From: "G.Durga Prasad" <gdprasad@...>
Date: 2007-05-23T00:21:30+09:00
Subject: Re: [QUIZ] Magic Squares (#124)

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$ cat magic_square.rb

#!/usr/bin/env ruby
# G.D.Prasad
class Array
  def / len           # Thanks to _why
  a=[]
  each_with_index do |x,i|
  a <<[] if i%len == 0
  a.last << x
  end
  a
  end
  def rotate_left
    self.push(self.shift)
  end
  def rotate_right
    self.unshift(self.pop)
  end
end

def rotate_array_right_index_times(arrays)
  arrays.each_with_index{|array,i| i.times{array = array.rotate_right}}
end

def show(rows,n)
  string  = rows.map{|r| r.inject(""){|s,e| s + e.to_s.center(5," ")
+"|"}}.join("\n"+"-"*6*n+"\n")
  puts string
end

n=ARGV[0].to_i
raise "Usage: magic_square (ODD_NUMBER>3) " if n%2==0 or n<3
nsq=n*n
arrays = ((1..nsq).to_a/n).each{|a| a.reverse!}
sum = nsq*(nsq+1)/(2*n)
(n/2).times{arrays = arrays.rotate_left}
rotate_array_right_index_times(arrays)
cols=arrays.transpose
rotate_array_right_index_times(cols)
rows=cols.transpose

puts;puts
show(rows,n)
puts
puts "  sum of each row,column or diagonal =  #{sum}"
puts;puts


On 5/18/07, Ruby Quiz <james@grayproductions.net> wrote:
> The three rules of Ruby Quiz:
>
> 1.  Please do not post any solutions or spoiler discussion for this quiz until
> 48 hours have passed from the time on this message.
>
> 2.  Support Ruby Quiz by submitting ideas as often as you can:
>
> http://www.rubyquiz.com/
>
> 3.  Enjoy!
>
> Suggestion:  A [QUIZ] in the subject of emails about the problem helps everyone
> on Ruby Talk follow the discussion.  Please reply to the original quiz message,
> if you can.
>
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
>
> A magic square of size N is a square with the numbers from 1 to N ** 2 arranged
> so that each row, column, and the two long diagonals have the same sum.  For
> example, a magic square for N = 5 could be:
>
>         +------------------------+
>         | 15 |  8 |  1 | 24 | 17 |
>         +------------------------+
>         | 16 | 14 |  7 |  5 | 23 |
>         +------------------------+
>         | 22 | 20 | 13 |  6 |  4 |
>         +------------------------+
>         |  3 | 21 | 19 | 12 | 10 |
>         +------------------------+
>         |  9 |  2 | 25 | 18 | 11 |
>         +------------------------+
>
> In this case the magic sum is 65.  All rows, columns, and both diagonals add up
> to that.
>
> This week's Ruby Quiz is to write a program that builds magic squares.  To keep
> the problem easy, I will say that your program only needs to work for odd values
> of N.  Try to keep your runtimes pretty reasonable even for the bigger values of
> N:
>
>         $ time ruby magic_square.rb 9
>         +--------------------------------------------+
>         | 45 | 34 | 23 | 12 |  1 | 80 | 69 | 58 | 47 |
>         +--------------------------------------------+
>         | 46 | 44 | 33 | 22 | 11 |  9 | 79 | 68 | 57 |
>         +--------------------------------------------+
>         | 56 | 54 | 43 | 32 | 21 | 10 |  8 | 78 | 67 |
>         +--------------------------------------------+
>         | 66 | 55 | 53 | 42 | 31 | 20 | 18 |  7 | 77 |
>         +--------------------------------------------+
>         | 76 | 65 | 63 | 52 | 41 | 30 | 19 | 17 |  6 |
>         +--------------------------------------------+
>         |  5 | 75 | 64 | 62 | 51 | 40 | 29 | 27 | 16 |
>         +--------------------------------------------+
>         | 15 |  4 | 74 | 72 | 61 | 50 | 39 | 28 | 26 |
>         +--------------------------------------------+
>         | 25 | 14 |  3 | 73 | 71 | 60 | 49 | 38 | 36 |
>         +--------------------------------------------+
>         | 35 | 24 | 13 |  2 | 81 | 70 | 59 | 48 | 37 |
>         +--------------------------------------------+
>
>         real    0m0.012s
>         user    0m0.006s
>         sys     0m0.006s
>
> For extra credit, support even values of N.  You don't need to worry about N = 2
> though as it is impossible.
>
>

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