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49
26401357
7.9
(a)
Each call to
qsort
costs
Θ(
i
log
i
)
. Thus, the total cost is
n
X
i
=1
i
log
i
=Θ(
n
2
log
n
)
.
(b)
Each call to
qsort
costs
Θ(
n
log
n
)
for length(L)
=
n
, so the total
cost is
Θ(
n
2
log
n
)
.
7.10
A
l
ltha
tweneedtodoisrede
f
ne the comparison test to use strcmp. The
quicksort algorithm itself need not change. This is the advantage of paramer
izing the comparator.
7.11
For
n
= 1000
,
n
2
=1
,
000
,
000
,
n
1
.
5
= 1000
∗
√
1000
≈
32
,
000
,and
n
log
n
≈
10
,
000
. So, the constant factor for Shellsort can be anything less
than about 32 times that of Insertion Sort for Shellsort to be faster. The
constant factor for Shellsort can be anything less than about 100 times that
of Insertion Sort for Quicksort to be faster.
7.12
(a)
The worst case occurs when all of the sublists are of size 1, except for
one list of size
i
−
k
+1
. If this happens on each call to SPLITk, then
the total cost of the algorithm will be
Θ(
n
2
)
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This note was uploaded on 12/27/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

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