1
GATE CSE 2011
+2
-0.6
Which of the given options provides the increasing order of asymptotic Complexity of functions f1, f2, f3 and f4?
f1 = 2n f2 = n3/2
f3(n) = $$n\,\log _2^n$$
f4 (n) = n log2n
A
f3, f2, f4, f1
B
f3, f2, f1, f4
C
f2, f3, f1, f4
D
f2, f3, f4, f1
2
GATE CSE 2011
+1
-0.3
A max-heap is a heap where the value of each parent is greater than or equal to the value of its children. Which of the following is a max-heap?
A
B
C
D
3
GATE CSE 2011
+2
-0.6
An undirected graph G(V, E) contains n ( n > 2 ) nodes named v1 , v2 ,….vn. Two nodes vi , vj are connected if and only if 0 < |i – j| <= 2. Each edge (vi, vj ) is assigned a weight i + j. A sample graph with n = 4 is shown below. What will be the cost of the minimum spanning tree (MST) of such a graph with n nodes?
A
$${1 \over {12}}(11{n^2} - 5n)$$
B
$${n^2}{\rm{ - }}\,n + 1$$
C
6n – 11
D
2n + 1
4
GATE CSE 2011
+2
-0.6
An undirected graph G(V, E) contains n ( n > 2 ) nodes named v1 , v2 ,….vn. Two nodes vi , vj are connected if and only if 0 < |i – j| <= 2. Each edge (vi, vj ) is assigned a weight i + j. A sample graph with n = 4 is shown below. The length of the path from v5 to v6 in the MST of previous question with n = 10 is
A
11
B
25
C
31
D
41
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