From: Bill Dolinar <ruby-talk@...>
Date: 2007-01-15T08:25:12+09:00
Subject: Re: [QUIZ] Number Spiral (#109) [solution]

#!/usr/bin/env ruby
# Script to print an N by N spiral as shown in the following example:
#
#  56   57   58   59   60   61   62   63
#
#  55   30   31   32   33   34   35   36
#
#  54   29   12   13   14   15   16   37
#
#  53   28   11    2    3    4   17   38
#
#  52   27   10    1    0    5   18   39
#
#  51   26    9    8    7    6   19   40
#
#  50   25   24   23   22   21   20   41
#
#  49   48   47   46   45   44   43   42
#
# Let item with value 0 be at x, y coordinate (0, 0).  Consider the
# spiral to be rings of numbers.  For the numbers 1 through 8 make
# up ring level 1, and numbers 9 through 24 make up ring level 2.
# To figure out the value at a particular x, y position, note that
# the first value at any level is (2 * level - 1) ** 2 and use that
# value to count up or down to the coordinate.

class Spiral

   def initialize(size)
     @size = size
     @center = size/2
   end

   # returns the value for a given row and column of output
   def position_value(row, col)
     x, y = coordinate = coordinate_for(row, col)
     level = [x.abs, y.abs].max
     if x < level && y > -level
       # return number for top left portion of ring
       first_number(level) +
           steps_between(first_coordinate(level), coordinate)
     else
       last_number(level) -
           steps_between(last_coordinate(level), coordinate)
     end
   end

   def maximum_value
     @size * @size - 1
   end

   def first_number(level)
     (2 * level - 1) ** 2
   end

   def last_number(level)
     first_number(level + 1) - 1
   end

   def first_coordinate(level)
     [-level, -level + 1]
   end

   def last_coordinate(level)
     [-level, -level]
   end

   def coordinate_for(row, col)
     [col - @center, @center - row]
   end

   def steps_between(point1, point2)
     (point1[0] - point2[0]).abs + (point1[1] - point2[1]).abs
   end
end


if __FILE__ == $0
   size = ARGV[0].to_i
   spiral = Spiral.new(size)
   width = spiral.maximum_value.to_s.length + 3
   (0...size).each do |row|
     (0...size).each do |col|
       print spiral.position_value(row, col).to_s.rjust(width)
     end
     print "\n\n"
   end
end