Which data structure is required to convert the infix to prefix notation?

It is always interesting to learn about the applications of Data Structures and Algorithms in our daily lives. One such application is Stack. We’ll now take a detailed look into Stacks.

What is a Stack?

A stack is an Abstract Data Type (ADT) that is commonly used in most programming languages. It gets its name from the way it behaves like a real-world stack, for example a deck of cards or a pile of plates. If we want to add or remove something from a stack, we can only do so from the top. For example, we can only place or remove a card or plate from the top of the stack. Likewise, the Stack ADT only allows all data operations at one end. At any given time, the only element we can access in a stack is the top element.

This feature makes it a LIFO data structure. LIFO stands for Last-in-first-out. Here, the element which is placed last is accessed first. There are several ways to implement a stack, including using an array, a structure, a pointer, or a linked list. A stack can be a fixed size or it may be dynamically resized.

An algorithm must have some operations to be performed. The following are the operations of Stack:

i) Push

ii) Pop

iii) Peek

iv) isEmpty

v) Size

i) Push

The adding of elements into the stack is known as Push operation.

ii) Pop

The removal of elements from the stack is known as Pop operation.

iii) Peek

The return of the top most value of the stack without having it removed from the stack.

iv) isEmpty

Checking for a stack if it is empty or not.

v) Size

At any given time, a stack will have a certain number of elements in it. This number can be determined by using a function.

Stack can be applied in a variety of applications. There are various conversion applications such as, conversion of Infix to Postfix, Infix to Prefix, and so on. One such application is the conversion of Infix to Prefix notation.

What is an Infix notation?

We’ll now look into what an Infix expression is.

Infix notation is a way of writing expressions in which the operators are placed between the operands. For example, in the expression A+B, the + symbol is an operator between the operands A and B. Other examples of infix notation include A*B and A/B. Since the operators are placed in between the operands, this is called an Infix expression.

What is a Prefix notation?

In this notation, the operator is written before the operands. For example, +ab is equivalent to the infix notation a + b. This notation is known as Prefix Notation.

Conversion of Infix to Prefix:

The compiler will scan the given expression from either left to right, or from right to left.

i) First, reverse the given infix expression.

ii) Then, scan the characters one by one.

iii) If the character is an operand, copy it to the prefix notation output.

iv) If the character is a closing parenthesis, push it to the stack.

v) If the character is an opening parenthesis, pop the elements in the stack until the corresponding closing parenthesis is found.

vi) If the character scanned is an operator, we'll check to see if it has precedence greater than or equal to the top of the stack.

vii) If it does, we'll push the operator to the stack.

viii) If the operator has lower precedence than the top of the stack, we'll pop the operator and output it to the prefix notation output.

ix) Then, we'll check the condition again with the new top of the stack.

x) After scanning all the characters, reverse the prefix notation output.

We’ll now look into the advantages and disadvantages of Stacks

Advantages of Stacks:

i) If you're looking for a way to manage data using the LIFO technique, stack is a great option.

ii) Stacks are also helpful for systematic memory management, and can be found in many virtual machines like JVM.

iii) One of the advantages of stack is that it's very efficient for function management since local variables and function parameters are stored in the stack and automatically destroyed once the function is returned.

iv) Additionally, stacks are more secure and reliable as they don't get corrupted easily.

v) Stack gives you control over memory allocation and deallocation. Stack automatically cleans up the objects for you.

Disadvantages of Stacks:

i) Stack memory is relatively small.

ii) The total size of the stack must be defined in advance.

iii) If too many objects are created, it can lead to stack overflow.

iv) Random access is not possible in a stack.

v) If the stack falls outside of memory, it can lead to abnormal termination.

Conclusion

In this article, we have discussed Stack, and one of its applications. The application that is discussed is the conversion of an expression from an Infix notation to a Prefix notation. Stack is an important concept in Data Structures and Algorithms. Stacks can be useful for keeping track of previous steps in a process. For example, parsing questions often uses stacks because of the LIFO (last in, first out) property. Stacks can also be used to implement recursive solutions iteratively. This means that instead of having the function call itself repeatedly, the function can keep track of what it needs to do next on a stack. Since Stacks are a prominent concept of Data Structures and Algorithms, it is necessary to ace a Full Stack interview.

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