Operators with the same precedence are evaluated in a specific manner, known as the order of evaluation or operator associativity. The order of evaluation can affect the outcome of a calculation, and it is important to understand how it works in order to write correct and efficient code.

In programming languages, operators can be grouped into different precedence levels. Operators with higher precedence are evaluated before operators with lower precedence. For example, in the expression 2 + 3 * 4, the multiplication operator (*) has higher precedence than the addition operator (+), so the multiplication is performed first, giving a result of 12, and then the addition is performed, giving a final result of 14.

However, when operators have the same precedence, the order of evaluation is determined by the associativity of the operator. There are two types of associativity: left-to-right and right-to-left.

Left-to-right associativity, also known as left associativity, means that operators are evaluated from left to right. For example, in the expression 2 + 3 – 1, both the addition and subtraction operators have the same precedence, and they are both left-associative. Therefore, the expression is evaluated as (2 + 3) – 1, giving a final result of 4.

Here is an example in Python:

```
>>> 2 + 3 - 1
4
```

Right-to-left associativity, also known as right associativity, means that operators are evaluated from right to left. For example, in the expression 2 ** 3 ** 2, both the exponentiation operator (**) has the same precedence, and they are both right-associative. Therefore, the expression is evaluated as 2 ** (3 ** 2), giving a final result of 512.

Here is an example in Python:

```
>>> 2 ** 3 ** 2
512
```

It's important to note that not all programming languages have the same associativity and precedence for operators, and some languages also have custom operator overloading which can change the way an operator behaves. Always check the language documentation to be aware of the order of precedence and associativity of operators in your language.

In conclusion, when operators have the same precedence, they are evaluated according to their associativity, either left-to-right or right-to-left. Understanding the order of evaluation is important for writing correct and efficient code, and it is essential to consult the documentation of your programming language to be aware of the associativity and precedence of operators.

In addition to understanding operator precedence and associativity, there are a few other related topics that are important to understand when writing code.

One of these topics is operator overloading. Operator overloading is a feature in some programming languages that allows operators (such as + or * ) to have different meanings depending on the context in which they are used. For example, in Python, the + operator can be used to add numbers together, but it can also be used to concatenate strings. This can be a powerful feature, but it can also lead to confusion if not used carefully.

Another topic that is related to operator precedence and associativity is the use of parentheses. Parentheses can be used to change the order of evaluation of an expression, by explicitly specifying which operations should be performed first. For example, in the expression 2 + (3 * 4), the multiplication is performed first, because it is enclosed in parentheses, giving a result of 12, and then the addition is performed, giving a final result of 14.

It's also important to be aware of the difference between mathematical and bitwise operators. Mathematical operators such as +, -, *, /, % are used to perform mathematical calculations, while bitwise operators such as &, |, ^, <<, >> are used to manipulate the individual bits of a number. These two types of operators have different precedence levels and associativity in many programming languages.

Finally, it's important to be aware of the difference between the assignment operator (=) and the comparison operator (==). The assignment operator is used to assign a value to a variable, while the comparison operator is used to compare the value of two expressions to see if they are equal. These two operators have different precedence levels and associativity in many programming languages.

In conclusion, understanding operator precedence and associativity is an important part of writing correct and efficient code. However, it's also important to understand related topics such as operator overloading, the use of parentheses, the difference between mathematical and bitwise operators and the difference between the assignment operator and the comparison operator.

## Popular questions

- What is the order of evaluation for operators with the same precedence?

The order of evaluation for operators with the same precedence is determined by the associativity of the operator. There are two types of associativity: left-to-right and right-to-left. Left-to-right associativity means that operators are evaluated from left to right, while right-to-left associativity means that operators are evaluated from right to left.

- Can you give an example of an expression with operators of the same precedence that uses left-to-right associativity?

An example of an expression with operators of the same precedence that uses left-to-right associativity is 2 + 3 – 1. Both the addition and subtraction operators have the same precedence and they are both left-associative. Therefore, the expression is evaluated as (2 + 3) – 1, giving a final result of 4.

```
>>> 2 + 3 - 1
4
```

- Can you give an example of an expression with operators of the same precedence that uses right-to-left associativity?

An example of an expression with operators of the same precedence that uses right-to-left associativity is 2 ** 3 ** 2. Both the exponentiation operator (**) has the same precedence and they are both right-associative. Therefore, the expression is evaluated as 2 ** (3 ** 2), giving a final result of 512.

```
>>> 2 ** 3 ** 2
512
```

- How does operator overloading affect the order of evaluation for operators with the same precedence?

Operator overloading can affect the order of evaluation for operators with the same precedence because it allows operators to have different meanings depending on the context in which they are used. For example, in Python, the + operator can be used to add numbers together, but it can also be used to concatenate strings. This can lead to confusion if not used carefully.

- How do parentheses affect the order of evaluation for operators with the same precedence?

Parentheses can be used to change the order of evaluation of an expression by explicitly specifying which operations should be performed first. For example, in the expression 2 + (3 * 4), the multiplication is performed first, because it is enclosed in parentheses, giving a result of 12, and then the addition is performed, giving a final result of 14.

It's important to note that parentheses can be used to change the order of evaluation of any expression, regardless of the precedence or associativity of the operators used.

### Tag

Associativity.