Prefix, Infix and Postfix are three different ways of representing mathematical expressions in computer programming languages, such as C++. Each method has its own advantages and disadvantages, and it is important for programmers to understand the differences between them in order to choose the most appropriate method for a given task. In this article, we will explore the concepts of Prefix, Infix and Postfix, and examine how they are used in C++ programming.
Prefix notation, also known as Polish notation, is a method of representing mathematical expressions in which the operator is placed before the operands. For example, the expression "5 + 6" would be written as "+ 5 6" in prefix notation. This method of notation has the advantage of being easy to parse and evaluate using a stack, as the order of the operators and operands is always consistent. However, it can be difficult for humans to read and understand, as the order of the operands is reversed compared to the way we typically write mathematical expressions.
Infix notation is the most commonly used method of representing mathematical expressions, and is the method we are most familiar with. In this method, the operator is placed between the operands, for example "5 + 6" would be written as "5 + 6" in infix notation. This method of notation is easy for humans to read and understand, but it can be difficult for a computer to evaluate, as the order of the operators and operands is not always consistent.
Postfix notation, also known as Reverse Polish notation, is a method of representing mathematical expressions in which the operator is placed after the operands. For example, the expression "5 + 6" would be written as "5 6 +" in postfix notation. This method of notation has the advantage of being easy to parse and evaluate using a stack, as the order of the operators and operands is always consistent. However, it can be difficult for humans to read and understand, as the order of the operands is reversed compared to the way we typically write mathematical expressions.
In C++, the process of converting between prefix, infix and postfix notation can be accomplished using a stack data structure. A stack is a last-in, first-out (LIFO) data structure, which means that the last item added to the stack is the first item to be removed. This is useful for parsing and evaluating mathematical expressions, as it allows the computer to keep track of the order of the operators and operands.
To convert an infix expression to prefix notation, a programmer can use the following algorithm:
- Initialize an empty stack.
- Iterate through the infix expression, character by character.
- If the current character is an operand, add it to the prefix expression.
- If the current character is an operator, push it onto the stack.
- If the current character is a left parenthesis, push it onto the stack.
- If the current character is a right parenthesis, pop operators from the stack and add them to the prefix expression until a left parenthesis is encountered.
- Repeat steps 2-6 until the end of the infix expression is reached.
- Pop any remaining operators from the stack and add them to the prefix expression.
To convert an infix expression to postfix notation, a programmer can use the following algorithm:
- Initialize an empty stack.
- Iterate through the infix expression, character by character.
- If the current character is an operand, add it to the postfix expression.
- If the current character is an operator, pop operators from the stack and
