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238
Solutions to Exercises
(c)
t
Penn{t}
j
m
S
17
341 2
3
2
{3,4,2Y
=
{I}
7f17f27f37f4
18
342 1
1
4
{4}C
=
{1,2,3}
7f17f27f37f4
19
4 1 2 3
3
3
{4, 1,
3}C
=
{2}
7f17f27f37f4
20
4 1 3 2
2
2
{4, 2Y
=
{I, 3}
7f17f27f37f4
21
4 2 1 3
3
3
{4,2,3}C
=
{I}
7f17f27f37f4
22
423 1
2
3
{4,3}C
=
{I, 2}
7f17f27f37f4
23
4 3 1 2
3
2
{4,3,2}C
=
{I}
7f17f27f37f4
24
432 1
2. (a)
12345
12354
12435
12453
12534
(b) [BB] 42531,43125,43152,43215,43251
3.
12543
13245
13254
13425
13452
(c) 41532,42135,42153,42315,42351
13524
13542
14235
14253
14325
14352
14523
14532
15234
15243
(a) [BB] We consider each part of Step 2. Finding the largest
j
such that 7f
j
<
7f
i+
1 requires at most
n
comparisons. At most another
n
comparisons are needed to find the minimum of {7fi
I
i
<
j,
7fi
>
7fj}. To find the complement of a subset
A
of {I, 2,
... ,
n}
requires searching
A
for each of the
elements 1,2,
... ,
n
and noting those which are not in
A.
Using the efficient binary search, each
search is
0
(log2
n),
adding another
n
10g2
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 Summer '10
 any
 Graph Theory

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