A solver of triangular subtraction problem

trisub.rb

#!/usr/bin/env ruby

# trisub.rb : a solver of triangular subtraction problem
#   by takehikom

# Usage:
#   ruby trisub.rb
#   ruby trisub.rb 4
#   ruby trisub.rb 5
#   ruby trisub.rb 6 # no answer
#   ruby trisub.rb blank

# Depends on:
#   UDデジタル教科書体; http://www.morisawa.co.jp/about/news/3681

def solve_trisub(n = 3)
  max = n * (n + 1) / 2
  a = (1..max).to_a
  a.permutation(n) do |b|
    c = 0
    1.upto(n) do |s|
      1.upto(n - s) do |t|
        b << (b[c] - b[c + 1]).abs
        c += 1
      end
      c += 1
    end
    if b.sort == a
      print_trisub(b, n)
      make_svg_trisub(b, n)
    end
  end
end

def print_trisub(b, n)
  puts [b[0, n], b, b.sort].map {|i| i.inspect }.join(" => ")
end

def make_svg_trisub(b, n)
  if Array === b
    filename = "#{n}_#{b[0, n].join('-')}.svg"
  else
    filename = "#{n}_blank.svg"
  end
  side = 80
  margin = 20
  strokewidth = side * 0.025
  fontsize = side * 0.8
  width = height = side * n + margin * 2
  code = <<"EOS"
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<svg xmlns="http://www.w3.org/2000/svg" width="#{width}" height ="#{height}">
  <rect x="0" y="0" width="#{width}" height="#{height}" style="fill:#cfc;stroke:none" />
EOS

  b = b.dup
  c = 0
  1.upto(n) do |s|
    1.upto(n - s + 1) do |t|
      x = side * (t - 1) + side * (s - 1) / 2 + margin
      y = side * (s - 1) + margin
      code += <<"EOS"
  <rect x="#{x}" y="#{y}" width="#{side}" height="#{side}" style="fill:white;stroke:black;stroke-width:#{strokewidth}" />
EOS

      if Array === b
        x2 = x + side / 2 - ((Numeric === b[c] && b[c] >= 10 && b[c] != 11) ? side / 14 : 0)
        y2 = y + side / 2 + side / 3
        code += <<"EOS"
  <text x="#{x2}" y="#{y2}" style="font-family:'UD Digi Kyokasho NK-R';font-size:#{fontsize}px;fill:black;stroke:none"><tspan style="text-align:center;text-anchor:middle;">#{b[c]}</tspan></text>
EOS
      end

      c += 1
    end
  end

  code += <<"EOS"
</svg>
EOS
  open(filename, "w").print code
end

if __FILE__ == $0
  if /blank/ =~ ARGV.first
    1.upto(5) do |n|
      make_svg_trisub(nil, n)
    end
    exit
  end

  solve_trisub((ARGV.shift || 3).to_i)
end