Brightness of Brain
Contest
Problem I
Time limit: 1 second Memory: 16 MB |
|
Playing With Fraction |
The Problem
Sometimes it may be found that some numbers if represented in
normal integer or floating point value will not be precise enough for some
calculation. For example some value like 10/3 if stored as integer the value stored
will be 3. Again if stored in floating point value it will be 3.3333 (plus some
extra digits of precision). Multiplying it with 3 again will give 9 and 9.9999
respectively. If we could keep the number as 10/3 , as we do in our
hand calculation (fractional arithmetic) then the problem can be solved. The object oriented
programming capability of newer computer languages gave us the power of doing
such things as other normal variables like integer.
Today's scientific calculators even can do such
calculations using fractional numbers. This problem also requires you to
evaluate some expressions containing, fractional numbers. The expression
may contain arbitrarily deep brackets. The expression may have
operators '+', '-' , '*' and '/'
representing corresponding operations. The operators '*' and '/' have same
precedence and have greater precedence then '+' and '-' which also have same
precedence among themselves. Operators having same precedence are evaluated from
left to right. Moreover brackets may override the precedence. No invalid expression will be present.
You have to process each such expression.
The Input
Each line contains an expression. Arbitrary number of spaces may be present in
the expression. A fractional number is represented by 'N'|'D'
where 'N' and 'D' are positive 32 bit integers. The integer
'D'
may not be present. Each line will not contain more then 500 characters. Input is terminated by end of file.
The Output
For each line of expression process the evaluated number reduced to their normal
form. A normal form of such number may be defined as having no common divisor in
numerator and denominator. If the number is invalid (i.e. denominator is 0) print "INVALID".
Don't print the denominator if it is unnecessary.
Sample
Input
3|2+3
(5|3-2|3)*1|3
Sample
Output
9|2
1|3
Suman Mahbub
Created: 08-07-2002
Updated: 14-12-2002