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Ch1 演算法基礎
第 21 題／共 57 題
◀
DS 21/57
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21. Asymptotic Notation、Recurrence Relation、Master Theorem
#DS-01-021
難
Asymptotic Notation
Recurrence Relation
Master Theorem
📝
☆
(5%). Which of the followings are true?
A
(A)
f
(
n
)
=
Θ
(
g
(
n
)
)
f(n) = \Theta(g(n))
f
(
n
)
=
Θ
(
g
(
n
))
if and only if
f
(
n
)
=
O
(
g
(
n
)
)
f(n) = O(g(n))
f
(
n
)
=
O
(
g
(
n
))
and
f
(
n
)
=
Ω
(
g
(
n
)
)
f(n) = \Omega(g(n))
f
(
n
)
=
Ω
(
g
(
n
))
.
B
(B)
f
(
n
)
=
o
(
g
(
n
)
)
f(n) = o(g(n))
f
(
n
)
=
o
(
g
(
n
))
if and only if
f
(
n
)
=
O
(
g
(
n
)
)
f(n) = O(g(n))
f
(
n
)
=
O
(
g
(
n
))
and
f
(
n
)
≠
Ω
(
g
(
n
)
)
f(n) \ne \Omega(g(n))
f
(
n
)
=
Ω
(
g
(
n
))
.
C
(C)
T
(
n
)
=
2
⋅
T
(
n
)
+
Θ
(
log
n
)
T(n) = 2\cdot T(\sqrt{n}) + \Theta(\log n)
T
(
n
)
=
2
⋅
T
(
n
)
+
Θ
(
lo
g
n
)
has a solution
T
(
n
)
=
O
(
(
log
n
)
2
)
T(n) = O((\log n)^2)
T
(
n
)
=
O
((
lo
g
n
)
2
)
.
D
(D)
T
(
n
)
=
8
⋅
T
(
n
/
3
+
12
)
+
n
2
T(n) = 8\cdot T(n/3+12) + n^2
T
(
n
)
=
8
⋅
T
(
n
/3
+
12
)
+
n
2
has a solution
T
(
n
)
=
Θ
(
n
2
)
T(n) = \Theta(n^2)
T
(
n
)
=
Θ
(
n
2
)
.
E
(E)
T
(
n
)
=
2
⋅
T
(
n
/
4
)
+
n
T(n) = 2\cdot T(n/4) + \sqrt{n}
T
(
n
)
=
2
⋅
T
(
n
/4
)
+
n
has a solution
T
(
n
)
=
Ω
(
n
)
T(n) = \Omega(\sqrt{n})
T
(
n
)
=
Ω
(
n
)
.
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