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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Q. How many B+ trees of order 3 can be constructed using 3 district keys?

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Q. Find the order of B+ tree leaf node using the following:

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

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Q. What is the name for the adjacency matrix?

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Q. To identify articulation points in a graph, ……….is very useful?

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Q. The name backtrack was first coined by ………..

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Q. In the backtracking Method, the modified criterion function is also known as………

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Q. In backtracking, the function which needs to be maximized or minimized for a given problem is known as………….

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