Q. An implementation of a queue Q, using two stacks S1 and S2, is given below:

void insert(Q, x) {
   push (S1, x);
}
  
void delete(Q){
   if(stack-empty(S2)) then
      if(stack-empty(S1)) then {
          print(“Q is empty”);
          return;
      }
      else while (!(stack-empty(S1))){
          x=pop(S1);
          push(S2,x);
      }
   x=pop(S2);
}

Let n insert and m (<=n) delete operations be performed in an arbitrary order on an empty queue Q. Let x and y be the number of push and pop operations performed respectively in the process. Which one of the following is true for all m and n?

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Q. Consider the following pseudo code. Assume that IntQueue is an integer queue. What does the function fun do?

void fun(int n)
{
IntQueue q = new IntQueue();
q.enqueue(0);
q.enqueue(1);
for (int i = 0; i < n; i++)
{
int a = q.dequeue();
int b = q.dequeue();
q.enqueue(b);
q.enqueue(a + b);
ptint(a);
}
}

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Q. Suppose implementation supports an instruction REVERSE, which reverses the order of elements on the stack, in addition to the PUSH and POP instructions. Which one of the following statements is TRUE with respect to this modified stack?

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Q. A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are performed efficiently. Which one of the following statements is CORRECT (n refers to the number of items in the queue)?

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Q. Suppose you are given an implementation of a queue of integers. The operations that can be performed on the queue are:

i. isEmpty (Q) — returns true if the queue is empty, false otherwise.
ii. delete (Q) — deletes the element at the front of the queue and returns its value.
iii. insert (Q, i) — inserts the integer i at the rear of the queue.
Consider the following function:

void f (queue Q) {
int i ;
if (!isEmpty(Q)) {
i = delete(Q);
f(Q);
insert(Q, i);
}
}

What operation is performed by the above function f ?

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Q. The following C declarations

struct node
{
int i;
float j;
};
struct node *s[10] ;

define s to be

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Q. The most appropriate matching for the following pairs

X: m=malloc(5); m= NULL; 1: using dangling pointers
Y: free(n); n->value=5; 2: using uninitialized pointers
Z: char *p; *p = ’a’; 3. lost memory

is:

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Q. The most appropriate matching for the following pairs

X: depth first search 1: heap
Y: breadth-first search 2: queue
Z: sorting 3: stack

is

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Q. Consider the following nested representation of binary trees: (X Y Z) indicates Y and Z are the left and right sub stress, respectively, of node X. Note that Y and Z may be NULL, or further nested. Which of the following represents a valid binary tree?

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Q. Let s be a sorted array of n integers. Let t(n) denote the time taken for the most efficient algorithm to determined if there are two elements with sum less than 1000 in s. which of the following statements is true?

a) t (n) is O(1)
b) n < t (n) < n log2n
c) n log 2 n < t (n) < (n/2)
d) t (n) = [/Tex]{n \choose 2} [/Tex]

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Q. Aliasing in the context of programming languages refers to

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Q. Consider the following C declaration

struct {
short s [5]
union {
float y;
long z;
}u;
} t;

Assume that objects of the type short, float and long occupy 2 bytes, 4 bytes and 8 bytes, respectively. The memory requirement for variable t, ignoring alignment considerations, is

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Q. The number of tokens in the following C statement

printf("i = %d, &i = %x", i, &i);

is

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Q. B+ trees are preferred to binary trees in databases because

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Q. 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, l, n);

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Q. 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?

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Q. The value of j at the end of the execution of the following C program.

int incr(int i)
{
static int count = 0;
count = count + i;
return (count);
}
main()
{
int i,j;
for (i = 0; i <=4; i++)
j = incr(i);
}

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Q. Randomized quicksort is an extension of quicksort where the pivot is chosen randomly. What is the worst case complexity of sorting n numbers using randomized quicksort?

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Q. Consider any array representation of an n element binary heap where the elements are stored from index 1 to index n of the array. For the element stored at index i of the array (i <= n), the index of the parent is

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Q. What is the minimum number of stacks of size n required to implement a queue of size n?

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