### 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) = (sqrt(n))

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

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

none of the above

Question 2. 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 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. 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 5. 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 6. 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 *p, *q;
q = NULL; p = head;
while (p-> next !=NULL)
{
q = p;
p = p->next;
}
_______________________________
}```

Choose the correct alternative to replace the blank line.

head = p; p->next = q; q->next = NULL;

Question 7. What is the time complexity of the following recursive function:
```
int DoSomething (int n)
{
if (n <= 2)
return 1;
else
return (DoSomething (floor(sqrt(n))) +  n);
}```

O(n)

O(nlogn)

O(logn)

O(loglogn)

Question 8. 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 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. 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