PREC = {:+ => 0,: => 0,:* => 1, => 1,:% => 1,:^ => 2}
LEFT_ASSOCS = {:+ => true,: => true,:* => true, => true,
:% => true,:^ => false}
RIGHT_ASSOCS = {:+ => true,: => false,:* => true, => false,
:% => false,:^ => true}
class TreeNode
attr_accessor :el,:left,:right
def initialize(el,left,right)
@el,@left,@right=el,left,right
end
def TreeNode.from_postfix(exp_arr)
stack = []
exp_arr.each do exp_str
if PREC.keys.include? exp_str.to_sym
op2,op1 = stack.pop,stack.pop
stack.push(TreeNode.new(exp_str.to_sym,op1,op2))
else
stack.push(exp_str.to_f)
end
end
stack.first
end
def to_minparen_infix
l,r = [left,right].map{oo.to_minparen_infix}
l = β(#{l})β if left.respond_to?(:el) and
(PREC[left.el]<PREC[self.el] or
(self.el==left.el and not LEFT_ASSOCS[left.el]))
r= β(#{r})β if right.respond_to?(:el) and
(PREC[right.el]<PREC[self.el] or
(self.el==right.el and not RIGHT_ASSOCS[right.el]))
l+" #{self.el} "+r
end
end
class Float
def to_minparen_infix
if self%1==0
to_i.to_s
else
to_s
end
end
end
puts TreeNode.from_postfix(ARGV.first.split(/ /)).to_minparen_infix
 Original Message 
From: Ruby Q. [email protected]
To: rubytalk ML [email protected]
Sent: Friday, November 30, 2007 7:28:17 AM
Subject: [QUIZ] Postfix to Infix (#148)
The three rules of Ruby Q.:

Please do not post any solutions or spoiler discussion for this
quiz until
48 hours have passed from the time on this message. 
Support Ruby Q. by submitting ideas as often as you can:
 Enjoy!
Suggestion: A [QUIZ] in the subject of emails about the problem helps
everyone
on Ruby T. follow the discussion. Please reply to the original quiz
message,
if you can.
========================================
There are many different ways to write mathematical equations. Infix
notation
is probably the most popular and yields expressions like:
2 * (3 + 5)
Some people like to work with a postfix notation (often called Reverse
Polish
Notation or just RPN) though, which doesnβt require parentheses for the
same
equation:
2 3 5 + *
You can compare the results of these equations using the Unix utilities
bc
(infix) and dc (postfix):
$ bc <<< '2 * (3 + 5)'
16
$ dc <<< '2 3 5 + * p'
16
The βpβ instruction tacked onto the end of the expression for dc just
tells it
to print the result.
This weekβs quiz is to write a script that translates postfix
expressions into
the equivalent infix expression. In the simplest form, your script
should
function as such:
$ ruby postfix_to_infix.rb '2 3 +'
2 + 3
At minimum, try to support the four basic math operators: +, , *, and
/. Feel
free to add others though. For numbers, remember to accept decimal
values.
You can count on the postfix expressions having spaces between each
term, if you
like. While dc is content with 2 3+p, you donβt have to support it
unless you
want to.
For an added bonus, try to keep the parentheses added to infix
expressions to
the minimum of what is needed. For example, prefer these results:
$ ruby postfix_to_infix.rb '56 34 213.7 + * 678 '
56 * (34 + 213.7)  678
$ ruby postfix_to_infix.rb '1 56 35 + 16 9  / +'
1 + (56 + 35) / (16  9)
to these:
$ ruby postfix_to_infix.rb '56 34 213.7 + * 678 '
((56 * (34 + 213.7))  678)
$ ruby postfix_to_infix.rb '1 56 35 + 16 9  / +'
(1 + ((56 + 35) / (16  9)))
Posting equations and your output is not a spoiler.
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