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601.

Let S be a stack of size n ≥1. Starting with the empty stack, suppose we push the first n natural numbers in sequence, and then perform n pop operations. Assume that Push and Pop operations take X seconds each, and Y seconds elapse between the end of one such stack operation and the start of the next operation. For m ≥1, define the stack-life of m as the time elapsed from the end of Push(m) to the start of the pop operation that removes m from S. The average stack-life of an element of this stack is [2 marks]
(A) n(X + Y)
(B) 3Y + 2X
(C) n(X + Y) - X
(D) Y + 2X

asked in Computer Science And Engineering, 2003

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602.

A data structure is required for storing a set of integers such that each of the following operations can be done in O(log n) time, where n is the number of elements in the set.
I. Deletion of the smallest element
II. Insertion of an element if it is not already present in the set
Which of the following data structures can be used for this purpose? [2 marks]
(A) A heap can be used but not a balanced binary search tree
(B) A balanced binary search tree can be used but not a heap
(C) Both balanced binary search tree and heap can be used
(D) Neither balanced binary search tree nor heap can be used

asked in Computer Science And Engineering, 2003

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603.

In a permutation a₁ ... a_n, of n distinct integers, an inversion is a pair (a_i, a_j) such that
i < j and a_i > a_j.

[1]	If all permutations are equally likely, what is the expected number of inversions in a randomly chosen permutation of 1. . . n? [2 marks] (a) n(n-1)/4 (b) n(n-1)/2 (c) n(n+1)/4 (d) 2n[log₂n]

[2]	What would be the worst case time complexity of the Insertion Sort algorithm, if the inputs are restricted to permutations of 1. . . n with at most n inversions? [2 marks] (A) Θ(n²) (B) Θ(n log n) (C) Θ(n^1.5) (D) Θ(n)

asked in Computer Science And Engineering, 2003

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604.

A program consists of two modules executed sequentially. Let f₁(t) and f₂(t) respectively denote the probability density functions of time taken to execute the two modules. The probability density function of the overall time taken to execute the program is given by
[2 marks]
(a) f₁ (t ) + f₂ (t )
(b) _o∫^t f₁ (x )f₂ (x ) dx
(c) _o∫^t f₁ (x )f₂ (t-x ) dx
(d) max (f₁(t), f₂(t))

asked in Computer Science And Engineering, 2003

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605.

Consider the syntax directed definition shown below.

Here, gen is a function that generates the output code, and newtemp is a function that returns the name of a new temporary variable on every call. Assume that ti’s are the temporary variable names generated by newtemp. For the statement ‘X : = Y + Z’, the 3-address code sequence generated by this definition is [2 marks]
(A) X = Y + Z
(B) t₁ = Y + Z; X = t₁
(C) t₁ = Y; t₂ = t₁ + Z; X = t₂
(D) t₁ = Y; t₂ = Z; t₃ = t₁ + t₂; X = t₃

asked in Computer Science And Engineering, 2003

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606.

Consider the grammar shown below
S -> i E t S S' | a
S' -> e S |∈
E -> b
In the predictive parse table, M, of this grammar, the entries M[ S' ,e] and M[ S' ,$] respectively are [2 marks]
(A) { S' -> e S} and{ S' ->∈}
(B) { S' -> e S}and { }
(C) { S' -> ∈} and { S' -> ∈}
(D) { S' -> e S, S' -> ∈} and { S' -> ∈}

asked in Computer Science And Engineering, 2003

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