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by Jay Anderson

For this quiz the goal is to make a constraint processing library for ruby. A
Constraint Satisfaction Problem consists of variables, domains for each
variable, and constraints among the variables. Here's a sample (Solutions DO NOT
need to follow this syntax, this is just an example):

a = IntVar.new(:a, (0..4).to_a) #Set up the variables and their domains.
b = IntVar.new(:b, (0..4).to_a)
c = IntVar.new(:c, (0..4).to_a)
con1 = a < b #Create constraints on the problem.
con2 = a + b == c
prob = Problem.new(con1, con2) #Create a problem with the constraints
solution = prob.solve #Find a solution
p solution

There are many solutions. It could return any (or all) of the following:

{:a => 0, :b => 1, :c => 1}
{:a => 0, :b => 2, :c => 2}
{:a => 0, :b => 3, :c => 3}
{:a => 0, :b => 4, :c => 4}
{:a => 1, :b => 2, :c => 3}
{:a => 1, :b => 3, :c => 4}

Another example would be to solve the magic square:

SIDE = 3
MAX = SIDE**2
SUM = (MAX*(MAX+1))/(2*SIDE)
square = Array.new(SIDE) do |x|
Array.new(SIDE) {|y| IntVar.new("#{x},#{y}", (1..MAX).to_a ) }
end
cons = []
zero = IntVar.new(:zero, [0])
SIDE.times do |row|
sum = zero
SIDE.times {|col| sum += square[col][row] }
cons << sum == SUM
end
SIDE.times do |col|
sum = zero
SIDE.times {|row| sum += square[col][row] }
cons << sum == SUM
end
#A constraint to ensure no two variables have the same value in a solution.
cons << AllDistinct.new(*square.flatten)
prob = Problem.new(*cons)
solution = prob.solve
p solution

There are many problems that can be solved through constraint programming (even
some past quizzes): gift exchanges, sudoku, magic squares, N queens,
cryptoarithmetics, scheduling problems, etc... So be creative here. Pick a
simple problem to solve with your Constraint Programming Engine.

Good luck!