be newly created in the process are (a) 2 (b) (c) 4 (d) 5

4 14. Let A be a two-dimensional array declared as follows: A: array [1. 10] [1 15] of integer; Assuming that each integer takes one memory locations the array is stored inrow-major order and the first element of the array is stored at location 100, whatis the address of the element A[i][j]? (a) 15i + j + 84 (b) 15j + i + 84 (c) 10i + j + 89 (d) 10j + i Let k be an integer greater than 1. Which of the following represents the growth rate of the expression as a function of n? (a) k n (b) n n k1 k (c) k (d) n 16. Which of the following is asymptotically smaller * log (b) log * (a) * (c)! (d)! 17. Suppose that the split at every level at quick sort are in proportion 1 to where constant. The minimum depth of a leaf in the recursion tree is approximately given by n 4 i1 k 1 0 is a 2 i (a) log1 (b) log 1 (c) log (d) log 18. Match the following (A) Tn Tn 1 (I) O (1) (B) Tn 2Tn 1 (II) O (2 n ) (C) Tn 2Tn 1 1 (III) O (n 2 ) (D) Tn 2Tn 1 2 (IV) O (n) (a) A-I, B-II, C-III, D-IV (b) A-I, B-II, C-IV, D-III (c) A-II, B-I, C-IV, D-III (d) A-I, B-II, C-I, D-II 19. void f 00 ( ) int a, b, c, d = 0; for (a = 1; a < 11; a++) for (b = 1; b < 11; b++) for (c = 1; c < 11; c++) if ((a + b + c)% = =.0) d = d + 1; What is the output of above program? (a) 81 (b) 4 (c) 412 (d) How many the following program prints void DS ( ) int m, n; for (m = 0; n = 100; n m > m n; ++m, n) printf ); (a) 50 (b) 51 (c) 100 (d) 101

5 21. A BST contains the value 1, 2,, 4, 5, 6, 7, 8. The tree traversal in preorder and the values are printed out. Which of the sequence is valid. (a) (b) (c) (d) In a B-tree of order 5 the following keys are inserted 7, 8, 14, 1, 20, 2, 6 and 5. How many elements are present in root of the tree (a) 1 (b) 2 (c) (d) 4 2. After partition in Quicksort around 15. How many elements will on left and right of 15 in following sequence: 80, 50, 0, 15, 10, 25, 9, 7, 6, 90, 1 (a) (5, 5) (b) (4,6) (c) (6, 5) (d) (6, 4) 24. For a 4-ary tree [Each node can contains maximum of 4 children]. What are the maximum and minimum number of nodes at hight h are respectively. (a) h 1 2 1, h 1 (b) h 1 4 1, h (c) 25. Consider the following statements h 1 4 1, h 1 1 I. maximum number of nodes possible in a heap of hight h is 2 1 II. Heapify algorithm takes O time 2 III. AnO n algorithm is always faster than an O n algorithm (d) h 1 4 1, h IV. The reason that we use randomization in quick sort is to eleminate the worst case scenario V. The heap sort uses extra memory space Which of the following is TRUE (a) I, II, V (b) I, II, III, IV (c) II, III, IV, V (d) None of these 5

6 6 UGC-NET/JRF-COMPUTER SCIENCE & APPLICATIONS UNIT TEST : DATA STRUCTURE Time: 01 : 00 Hour Date : M.M. : 50 ANSWER KEY 1. (d) 2. (d). (b) 4. (a) 5. (c) 6. (a) 7. (b) 8. (c) 9. (d) 10. (b) 11. (a) 12. (d) 1. (d) 14. (a) 15. (a) 16. (a) 17. (c) 18. (d) 19. (b) 20. (a) 21. (d) 22. (b) 2. (a) 24. (c) 25. (b)