From: draq <boyang.xia@...>
Date: 2005-12-13T02:02:58+09:00
Subject: Re: Calculating single-digit summands

This is a newer algorithm which works much more faster.

def sum (arr)
# sorry James Edward Gray II, but I'm not using an enum.
  i = 0
  arr.each do |k| i += k end
  i
end

def arr (depth, min=1, max=10-depth,t=[], arr=[])
  (min..max).each do |i|
    t[depth-1] = i if depth > 0
    arr(depth-1, i+1, max+1, t, arr) if depth > 1
    arr << t.reverse.clone if depth == 1
  end

  arr
end

def calc (number, depth)
  arri = arr(depth)

  arri.each do |a|
    arri.delete_if { |a| sum(a) != number }
  end

  arri
end

# examples
calc(24, 3).each do |a| print "#{a} - " end puts
calc(24, 4).each do |a| print "#{a} - " end puts
# even summands of 45 can be calculated now. It was impossible with the
older algorithm.
calc(45, 9).each do |a| print "#{a} - " end puts