1
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Suppose there are $$\lceil \log n \rceil$$ sorted lists of $$\left\lfloor {{n \over {\log n}}} \right\rfloor $$ elements each. The time complexity of producing a sorted list of all these elements is :
(Hint : Use a heap data structure)
A
$$O(n \log \log n)$$
B
$$\Theta(n \log n)$$
C
$$\Omega(n \log n)$$
D
$$\Omega\left(n^{3/2}\right)$$
2
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Let G(V, E) 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:
A
$$O\left( {{{\left| V \right|}^2}} \right)$$
B
$$O\left(|E|+|V|\log |V|\right)$$
C
$$O\left(|V|\log|V|\right)$$
D
$$O\left(\left(|E|+|V|\right)\log|V|\right)$$
3
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Suppose T(n) = 2T (n/2) + n, T(0) = T(1) = 1
Which one of the following is FALSE?
A
T(n) = O(n2)
B
$$T\left( n \right){\rm{ }} = {\rm{ }}\theta \left( {n{\rm{ }}\,log\,{\rm{ }}n} \right)$$
C
$$T\left( n \right){\rm{ }} = {\rm{ }}\Omega ({n^2})$$
D
T(n) = O(n log n)
4
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable. Which one of the following is TRUE?
A
P3 is decidable if P1 is reducible to P3
B
P3 is undecidable if P3 is reducible to P2
C
P3 is undecidable if P2 is reducible to P3
D
P3 is decidable if P3 is reducible to P2 's complement
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