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March 17
HW5: Exponentiation
Due April 2
This assignment studies numeric computations with big integers, both theoretically and in Perl.
(We also cover Perl arrays.) The assignment is based on CLRS Problem 313 part c (p.903). Begin
by solving that problem.
Part A
Download
m
add.pl
and run it.
This program illustrates a number of Perl features, that we’ll
review in recitation. Notice that the output of
m
add.pl
shows it uses linear time, as you’d guess.
Modify
m
add.pl
to do the following experiment:
•
Loop
num
from 2000 to 64000, doubling each time.
•
For each value of
num
, compute
F
n
for
n
equal to
num
, in two di±erent ways.
•
The ²rst way is the naive algorithm – it’s the standard way to compute Fibonacci’s, using the
de²nition
F
n
+2
=
F
n
+1
+
F
n
.
•
The second way is your solution to the CLRS problem.
•
Record the time for both computations.
Print out a table of timings whose ²rst line will look
like this:
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 Fall '07
 GABOW
 Algorithms

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