Welcome to Data Structure Quiz, Intermediate Level !!

Question 1. Consider the following C code segment:
int IsPrime(n) 
{ 
    int i,n; 
    for(i=2;i<=sqrt(n); i++  ) 
         if(n%i == 0) 
         {
               printf("Not Prime\n"); 
               return 0;
         } 
    return 1; 
}

Let T(n) denotes the number of times the for loop is executed by the program on input n. Which of the following is TRUE?

T(n) = O(sqrt(n)) and T(n) = Omega(sqrt(n))

T(n) = O(sqrt(n)) and T(n) = Omega(1)

T(n) = O(n) and T(n) = Omega(sqrt(n))

none of the above

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. Consider the following C program segment where CellNode represents a node in a binary tree:
struct CellNode
{
  struct CellNOde *leftChild;
  int element;
  struct CellNode *rightChild;
};

int GetValue(struct CellNode *ptr)
{
  int value = 0;
  if (ptr != NULL)
  {
   if ((ptr->leftChild == NULL) &&
        (ptr->rightChild == NULL))
      value = 1;
   else
      value = value +  GetValue(ptr->leftChild)
                   +  GetValue(ptr->rightChild);
  }
  return(value);
}

The value returned by GetValue() when a pointer to the root of a binary tree is passed as its argument is:

the number of nodes in the tree

the number of internal nodes in the tree

the number of leaf nodes in the tree

the height of the tree

Question 4. What is the maximum height of any AVL tree with 7 nodes? Assume that the height of a tree with a single node is 0.

2

3

4

5

Question 5. To implement Dijkstra's shortest path algorithm on unweighted graphs so that it runs in linear time, the data structure to be used is:

Queue

Stack

Heap

B-Tree

Question 6. What is the best definition of a collision in a hash table?

Two entries are identical except for their keys.

Two entries with different data have the exact same key.

Two entries with different keys have the same exact hash value.

Two entries with the exact same key have different hash values.

Question 7. Let X be a problem that belongs to the class NP. Then which one of the following is TRUE?

There is no polynomial time algorithm for X.

If X can be solved deterministically in polynomial time, then P = NP.

If X is NP-hard, then it is NP-complete.

X may be undecidable.

Question 8. Consider a binary max-heap implemented using an array. Which one of the following array represents a binary max-heap?

25,12,16,13,10,8,14

25,14,13,16,10,8,12

25,14,16,13,10,8,12

25,14,12,13,10,8,16

Question 9. A program P reads in 500 integers in the range [0..100] representing the scores of 500 students. It then prints the frequency of each score above 50. What would be the best way for P to store the frequencies?

An array of 50 numbers

An array of 100 numbers

An array of 500 numbers

A dynamically allocated array of 550 numbers

Question 10. Consider the following algorithm for searching for a given number x in an unsorted array A[1..n] having n distinct values:
1) Choose an i uniformly at random from 1..n;
2) If A[i] = x then Stop else Goto 1;
Assuming that x is present in A, what is the expected number of comparisons made by the algorithm before it terminates?

n

n - 1

2n

n/2