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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Q. What is printed by the print statements in the program P1 assuming call by reference parameter passing?

Program P1()
{
x = 10;
y = 3;
func1(y,x,x);
print x;
print y;
}
func1(x,y,z)
{
y = y+4;
z = x+y+z;
}

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Q. Consider the following three C functions :

[PI] int * g (void)
{
int x= 10;
return (&x);
}

[P2] int * g (void)
{
int * px;
*px= 10;
return px;
}

[P3] int *g (void)
{
int *px;
px = (int *) malloc (sizeof(int));
*px= 10;
return px;
}

Which of the above three functions are likely to cause problems with pointers?

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Q. Consider the following program

Program P2
var n: int:
procedure W(var x: int)
begin
x=x+1;
print x;
end

procedure D
begin
var n: int;
n=3;
W(n);
end
begin //beginP2
n=10;
D;
end

If the language has dynamic scoping and parameters are passed by reference, what will be printed by the program?

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Q. In the C language

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Q. The results returned by functions under value-result and reference parameter passing conventions

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Q. Consider the following declaration of a two dimensional array in C:

char a[100][100];

Assuming that the main memory is byte-addressable and that the array is stored starting from memory address 0, the address of a [40][50] is :

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

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Q. 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 ?

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Q. The running time of the following algorithm Procedure A(n)

If n < = 2 return (1)
else return (A(Image not present√nImage not present));

is best described by :

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Q. A weight-balanced tree is a binary tree in which for each node, the number of nodes in the left subtree is at least half and at most twice the number of nodes in the right subtree. The maximum possible height (number of nodes on the path from the root to the furthest leaf) of such a tree on n nodes is best described by which of the following?

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Q. Consider the following C function.

float f(float x, int y)
{
float p, s; int i;
for (s=1, p=1, i=1; i < y; i ++)
{
p*= x/i;
s+=p;
}
return s;
}

For large values of y, the return value of the function f best approximates

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Q. Assume the following C variable declaration

int *A [10], B[10][10]; 

Of the following expressions:

I A[2]
II A[2][3]
III B[1]
IV B[2][3]

which will not give compile-time errors if used as left hand sides of assignment statements in a C program?

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Q. Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an initially empty binary search tree. The binary search tree uses the usual ordering on natural numbers. What is the in-order traversal sequence of the resultant tree ?

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Q. Consider the following three claims

1. (n + k)^m = Θ(n^m), where k and m are constants
2. 2^(n + 1) = O(2^n)
3. 2^(2n + 1) = O(2^n)

Which of these claims are correct ?

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Q. The unusual Θ(n^2) implementation of Insertion Sort to sort an array uses linear search to identify the position where and element is to be inserted into the already sorted part of the array. If, instead, we use binary search to identify the position, the worst case running time will

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