Home Theory What are infix, postfix and prefix expressions?

# What are infix, postfix and prefix expressions?

Stacks can be used to implement algorithms involving Infix, postfix and prefix expressions. So let us learn about them:-

#### INFIX:-

An infix expression is a single letter, or an operator, proceeded by one infix string and followed by another infix string.
A
A + B
(A + B) + (C – D)

#### PREFIX:-

A prefix expression is a single letter, or an operator, followed by two prefix strings. Every prefix string longer than a single variable contains an operator, first operand and second operand

A
+ A B
+ + A B – C D

#### POSTFIX:-

A postfix expression (also called Reverse Polish Notation) is a single letter or an operator, preceded by two postfix strings. Every postfix string longer than a single variable contains first and second operands followed by an operator.

A
A B +
A B + C D –

Prefix and postfix notations are methods of writing mathematical expressions without parenthesis. Time to evaluate a postfix and prefix expression is O(n), where n is the number of elements in the array.

 INFIX PREFIX POSTFIX A + B + A B A B + A + B – C – + A B C A B + C – (A + B) * C – D – * + A B C D A B + C * D –

To study further, we must also know the operator precedence and their associativity:-

 TOKEN OPERATOR PRECEDENCE ASSOCIATIVITY ( ) [ ] – . function call array element struct or union member 17 left-to-right — ++ increment, decrement 16 left-to-right ! ~ – + & * sizeof logical NOT one’s complement unary minus or plus address or indirection size (in bytes) 15 right-to-left (type) type cast 14 right-to-left * / % multiplicative 13 left-to-right + – binary add or subtract 12 left-to-right << >> shift 11 left-to-right > >= < <= relational 10 left-to-right == != equality 9 left-to-right & bitwise AND 8 left-to-right ^ bitwise XOR 7 left-to-right | bitwise OR 6 left-to-right && logical AND 5 left-to-right || logical OR 4 left-to-right ? : conditional 3 right-to-left = += /= *= %= &= ^= assignment 2 right-to-left , comma 1 left-to-right

#### 1 comment

May 3, 2021 - 05:34

Itâ€™s not acceptable to use the word your defining as part of the definition. English 101.