Welcome to Data Structure Quiz, Randomly Selected !!

Question 1. A set X can be represented by an array x[n] as follows:
array pic
Consider the following algorithm in which x,y and z are Boolean arrays of size n:
algorithm zzz(x[] , y[], z []) 
{ 
    int i; 
    for (i=O; i<n;   ++i) 
    z[i] = (x[i] ^ ~y[i]) U (~x[i] ^ y[i]) 
}

The set Z computed by the algorithm is:

(X Intersection Y)

(X Union Y)

(X-Y) Intersection (Y-X)

(X-Y) Union (Y-X)

Question 2. The inorder and preorder traversal of a binary tree are d b e a f c g and a b d e c f g, respectively. The postorder traversal of the binary tree is:

d e b f g c a

e d b g f c a

e d b f g c a

d e f g b c a

Question 3. In the worst case, the number of comparisons needed to search a singly linked list of length n for a given element is

log 2 n

n/2

log 2 n - 1

n

Question 4. Consider a hash table of size seven, with starting index zero, and a hash function (3x + 4)mod7. Assuming the hash table is initially empty, which of the following is the contents of the table when the sequence 1, 3, 8, 10 is inserted into the table using closed hashing? Note that '_' denotes an empty location in the table.

8, _, _, _, _, _, 10

1, 8, 10, _, _, _, 3

1, _, _, _, _, _,3

1, 10, 8, _, _, _, 3

Question 5. The running time of the following algorithm
Procedure A(n)
If n <= 2 return(1) else return A(sqrt(n));
is best described by

O(n)

O(log n)

O(1og log n)

O(1)

Question 6. Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a postorder, inorder and preorder traversal. Respectively, of a complete binary tree. Which of the following is always true?

LASTIN = LASTPOST

LASTIN = LASTPRE

LASTPRE = LASTPOST

none of the above

Question 7. Consider the following recurrence:
recurrence
Which one of the following is true?

T(n) = Theta(loglogn)

T(n) = Theta(logn)

T(n) = Theta(sqrt(n))

T(n) = Theta(n)

Question 8. Suppose you are given an array s[1...n] and a procedure reverse (s,i,j) which reverses the order of elements in a between positions i and j (both inclusive). What does the following sequence do, where 1 < k <= n:
  reverse (s, 1, k);
  reverse (s, k + 1, n);
  reverse (s, 1, n);

Rotates s left by k positions

Leaves s unchanged

Reverses all elements of s

none of the above

Question 9. In quick sort, for sorting n elements, the (n/4)th smallest element is selected as pivot using an O(n) time algorithm. What is the worst case time complexity of the quick sort?

O(n)

O(nlogn)

O(n^2)

O(n^2logn)

Question 10. Consider the following functions:
f(n) = 2^n
g(n) = n!
h(n) = n^logn
Which of the following statements about the asymptotic behavior of f(n), g(n), and h(n) is true?

f(n) = O(g(n)); g(n) = O(h(n))

f(n) = Omega(g(n)); g(n) = O(h(n))

g(n) = O(f(n)); h(n) = O(f(n))

h(n) = O(f(n)); g(n) = Omega(f(n))