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Recent questions tagged asymptotic-notation
46
votes
5
answers
541
GATE CSE 2011 | Question: 37
Which of the given options provides the increasing order of asymptotic complexity of functions $f_1, f_2, f_3$ and $f_4$? $f_1(n) = 2^n$ $f_2(n) = n^{3/2}$ $f_3(n) = n \log_2 n$ $f_4(n) = n^{\log_2 n}$ $f_3, f_2, f_4, f_1$ $f_3, f_2, f_1, f_4$ $f_2, f_3, f_1, f_4$ $f_2, f_3, f_4, f_1$
go_editor
asked
in
Algorithms
Sep 29, 2014
by
go_editor
17.9k
views
gatecse-2011
algorithms
asymptotic-notation
normal
45
votes
8
answers
542
GATE CSE 1999 | Question: 2.21
If $T_1 = O(1)$, give the correct matching for the following pairs: $\begin{array}{l|l}\hline \text{(M) $T_n = T_{n-1} + n$} & \text{(U) $T_n = O(n)$} \\\hline \text{(N) $T_n = T_{n/2} + n$} & \text{(V) $T_n = O(n \log n)$ ... $\text{M-W, N-U, O-X, P-V}$ $\text{M-V, N-W, O-X, P-U}$ $\text{M-W, N-U, O-V, P-X}$
Kathleen
asked
in
Algorithms
Sep 23, 2014
by
Kathleen
14.9k
views
gate1999
algorithms
recurrence-relation
asymptotic-notation
normal
match-the-following
33
votes
5
answers
543
GATE CSE 2005 | Question: 37
Suppose $T(n) =2T (\frac{n}{2}) + n$, $T(0) = T(1) =1$ Which one of the following is FALSE? $T(n)=O(n^2)$ $T(n)=\Theta(n \log n)$ $T(n)=\Omega(n^2)$ $T(n)=O(n \log n)$
Kathleen
asked
in
Algorithms
Sep 22, 2014
by
Kathleen
9.6k
views
gatecse-2005
algorithms
asymptotic-notation
recurrence-relation
normal
77
votes
5
answers
544
GATE CSE 2004 | Question: 29
The tightest lower bound on the number of comparisons, in the worst case, for comparison-based sorting is of the order of $n$ $n^2$ $n \log n$ $n \log^2n$
Kathleen
asked
in
Algorithms
Sep 18, 2014
by
Kathleen
33.4k
views
gatecse-2004
algorithms
sorting
asymptotic-notation
easy
53
votes
3
answers
545
GATE CSE 2003 | Question: 20
Consider the following three claims: $(n+k)^m = \Theta(n^m)$ where $k$ and $m$ are constants $2^{n+1} = O(2^n)$ $2^{2n+1} = O(2^n)$ Which of the following claims are correct? I and II I and III II and III I, II, and III
Kathleen
asked
in
Algorithms
Sep 16, 2014
by
Kathleen
18.5k
views
gatecse-2003
algorithms
asymptotic-notation
normal
63
votes
7
answers
546
GATE CSE 2001 | Question: 1.16
Let $f(n) = n^2 \log n$ and $g(n) = n(\log n)^{10}$ be two positive functions of $n$. Which of the following statements is correct? $f(n) = O(g(n)) \text{ and } g(n) \neq O(f(n))$ $g(n) = O(f(n)) \text{ and } f(n) \neq O(g(n))$ $f(n) \neq O(g(n)) \text{ and } g(n) \neq O(f(n))$ $f(n) =O(g(n)) \text{ and } g(n) = O(f(n))$
Kathleen
asked
in
Algorithms
Sep 14, 2014
by
Kathleen
18.6k
views
gatecse-2001
algorithms
asymptotic-notation
time-complexity
normal
79
votes
10
answers
547
GATE CSE 2000 | Question: 2.17
Consider the following functions $f(n) = 3n^{\sqrt{n}}$ $g(n) = 2^{\sqrt{n}{\log_{2}n}}$ $h(n) = n!$ Which of the following is true? $h(n)$ is $O(f(n))$ $h(n)$ is $O(g(n))$ $g(n)$ is not $O(f(n))$ $f(n)$ is $O(g(n))$
Kathleen
asked
in
Algorithms
Sep 14, 2014
by
Kathleen
22.7k
views
gatecse-2000
algorithms
asymptotic-notation
normal
39
votes
5
answers
548
GATE CSE 2008 | Question: 39
Consider the following functions: $f(n) = 2^n$ $g(n) = n!$ $h(n) = n^{\log n}$ Which of the following statements about the asymptotic behavior of $f(n)$, $g(n)$ and $h(n)$ ... $h\left(n\right)=O\left(f\left(n\right)\right); g\left(n\right) = \Omega\left(f\left(n\right)\right)$
Kathleen
asked
in
Algorithms
Sep 12, 2014
by
Kathleen
16.2k
views
gatecse-2008
algorithms
asymptotic-notation
normal
42
votes
4
answers
549
GATE CSE 2012 | Question: 18
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? $A(n) = \Omega (W(n))$ $A(n) = \Theta (W(n))$ $A(n) = \text{O} (W(n))$ $A(n) = \text{o} (W(n))$
gatecse
asked
in
Algorithms
Aug 5, 2014
by
gatecse
14.3k
views
gatecse-2012
algorithms
easy
asymptotic-notation
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