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Section 8.3
235
16. [BB] Sort the list into increasing order
al
~
a2
~
...
~
an.
If
n
=
2m
+
1 is odd, the median is
am;
if
n
=
2m is even, the median is
~
(am
+
am
+
1). Since determining the parity of
n
adds only another
operation, the complexity of this algorithm is the complexity of the sort, at best
0
(
n
log
n).
17. (a) [BB] Here's the bubble sort.
k
=
7:
a,b,c,d,u,v,w,x
+
a,b,c,d,u,v,w,x
+
a,c,b,d,u,v,w,x
+
a,
c,
d, b,
u, v, w, x
+
a,c,
d,
u,
b,
v, w, x

+
a,
c,
d,
u,
b,
v, w, x
+
a,
c,
d,
u,
b,
v, w, x
k
=
6:
a,c,d,u,b,v,x,w
+
a,c,d,u,b,v,x,w
+
a,d,c,u,b,v,x,w
+
a, d, u,
c,
b, v, x, w
+
a,d, u,
c,
b, v, x, w
+
a;tI:u,
c,
b, v, x, w
k
=
5:
a,d,u,c,b,x,v,w
+
d,a,u,c,b,x,v,w
+
d,a,u,c,b,x,v,w
+
d,
a, u,
c,
b,
x, v, w
+
d,
a, u,
c,
b,
x, v, w

k
=
4:
d, a, u,
c,
x, b, v, w
+
d, a, u,
c,
x, b, v, w
+
d, a, u,
c,
x, b, v, w
+
d,a,u,c,x,b,v,w


k
=
3:
d,a,u,c,x,b,v,w
+
d,a,u,c,x,b,v,w
+
d,a,u,c,x,b,v,w
k
=
2:
d,
a, u,
c,
x,
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 Summer '10
 any
 Graph Theory

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