Computer programming - Homework 3

Balanced parantheses
A string of parantheses is balanced if it is empty or has the form (s₁)s₂ where s₁ and s₂ are strings of balanced parantheses.
Each balanced string is given a number: N(empty) = 0, N((s1)s2) = 2^N(s1)(2N(s2)+1).
a) Write a function that prints the string of balanced parantheses for an unsigned number given as parameter.
b) Write a function that reads a string of balanced parantheses from input (until the first character that does not match) and returns the number corresponding to the string.