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Computer Science 130B
winter 2012
Written Assignment #1
Due: 4pm Friday, January 20th
Problem 1
In divideandconquer, the way a problem is divided into pieces often affects the effectiveness and appli
cability of the proposed solution. Consider the Towers of Hanoi problem again. Define the original problem as
Hanoi
(
n, A, B, C
)
,
where the first parameter denotes the number of disks, the second parameter the starting peg, the third parameter the
ending peg, and the last parameter the temporary storage peg.
a.
Consider the following divideandconquer strategy:
Hanoi
(
n, A, B, C
)
⇒
Hanoi
(1
, A, C, B
) +
Hanoi
(
n

1
, A, B, C
) +
Hanoi
(1
, C, B, A
)
,
which divides the original problem into
two
instances of size 1 and
one
instance of size
n

1
. If you think the strategy
will work, give the detailed motion sequence for Hanoi(4,A,B,C) and estimate the complexity of the algorithm. If you
think the strategy will not work, provide a counterexample.
b.
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 Spring '12
 Drexel
 Computer Science

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