From: "Alexandru E. Ungur" <alexandru@...>
Date: 2006-06-26T14:39:24+09:00
Subject: [SOLUTION] [QUIZ] pp Pascal (#84)

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Hi all,

Here's my solution to the quiz:
I attached two different solutions actually.

First is pascal.rb, which is the first I did before asking for
any clarifications/hints :) The triangle resulted is far from
perfect, but I liked being able to use the 'multi' module which
I just learned about :)

The second, pascal-mini, does output a perfect triangle, and allows for
playing with two options: 'B' and 'S'. B represents the numerotation
based. By default it is 10, so nothing unusual, but you can change it
to 16 and display hexa numbers, or even to 32 and display numbers in
the 32 based numerotation system :) Looks nicer and more compact for
larger triangles. All triangles in the attached sample.txt are from 
this script. The Ruby code however is very ugly I agree, I just wanted
to find out how much I can squeeze it :)

Thanks for the fun Ruby quiz!

Have a great day everyone,
Alex

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f=proc{|n|n>1?n*f[n-1]:1} # Factorial
c=proc{|r,i|f[r]/(f[i]*f[r-i])} # Compute cell[r(ow),i(ndex)]
t,rows,B,S=[],(ARGV[0]||10).to_i,10,' '; W=c[rows-1,rows/2].to_s(B).length # Init vars
rows.times{|r|l=[];(r+1).times{|i|l<<(((s=c[r,i].to_s(B)).length<W)?S*(W-s.length)+s:s).upcase};t<< l}
tl=t[-1].join(' ').length; t.map{|r|c=r.join(' ');puts ' '*((tl-c.length)/2)<< c} # Display result

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require 'rubygems'
require 'multi'

SEP = ' '*3; rows = (ARGV[0] || 10).to_i

multi(:pascal, [1])    { [1] }
multi(:pascal, [2])    { [1, 1] }
multi(:pascal, Array)  { |a| result=[1]; 0.upto(a.length-2){ |i| result << a[i]+a[i+1] }; result+[1] }

last, triangle = [], []
rows.times { |n| triangle << last = (n<2) ? pascal([n+1]) : pascal(last) }
len = triangle[-1].join(SEP).length
triangle.map { |row| c = row.join(SEP); puts ' '*((len - c.length) / 2) << c }

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                    1
                  1   1
                1   2   1
              1   3   3   1
            1   4   6   4   1
          1   5  10  10   5   1
        1   6  15  20  15   6   1
      1   7  21  35  35  21   7   1
    1   8  28  56  70  56  28   8   1
  1   9  36  84 126 126  84  36   9   1

                  001
                001 001
              001 002 001
            001 003 003 001
          001 004 006 004 001
        001 005 010 010 005 001
      001 006 015 020 015 006 001
    001 007 021 035 035 021 007 001
  001 008 028 056 070 056 028 008 001
001 009 036 084 126 126 084 036 009 001

             01
            01 01
          01 02 01
         01 03 03 01
       01 04 06 04 01
      01 05 0A 0A 05 01
    01 06 0F 14 0F 06 01
   01 07 15 23 23 15 07 01
 01 08 1C 38 46 38 1C 08 01
01 09 24 54 7E 7E 54 24 09 01

                                  1
                                1   1
                              1   2   1
                            1   3   3   1
                          1   4   6   4   1
                        1   5   A   A   5   1
                      1   6   F   K   F   6   1
                    1   7   L  13  13   L   7   1
                  1   8   S  1O  26  1O   S   8   1
                1   9  14  2K  3U  3U  2K  14   9   1
              1   A  1D  3O  6I  7S  6I  3O  1D   A   1
            1   B  1N  55  AA  EE  EE  AA  55  1N   B   1
          1   C  22  6S  FF  OO  SS  OO  FF  6S  22   C   1
        1   D  2E  8U  MB 187 1LK 1LK 187  MB  8U  2E   D   1
      1   E  2R  BC  V9 1UI 2TR 3B8 2TR 1UI  V9  BC  2R   E   1
    1   F  39  E7 1AL 2TR 4SD 693 693 4SD 2TR 1AL  E7  39   F   1
  1   G  3O  HG 1OS 48G 7Q8 B5G CI6 B5G 7Q8 48G 1OS  HG  3O   G   1

                                                    1
                                                 1     1
                                              1     2     1
                                           1     3     3     1
                                        1     4     6     4     1
                                     1     5    10    10     5     1
                                  1     6    15    20    15     6     1
                               1     7    21    35    35    21     7     1
                            1     8    28    56    70    56    28     8     1
                         1     9    36    84   126   126    84    36     9     1
                      1    10    45   120   210   252   210   120    45    10     1
                   1    11    55   165   330   462   462   330   165    55    11     1
                1    12    66   220   495   792   924   792   495   220    66    12     1
             1    13    78   286   715  1287  1716  1716  1287   715   286    78    13     1
          1    14    91   364  1001  2002  3003  3432  3003  2002  1001   364    91    14     1
       1    15   105   455  1365  3003  5005  6435  6435  5005  3003  1365   455   105    15     1
    1    16   120   560  1820  4368  8008 11440 12870 11440  8008  4368  1820   560   120    16     1

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