6.046
Fall
2004
Quiz
Review—from
6.046
Spring
2002:
1.
Recurrences
(20
points)
Solve
the
following
recurrences
(provide
only
the
�()
bounds).
You
can
assume
T
(
n
)
=
1
for
n
smaller
than
some
constant
in
all
cases.
You
do
not
have
to
provide
justifications,
just
write
the
solutions.
•
T
(
n
)
=
T
(
n/
7)
+
1
•
T
(
n
)
=
3
T
(
n/
3)
+
n
•
T
(
n
)
=
5
T
(
n/
5)
+
n
log
n
•
T
(
n
)
=
10
T
(
n/
3)
+
n
1
.
1
2.
True
or
False,
and
Justify
(32
points)
Circle
T
or
F
for
each
of
the
following
statements
to
indicate
whether
the
statement
is
true
or
false,
respectively.
If
the
statement
is
correct,
brieﬂy
state
why.
If
the
statement
is
wrong,
explain
why.
Your
justification
is
worth
more
points
than
your
trueorfalse
designation.
T
F
The
solution
to
the
recurrence
T
(
n
) =
T
(
n/
3)
+
T
(
n/
6)
+
n
�
log
n
is
T
(
n
)
=
�(
n
�
log
n
)
(assume
T
(
n
)
=
1
for
n
smaller
than
some
constant
c
).
T
F
Radix
sort
works
in
linear
time
only
if
the
elements
to
sort
are
integers
in
the
range
{
1
. . . cn
}
,
for
some
c
=
O
(1).
T
F
There
exists
a
comparisonbased
sorting
algorithm
that
can
sort
any
6element
array
using
at
most
9
comparisons.
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 Fall '08
 ErikDemaine
 Algorithms, Array, Latin alphabet, Tim, comparisonbased sorting algorithm

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