1
GATE CSE 2012
+1
-0.3
Let W(n) and A(n) denote respectively, the worst case and average case running time of an algorithm executed on an input of size n. Which of the following is ALWAYS TRUE?
A
$$A(n) = \Omega (W(n))$$
B
$$A(n) = \Theta (W(n))$$
C
$$A(n) = O (W(n))$$
D
$$A(n) = 0 (W(n))$$
2
GATE CSE 2012
+2
-0.6
A list of n strings, each of length n, is sorted into lexicographic order using the merge-sort algorithm. The worst case running time of this computation is
A
O(n log n)
B
O(n2 log n)
C
O(n2 + log n)
D
O(n2)
3
GATE CSE 2012
+2
-0.6
Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices S and T. Which one will be reported by Dijkstra’s shortest path algorithm? Assume that, in any iteration, the shortest path to a vertex v is updated only when a strictly shorter path to v is discovered.
A
SDT
B
SBDT
C
SACDT
D
SACET
4
GATE CSE 2012
+1
-0.3
Given the language L= { ab, aa, baa }, which of the following strings are in L* ?

1) abaabaaabaa
2) aaaabaaaa
3) baaaaabaaaab
4) baaaaabaa

A
1,2 and 3
B
2,3 and 4
C
1,2 and 4
D
1,3 and 4
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