Is an Operator Determines the Order in Which an Expression Is Evaluated?

Yes, but it's more precise to say that operator precedence and associativity determine the order in which an expression is evaluated.

Understanding Operator Precedence and Associativity

Operator precedence dictates which operations are performed first in an expression. For example, multiplication and division generally have higher precedence than addition and subtraction.

Associativity determines the direction (left-to-right or right-to-left) in which operators of the same precedence are evaluated, as defined in the reference about operator precedence.

How Operator Precedence Works

Consider the expression:

3 + 4 * 2

Due to operator precedence, the multiplication (4 * 2) is performed before the addition (3 + ...). Therefore, the expression is evaluated as:

1. 4 * 2 = 8
2. 3 + 8 = 11

Associativity's Role

Associativity comes into play when you have multiple operators of the same precedence. For example:

10 - 4 - 2

Subtraction is left-associative, meaning it's evaluated from left to right. Thus:

1. 10 - 4 = 6
2. 6 - 2 = 4

If subtraction were right-associative (which it isn't in most common programming languages), it would be evaluated as 10 - (4 - 2) = 10 - 2 = 8, yielding a different result.

Examples

• Parentheses: Parentheses have the highest precedence and can be used to override the default order of operations. (3 + 4) * 2 evaluates to 7 * 2 = 14.
• Exponentiation: Often has right-to-left associativity. 2 ^ 3 ^ 2 is often evaluated as 2 ^ (3 ^ 2) = 2 ^ 9 = 512. (Note: the ^ symbol is used to denote exponentiation for this example. Some languages might use **.)
• Common mistakes: Forgetting operator precedence can lead to incorrect results. Always use parentheses to clarify your intent, especially in complex expressions.