Infix Expressions
Infix expressions are mathematical expressions where the operator is placed between its operands. This is the most common mathematical notation used by humans. For example, the expression “2 + 3” is an infix expression, where the operator “+” is placed between the operands “2” and “3”.
Infix notation is easy to read and understand for humans, but it can be difficult for computers to evaluate efficiently. This is because the order of operations must be taken into account, and parentheses can be used to override the default order of operations.
Common way of writing Infix expressions:
- Infix notation is the notation that we are most familiar with. For example, the expression “2 + 3” is written in infix notation.
- In infix notation, operators are placed between the operands they operate on. For example, in the expression “2 + 3”, the addition operator “+” is placed between the operands “2” and “3”.
- Parentheses are used in infix notation to specify the order in which operations should be performed. For example, in the expression “(2 + 3) * 4”, the parentheses indicate that the addition operation should be performed before the multiplication operation.
Operator precedence rules:
Infix expressions follow operator precedence rules, which determine the order in which operators are evaluated. For example, multiplication and division have higher precedence than addition and subtraction. This means that in the expression “2 + 3 * 4”, the multiplication operation will be performed before the addition operation.
Here’s the table summarizing the operator precedence rules for common mathematical operators:
| Operator | Precedence |
|---|---|
| Parentheses () | Highest |
| Exponents ^ | High |
| Multiplication * | Medium |
| Division / | Medium |
| Addition + | Low |
| Subtraction – | Low |
Evaluating Infix Expressions
Evaluating infix expressions requires additional processing to handle the order of operations and parentheses. First convert the infix expression to postfix notation. This can be done using a stack or a recursive algorithm. Then evaluate the postfix expression.
Infix, Postfix and Prefix Expressions/Notations
Mathematical formulas often involve complex expressions that require a clear understanding of the order of operations. To represent these expressions, we use different notations, each with its own advantages and disadvantages. In this article, we will explore three common expression notations: infix, prefix, and postfix.
Table of Content
- Infix Expressions
- Advantages of Infix Expressions
- Disadvantages Infix Expressions
- Prefix Expressions (Polish Notation)
- Advantages of Prefix Expressions
- Disadvantages of Prefix Expressions
- Postfix Expressions (Reverse Polish Notation)
- Advantages of Postfix Notation
- Disadvantages of Postfix Expressions
- Comparison of Infix, Prefix and Postfix Expressions
- Frequently Asked Questions on Infix, Postfix and Prefix Expressions