Welcome to Data Structure Quiz, Intermediate Level !!

Question 1. 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

Question 2. 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 3. 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 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. 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 6. 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 7. An element in an array X is called a leader if it is greater than all elements to the right of it in X. The best algorithm to find all leaders in an array

Solves it in linear time using a left to right pass of the array

Solves it in linear time using a right to left pass of the array

Solves it using divide and conquer in time O(nlogn)

Solves it in time O(n^2)

Question 8. The number of leaf nodes in a rooted tree of n nodes, with each node having 0 or 3 children is:

n/2

(n-1)/3

(n-1)/2

(2n +1)/3

Question 9. We are given a set of n distinct elements and an unlabeled binary tree with n nodes. In how many ways can we populate the tree with the given set so that it becomes a binary search tree?

0

1

n!

(1/(n + 1)).2nCn

Question 10. 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.