From: Rick DeNatale <rick.denatale@...>
Date: 2008-07-14T10:45:20+09:00
Subject: Re: [QUIZ] Symbolify (#169)

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Here's a fairly straightforward solution, this passes the tests and works
for both positive and negative integers:

def symbolify(i)
  digits = [
    "?(-?(",
    "?)-?(",
    "?*-?(",
    "?--?*",
    "(?*-?()*(?*-?()",
    "?--?(",
    "(?--?*)*(?*-?()",
    "(((?*-?()*(?*-?())*(?*-?())-(?)-?()",
    "((?*-?()*(?*-?())*(?*-?()",
    "((?*-?()*(?--?())-(?)-?()",
    "(?*-?()*(?--?()"
  ]

  if i < 0
    "-(#{symbolify(-i)})"
  else
    if i < 9
      digits[i]
    else
      i.abs.to_s.split(//).map {|digit| digits[digit.to_i]}.inject(nil) {
|answer, rep| answer ? "((#{rep})--(#{answer})*(#{digits[10]}))": rep }
    end
  end
end

The basic approach is to generate an expression which works like a lexical
scan of the decimal representation of the (positive) integer, i.e. it's the
closed form of

 val = 0
 i.to_s(10).split(//).each |digit|
    val = val * 10 + digit.to_i
 end

except the the digits are represented by expressions following the rules.

For the positive integers <= 1000 the longest string generated was  157
characters for i = 777.

For the negative integers >= 1000 the longest string generate was 160
characters for i = -777 (i.e) the same string wrapped in parentheses
preceded by a -
-- 
Rick DeNatale

My blog on Ruby
http://talklikeaduck.denhaven2.com/

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