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451.

Let P, Q and R be tree atomic prepositional assertions. Let X denote (P∨Q)→R and Y denotes (P→R)∨(Q→R). which one of the following is a tautology? [2 marks]
(a) X ≡ Y
(b) X → Y
(c) Y → X
(d) ¬Y→X

asked in Computer Science And Engineering, 2005

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452.

Suppose there are Γlogn‾| sorted lists of L n logn _| elements each. The time complexity of producing a sorted list of all these elements is: (Hint: Use a heap data structure)
[2 marks]
(a) O(n log log n)
(b) θ(n log n)
(c) Ω(n log n)
(d) Ω(n^3/2)

asked in Computer Science And Engineering, 2005

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453.

Let G(V,E) be an undirected graph with positive edge weights. Dijkstra’s single source shortest path algorithm can be implemented using the binary heap data structure with time complexity: [2 marks]
(a) O(|V|²)
(b) O(|E| + |V|log|V|)
(c) O(|V|log|V|)
(d) O((|E| + |V|)log|V|)

asked in Computer Science And Engineering, 2005

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454.

Suppose T(n) = 2T(n/2) + n, T(0)=T(1) = 1
Which one of the following is FALSE? [2 marks]
(a) T(n) = O(n²)
(b) T(n) = θ(n logn)
(c) T(n) = Ω(n²)
(d) T(n) = O(n logn)

asked in Computer Science And Engineering, 2005

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455.

In a complete k-ary tree, every internal node has exactly k children. The number of leaves in such a tree with n internal nodes is: [2 marks]
(a) nk
(b) (n – 1) k + 1
(c) n(k – 1) + 1
(d) n(k – 1)

asked in Computer Science And Engineering, 2005

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456.

How many distinct binary search trees can be created out of 4 distinct keys?
[2 marks]
(a) 5
(b) 14
(c) 24
(d) 42

asked in Computer Science And Engineering, 2005

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