Expression

Expression

Expression is a string of operands and operators. Operands are some numeric values and operators are of two types: Unary operators and Binary operators. Unary operators are '+' and '-' and binary operators are '+', '-', '*', '/' and exponential. In general, there are three types of expressions:

1. Infix expression 2. Postfix expression 3. Prefix expression.

One of the application of stack is conversion of expression. First of all, let us see these expressions with the help of examples :

1. Infix Expression :

In this type of expressions the arrangement of operands and operator is as follows:

Infix expression = operand1 operator operand2

For example

1. (a+b)

2 (a+b) * (c-d)

3. (a+b/e) * (d+f).

Parenthesis can be used in these expressions. Infix expression are the most natural way of representing the expressions.

2. Postfix Expression :

In this type of expressions the arrangement of operands and operator is as follows:

Postfix expression = operand1 operand2 operator

For example

1. ab+

2. ab + cd - *

3. ab+e/df + *

In postfix expression there is no parenthesis used. All the corresponding operands come first and then operator can be placed.

3. Prefix Expression :

In prefix expression the arrangement of operands and operators is as follows

Prefix expression = operator operand1 operand2

For example

1. + ab

2. *+ ab - cd

3. */ +abe + df

In prefix expression, there is no parenthesis used. All the corresponding operators come first and then operands are arranged.

To evaluate infix expression, we need the precedence and associativity of the operators. And which is really a complex task. But in prefix and postfix expressions corresponding operators are with their respective operands. But these algorithms strongly recommend the use of stack.

Let us now, discuss the conversion procedures of these expression.