Question

3. Given to you are some of the applications of linear data structures: Matching braces/paranthesis in a program Managing function calls in a program (Backtracking) Transferring data asynchronously between two processes/devices/programs illustrate using suitable example/diagram any one of the above applications by identifying a suitable linear data structure and how this data strucuture can be used to peform the above operations. (20 marks)

Answer 1

3. Matching braces/ paranthesis in a program

Matching braces/ paranthesis in a program i.e checking whether the program has valid paranthesis or not depending on rules of production. Matching paranthesis checks that whether there is a proper matching of the braces like every braces should be closed by braces of same category, also each braces should exist in pair and the order of opening of braces should be reverse of order of closing.

This type of checking can be easily performed using a linear data structure stack. Stack is a linear data structure with the Last in First out (LIFO) property. It supports two types of operations a push ( in which a token is pushed to Stack) and a pop ( in which the top of stack is popped out).

For understanding how it actually performs the braces matching task, Let's consider a basic example of checking balanced paranthesis in an input expression.

Suppose the input string is [{( a+b)*c} *d]

Now define a Stack S

The steps to check for balanced paranthesis will be,

• Start reading the input string from the first position, if the token is an opening brace then push it on stack
• If the token is a closing brace then match the top of stack with the closing brace, if there's a match pop the top and continue reading token.
• If the top of stack doesn't match the closing brace, then the input does not have balances paranthesis
• If after processing each tokens in input string, the stack isn't empty and have some opening braces left. The also input string isn't balanced
• Otherwise balanced

For the given String, the stack at each read will be as follows

S = empty

S= '['

S= '[' , '{'

S = '[' , '{' , '('

S = '[' , '{'

S= '['

S = empty

Therefore in this case the input string has balanced paranthesis.