例の数珠を求めるrubyのスクリプト

require 'set'

class Array
def psum( i, n ) begin
sum = 0
l = self.length
for i.upto(i+n-1) do |j| begin
return nil if self[j].nil?
index = j % l
sum = sum + self[index]
end

return sum
end

def which_nil
self.each_index do |i|
return i if self[i].nil?
end
return nil
end
end

def M(n) begin
return n*(n-1)+1
end

def check( a ) begin
s = Set.new( [] )
n = a.length
for 1.upto(n-1) do |k|
for 0.upto(n-1) do |i|
sum = a.psum(i,k)
if !sum.nil? begin
if s.include?(sum) || sum>M(n)
return nil
else
s.add( sum )
end
end
end
end
sum = a.psum(0,n)
return nil if !sum.nil? && sum>M(n)
return s
end


#配列中に i の数字を作る部分列を作るようにする
def search( a, created, i ) begin
if created.include?(i)
if i==M(a.length)
p a
return
else
search( a, created, i+1 )
end
else
# i を追加する
b = a
a.each_index |j|
if a[j].nil?
b = a.clone
b[j]=i
s = check( b )
if s.nil?
search( b, s, i+1 )
end
end
end
end
end


n = 6　　　#数珠の個数
for n.times
a.push(nil)
end

search( a, Set.new([]), 1 )