INFIX, POSTFIX, PREFIX EXPRESSIONS
What is an Expression?
An Expression is a combination of operands (that can be numbers constants, variables), operators and symbols of grouping(brackets, curly braces) written is a specific format/way.
Types
Depending on how the expression is written, we can classify it into 3 types:
-
Infix Expression:
Expression in which the operator appears in between the
operands and it is simply of the form (operand1 operator
operand2).
E.g. A+B -
Postfix Expression:
Expression in which the operator appears after the operands
and it is simply of the form (operand1 operand2 operator).
E.g. AB+ -
Prefix Expression:
Expression in which the operator appears before the operands
and is simply of the form (operator operand1 operand2).
E.g. +AB
Order of Precedence & Associativity
| Precedence | Name | Sybmols | Associativity |
|---|---|---|---|
| 1 | Parentheses | { } [ ] ( ) | Same |
| 2 | Exponent | ^ | Right to Left |
| 3 | Division & Multiplication | / * | Left to Right |
| 4 | Addition & Subraction | + - | Left to Right |
Need of these expressions
Infix expressions are human readable but not efficient for machine reading. Prefix and Postfix expressions do not need the concept of precedence & associativity hence it becomes highly efficient to parse expressions in prefix or postfix formats.
Will study the conversion of one type to another type & evaluation of expressions in seperate blog posts along with implemention using C++.
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