CS 405/505 ASSIGNMENT #5
Due Thursday, October 18, 2007
1. Roman numerals use the following symbols:
I(one)
V(five)
X(ten)
L(fifty)
C(one hundred)
D(five hundred)
M(one thousand)
These are usually written in linear order (e.g., I,II,III) with smaller numerals always
following larger numerals except when they are to be subtracted (e.g., IV means 5 - 1).
Subtractions are used instead of writing four consecutive occurrences of the same symbol
(i.e., IV should be used instead of IIII,MCM instead of MDCCCC, etc.). Only symbols which are
powers of 10 may be used in subtractions (i.e., I,X,C, and M). Furthermore, subtraction rules
require that a symbol representing 10xmay not precede any symbol larger than 10x+1 (e.g.,
IC is not permitted to represent 99 but XC is 90). Write a LISP function (romanToDecimal
RomanNumeral) which takes a Roman numeral as a list of digits and returns the decimal
equivalent if the Roman numeral is well formed and error otherwise. Test your function as
follows:
(a) (romanToDecimal โ(C D V)) โ405
(b) (romanToDecimal โ(M M V I I)) โ2007
(c) (romanToDecimal โ(M M M C M X C I X)) โ3999
(d) (romanToDecimal โ(M I M)) โerror
2. DNA is a two-stranded molecule. Each strand is a polynucleotide composed of A (adenosine),
T (thymidine), C (cytidine), and G (guanosine) residues. The two strands of DNA run
antiparallel (i.e., at each nucleotide residue along the double-stranded DNA molecule, the
nucleotides are complementary). That is, A forms two hydrogen-bonds with T; C forms three
hydrogen bonds with G. In most cases the two-stranded, antiparallel, complementary DNA
molecule folds to form a helical structure, which resembles a spiral staircase. This is the reason
why DNA has been referred to as the โDouble Helix.โ An example of two complementary
strands of DNA would be:
ATGGAATTCTCGCTC
TACCTTAAGAGCGAG
This genetic sequencing problem is to find complementary matching strands of DNA. Write a
LISP function (matchDNA strand1 strand2) that takes two strands as lists of nucleotides,
and returns: 1) the beginning part of the second strand which does not match, 2) the part
of the second strand which the first string matches, and 3) the remaining part of the second
strand which does not match. Note that if there is no match, the second and third components
will be null. If there are multiple matching strings, returning only the first match is sufficient.
Test your function as follows:
