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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 doesn’t 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 “p” instruction tacked onto the end of the expression for dc just
tells it
to print the result.
This week’s 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 don’t 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.