Asp Forum - Re: [QUIZ] Preferable Pairs (#165

Steven Hahn

6/9/2008 2:25:00 AM

Ok, I think this one will always find the optimal solution, because it is =
exhaustive. Some people were saying that this is the Stable Roommates prob=
lem; I am not familiar with that, but a greedy solution definitely wouldn't=
work. Also, I agree that this does seem like it is NP-Complete, because g=
reedy does not work and there are O(n!) potential solutions... I believe (n=
-1)!! to be exact. I didn't put in much in the way of optimizations, so it =
should not handle a large set of input date. Since, the input is already YA=
ML-ready, the following program expects the input to be a YAML file name.
---------------------------------------------------------------------------=
------
require 'yaml'

#execute program by providing a file name with the data in YAML format

#Example YAML file contents:

#David: Helen Vicki Joseph

#Helen: David Vicki Joseph

#Joseph: Vicki Helen David

#Vicki: David Helen Joseph

class PairCalculator
def initialize(filename)
#read data into hash from YAML file
@pairs_hash =3D YAML::load_file(filename)
@num_people =3D @pairs_hash.length
@num_choices =3D @num_people - 1
=20
#build array of all possible pairs
@all_pairs =3D get_all_pairs
end
=20
#finds the nth choice of a person for some value n, 0 would be
#the first choice, 1 second, etc.
def get_nth_choice(person, n)
@pairs_hash[person].scan(/\w+/)[n]
end
=20
#this method returns 0 if the pair is only one name
#otherwise it calculates the sum of the squares of the individual
#preference indexes, 0=3Dbest, 1=3Dnext best, etc.
def get_pair_value(pair)
pair_array =3D pair.split(" ")
return 0 if(pair_array.length=3D=3D1)
return @pairs_hash[pair_array[0]].scan(/\w+/).index(pair_array[1])**2 +
@pairs_hash[pair_array[1]].scan(/\w+/).index(pair_array[0])**2
end

#this method calculates the value of a possible solution of pairs
def get_pair_set_val(pair_set)
val =3D 0
pair_set.each {|next_pair| val +=3D get_pair_value(next_pair)}
return val
end
=20
#this method calculates a list of pairs from the pair array minus the
#head_pair and any similar pairs (see similar? method for more details).
def get_tail(pair_array, head_pair)
tail_array =3D []
pair_array.each do |next_pair|
#remove all pairs with common partners
tail_array +=3D [next_pair] unless(similar?(head_pair, next_pair))
end
return tail_array
end
=20
#pairs are considered similar if they share a common name or they
#are both a single name (this case makes sure that only one single
#name can be selected in any given solution
def similar?(pair1, pair2)
#returns true if they are both length of 1
return true if(pair1.split(" ").length=3D=3D1 and
pair2.split(" ").length=3D=3D1)

#returns true if the pairs have common partners
pair1.split(" ").each do |next_name|
if(pair2.include?(next_name))
return true
end
end
return false
end

#this method generates a list of all possible pairs
def get_all_pairs
all_pairs =3D []
@pairs_hash.each_key do |p1|
1.upto(@num_choices) do |cnt|
#select the next person in the list
p2 =3D get_nth_choice(p1, cnt-1)
all_pairs +=3D [p1 + " " + p2]
end
#add individual names if there are an odd number of people
all_pairs +=3D [p1] if (@num_people & 1 =3D=3D 1)
end
return all_pairs
end
=20
#this method executes an exhaustive search of all pair sets for
#each set it calculates the value with the best found up to that
#point. if the value is lower then it saves the new solution.
def get_preferred_pairs(pair_array=3D@all_pairs)
solution =3D []
solution_value =3D 1.0/0.0
#base case: pair_array is empty
if(pair_array.length=3D=3D0)
return solution
end
=20
#iterate over all pairs in the array use each one as the head
#in a potential solution
pair_array.each do |pair|
#get the next potential solution
pair_set =3D [pair] +
get_preferred_pairs(get_tail(pair_array, pair)) #recursive call
#calculate the value of the next potential solution
pair_set_val =3D get_pair_set_val(pair_set)
if(solution_value>pair_set_val)
#better solution has been found... save it!
solution =3D pair_set
solution_value =3D pair_set_val
end
end
return solution
end
end

if(ARGV.length =3D=3D 0)
puts "Usage: provide YAML file name as the argument."
exit 0
end

pc =3D PairCalculator.new(ARGV[0])
pair_set =3D pc.get_preferred_pairs
pair_set.each {|pair| puts pair}
puts "Pair set value: #{pc.get_pair_set_val(pair_set)}"

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comp.lang.ruby

Re: [QUIZ] Preferable Pairs (#165

Steven Hahn

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