Q. The best data structure to check whether an arithmetic expression has balanced parentheses is a

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Q. Consider the following C function:

int f(int n)
{
static int i = 1;
if (n >= 5)
return n;
n = n+i;
i++;
return f(n);
}

The value returned by f(1) is

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Q. Consider the following program fragment for reversing the digits in a given integer to obtain a new integer. Let n = D1D2…Dm

int n, rev;
rev = 0;
while (n > 0)
{
rev = rev*10 + n%10;
n = n/10;
}

The loop invariant condition at the end of the ith iteration is:

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Q. Consider the following C program segment:

char p[20];
char *s = "string";
int length = strlen(s);
int i;
for (i = 0; i < length; i++)
p[i] = s[length — i];
printf("%s",p);

The output of the program is

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Q. Consider the label sequences obtained by the following pairs of traversals on a labeled binary tree. Which of these pairs identify a tree uniquely ?

(i) preorder and postorder
(ii) inorder and postorder
(iii) preorder and inorder
(iv) level order and postorder

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Q. Two matrices M1 and M2 are to be stored in arrays A and B respectively. Each array can be stored either in row-major or column-major order in contiguous memory locations. The time complexity of an algorithm to compute M1 × M2 will be

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Q. Consider the following C program

main()
{
int x, y, m, n;
scanf ("%d %d", &x, &y);
/* Assume x > 0 and y > 0 */
m = x;
n = y;
while (m! = n)
{
if (m > n)
m = m - n;
else
n = n - m;
}
print f ("% d", n);
}

The program computes

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Q. What does the following algorithm approximate?

x = m;
y = 1;
while (x - y > e)
{
x = (x + y)/2;
y = m/x;
}
print(x);

(Assume m > 1, e > 0).

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Q. Consider the following C program segment

struct CellNode
{
struct CelINode *leftchild;
int element;
struct CelINode *rightChild;
}

int Dosomething(struct CelINode *ptr)
{
int value = 0;
if (ptr != NULL)
{
if (ptr->leftChild != NULL)
value = 1 + DoSomething(ptr->leftChild);
if (ptr->rightChild != NULL)
value = max(value, 1 + DoSomething(ptr->rightChild));
}
return (value);
}

The value returned by the function DoSomething when a pointer to the root of a non-empty tree is passed as argument is

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Q. The order of an internal node in a B+ tree index is the maximum number of children it can have. Suppose that a child pointer takes 6 bytes, the search field value takes 14 bytes, and the block size is 512 bytes. What is the order of the internal node?

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Q. Let A[1, ..., n] be an array storing a bit (1 or 0) at each location, and f(m) is a unction whose time complexity is θ(m). Consider the following program fragment written in a C like language:

counter = 0;
for (i = 1; i < = n; i++)
{
if (A[i] == 1)
counter++;
else {
f(counter);
counter = 0;
}
}

The complexity of this program fragment is

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Q. The time complexity of the following C function is (assume n > 0)

int recursive (int n) {
if (n == 1)
return (1);
else
return (recursive (n - 1) + recursive (n - 1));
}

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Q. A program takes as input a balanced binary search tree with n leaf nodes and computes the value of a function g(x) for each node x. If the cost of computing g(x) is min{no. of leaf-nodes in left-subtree of x, no. of leaf-nodes in right-subtree of x} then the worst-case time complexity of the program is

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Q. Choose the best matching between the programming styles in Group 1 and their characteristics in Group 2.

 Group-1 Group-2
 P.  Functional 1. Command-based, procedural
 Q.  Logic   2. Imperative, abstract data type
 R.  Object-oriented  3. Side-effect free, declarative, expression evaluation
 S.  Imperative   4. Declarative, clausal representation, theorem proving

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Q. How many B-tree of order 3 can be constructed using 3 district keys?

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Q. Which of the following is a minimum number of leaf nodes in a B-Tree of order 4 with height 3?

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Q. If we are accessing a block in 100 block index using binary search, how many block read is Required to access the data in 100th block?

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Q. Find the minimum number of elements that need to be placed in a B-tree of order 3 to reach 4 Levels?

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Q. Construct a B+ tree for (1, 4, 7, 10, 17, 21, 31, 25, 19, 20, 28, 42) with n = 4. What is the key value at the root node?

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Q. Calculate the order of B – tree using the following:

Block size = 512 bytes
Record pointer = 7 bytes
Block pointer = 6 bytes
Key filed = 9 bytes

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