2. Practical application 1: Arithmetic operations.
(a) Design an algorithm that takes a string, which represents an arithmetic operation, as input
and checks whether or not the brackets are correct (balanced) or incorrect (unbalanced). The
input string may contain a combination of the following characters:
{,},[,],(,),0,1,2,3,4,5,6,7,8,9,+,-,*,/. An obvious hint for this algorithm is to use the stack-
based solution discussed in class as a template, and hence you can use the stack implemented
in #1. Your algorithm must not check the correctness of the arithmetic operators/operands,
but only check for balanced brackets. Your algorithm should also show an error message
when the string contains a character that is not one of those listed above. Provide the
pseudocode of the algorithm.
(b) Implement the algorithm of (a) in your favorite programming language. Run the program
in several cases, including the following (more examples to be asked when the assignment is
submitted):
i. \((9*[3*\{[(3+3)/5]*7\}])\)
ii. \{3*(2+[3-[4/[6/9]]])\}
iii. \(((3*(9-(4*(6-5))))\)
iv. \{2-{3*{6/[[[(((9-0)))]]]}}/7\}
(c) Assuming an input string of size $n$: (i) what is the worst-case time that your algorithm
takes to decide whether or not the string is correct (balanced) or incorrect (unbalanced)? (ii)
Why? Give your answers in terms of the O-notation.
