## Table of Contents

## Section 1: Introduction

Welcome to this comprehensive guide on understanding **operator precedence** and **associativity** in Python. As a programmer, it's essential to have a strong grasp of these concepts to write efficient, readable, and *bug-free* code. In this article, we'll dive deep into the world of operators, precedence, and associativity, explaining their importance and providing clear examples to help you become a Python expert.

### 1.1 Operator Precedence and Associativity

**Operators** are the building blocks of expressions in Python. They allow us to perform various operations like arithmetic, comparisons, and logic. **Operator precedence** and **associativity** are two critical factors that dictate the order in which operations are carried out in an expression.

**Precedence** refers to the priority given to different operators, while **associativity** determines the order in which operators with the same precedence are executed. Both of these factors come into play when you're working with complex expressions that involve multiple operators.

### 1.2 Importance of Understanding Operator Precedence and Associativity

Understanding **operator precedence** and **associativity** is crucial for several reasons:

**Accurate calculations:**Properly applying precedence and associativity rules ensures that your expressions are evaluated as intended, yielding accurate results and preventing logical errors in your code.**Code readability:**Knowing how operators work helps you write code that is easier to read and understand, both for yourself and others who may need to maintain or extend your work.**Debugging:**When you encounter issues in your code, understanding precedence and associativity can help you quickly identify and fix potential problems related to the order of operations.**Code optimization:**A solid grasp of these concepts allows you to optimize your code, making it more efficient and reducing the chances of performance bottlenecks.

In the following sections, we'll dive deeper into the world of operator precedence and associativity, providing examples and best practices to help you improve your Python programming skills.

## Section 2: Operator Precedence in Python

In Python, different operators have different **precedence levels**, which determine the order in which they are executed.

When an expression involves multiple operators, Python will evaluate them based on their precedence levels before producing the final result.

### 2.1 Arithmetic Operators

**Arithmetic operators** are used for mathematical operations like *addition*, *subtraction*, *multiplication*, and *division*.

Here's a list of arithmetic operators in Python, ordered from **highest** to **lowest** precedence:

- Exponentiation (
******) - Unary positive/negative (
**+x**,**-x**) - Multiplication (
*****), Division (**/**), Floor Division (**//**), and Modulus (**%**) - Addition (
**+**) and Subtraction (**-**)

**Examples:**

result1 = 8 + 2 * 3 - 4 / 2 # 2 * 3 = 6, 4 / 2 = 2, 8 + 6 = 14, 14 - 2 = 12 result2 = (3 + 5) * 2 - 6 / 3 # 3 + 5 = 8, 6 / 3 = 2, 8 * 2 = 16, 16 - 2 = 14 result3 = 4 ** 2 // 3 * 5 % 7 # 4 ** 2 = 16, 16 // 3 = 5, 5 * 5 = 25, 25 % 7 = 4 result4 = 2 ** 3 * 4 + 5 # 2 ** 3 = 8, 8 * 4 = 32, 32 + 5 = 37 result5 = 10 / 2 * 3 + 4 # 10 / 2 = 5.0, 5.0 * 3 = 15.0, 15.0 + 4 = 19.0

### 2.2 Comparison Operators

**Comparison operators** are used to compare values and produce a **boolean** result (*True* or *False*) based on the outcome of the comparison. These operators have lower precedence than arithmetic operators.

Here's a list of comparison operators in Python, ordered from **highest** to **lowest** precedence:

- Less than (
**<**) - Less than or equal to (
**<=**) - Greater than (
**>**) - Greater than or equal to (
**>=**) - Equal to (
**==**) - Not equal to (
**!=**)

When multiple comparison operators are used in an expression, they are evaluated from **left** to **right**.

**Examples:**

result1 = 3 * 2 > 4 + 2 == 6 # 3 * 2 = 6, 4 + 2 = 6, so 6 > 6 is False, # 6 == 6 is True, the result is False result2 = 5 < 10 > 3 # 5 < 10 is True, 10 > 3 is True, so the result is True result3 = 10 - 3 < 5 != 3 * 2 # 10 - 3 = 7, 3 * 2 = 6, so 7 < 5 is False, # 5 != 6 is True, the result is False result4 = 7 >= 5 == 2 + 3 # 7 >= 5 is True, 5 == 2 + 3 is True, so the result is True result5 = 5 * 2 >= 10 == 2 ** 3 # 5 * 2 = 10, 2 ** 3 = 8, so 10 >= 10 is True, # 10 == 8 is False, the result is False

### 2.3 Logical Operators

**Logical operators** are used to perform logical operations, such as *AND*, *OR*, and *NOT*, on **boolean** values. They have lower precedence than arithmetic and comparison operators.

Here's a list of logical operators in Python, ordered from **highest** to **lowest** precedence:

- NOT (
**not**) - AND (
**and**) - OR (
**or**)

**Examples:**

result1 = not 5 > 2 and 4 < 6 # not (5 > 2) and (4 < 6), # not True and True, False and True, the result is False result2 = 3 < 7 or 8 > 12 and not 10 == 5 * 2 # (3 < 7) or (8 > 12) and not (10 == 5 * 2), # True or False and not True, True or False, the result is True result3 = not 7 < 5 or 3 * 2 == 6 and 4 + 2 > 5 # not (7 < 5) or (3 * 2 == 6) and (4 + 2 > 5), # not False or True and True, True or True, the result is True result4 = not (10 > 8 and 6 / 3 == 2) or 12 - 3 < 9 # not ((10 > 8) and (6 / 3 == 2)) or (12 - 3 < 9), # not (True and True) or False, not True or False, the result is False result5 = 2 * 2 == 4 and not 6 > 10 or 8 < 5 # (2 * 2 == 4) and not (6 > 10) or (8 < 5), # True and not False or False, True and True or False, the result is True

### 2.4 Bitwise Operators

**Bitwise operators** are used to perform operations on *binary numbers*, or the individual *bits* within integer values. They have higher precedence than logical operators but lower precedence than comparison operators.

Here's a list of bitwise operators in Python, ordered from **highest** to **lowest** precedence:

- Bitwise NOT (
**~**) - Bitwise AND (
**&**) - Bitwise XOR (
**^**) - Bitwise OR (
**|**)

**Examples:**

result1 = 5 & 3 | 4 ^ 6 # (5 & 3) | (4 ^ 6), 1 | 2, the result is 3 result2 = ~4 & 5 | 6 ^ 3 # (~4) & 5 | (6 ^ 3), -5 & 5 | 5, 1 | 5, the result is 5 result3 = 7 & 3 ^ 5 | 2 # (7 & 3) ^ (5 | 2), 3 ^ 7, the result is 4 result4 = 12 | 5 & 6 ^ 3 # (12 | 5) & (6 ^ 3), 13 & 5, the result is 5 result5 = 4 ^ 2 & 6 | 1 # (4 ^ 2) & (6 | 1), 6 & 7, the result is 6

### 2.5 Precedence Rules and Hierarchy

In Python, operators have a defined **order of precedence** that determines the evaluation order of expressions.

Here is a summary of the operator precedence hierarchy, ordered from **highest** to **lowest** precedence:

- Parentheses
**()** - Exponentiation
****** - Bitwise NOT
**~**, Unary plus**+**, Unary minus**-** - Multiplication
*****, Division**/**, Floor division**//**, Modulus**%** - Addition
**+**, Subtraction**-** - Bitwise shift left
**<<**, Bitwise shift right**>>** - Bitwise AND
**&** - Bitwise XOR
**^** - Bitwise OR
**|** - Comparison operators (
**<**,**<=**,**>**,**>=**,**!=**,**==**) - Identity operators (
**is**,**is not**) - Membership operators (
**in**,**not in**) - Logical NOT
**not** - Logical AND
**and** - Logical OR
**or**

Precedence | Operator | Description |
---|---|---|

1 | () | Parentheses |

2 | ** | Exponentiation |

3 | ~, +, - (unary) | Bitwise NOT, unary plus, and minus |

4 | *, /, //, % | Multiplication, division, floor division, and modulo |

5 | +, - (binary) | Addition and subtraction |

6 | <<, >> | Bitwise shift left and right |

7 | & | Bitwise AND |

8 | ^ | Bitwise XOR |

9 | | | Bitwise OR |

10 | <, <=, >, >=, !=, == | Comparison operators |

11 | is, is not | Identity operators |

12 | in, not in | Membership operators |

13 | not | Logical NOT |

14 | and | Logical AND |

15 | or | Logical OR |

### 2.6 Examples of Operator Precedence

**Example 1:**

result = 2 + 3 * 4 ** 2 - 1 # 2 + 3 * (4 ** 2) - 1, 2 + 3 * 16 - 1, 2 + 48 - 1, # the result is 49

Explanation:

- Exponentiation:
**4 ** 2**evaluates to**16** - Multiplication:
**3 * 16**evaluates to**48** - Addition:
**2 + 48**evaluates to**50** - Subtraction:
**50 - 1**evaluates to**49**

**Example 2:**

result = 4 * 2 + 5 & 3 | 2 # (4 * 2 + 5) & (3 | 2), 13 & 3, the result is 1

Explanation:

- Multiplication:
**4 * 2**evaluates to**8** - Addition:
**8 + 5**evaluates to**13** - Bitwise OR:
**3 | 2**evaluates to**3** - Bitwise AND:
**13 & 3**evaluates to**1**

**Example 3:**

result = not 4 < 2 or 3 + 1 == 2 * 2 and 6 / 2 > 2 # not (4 < 2) or ((3 + 1 == 2 * 2) and (6 / 2 > 2)), # not False or (True and True), the result is True

Explanation:

- Comparison:
**4 < 2**evaluates to**False** - Addition:
**3 + 1**evaluates to**4** - Multiplication:
**2 * 2**evaluates to**4** - Comparison:
**4 == 4**evaluates to**True** - Division:
**6 / 2**evaluates to**3** - Comparison:
**3 > 2**evaluates to**True** - Logical AND:
**True and True**evaluates to**True** - Logical NOT:
**not False**evaluates to**True** - Logical OR:
**True or True**evaluates to**True**

These examples demonstrate how operator precedence is applied when evaluating expressions with multiple operators in Python.

## Section 3: Operator Associativity in Python

### 3.1 Left-to-Right Associativity

**Operator associativity** determines the order in which operators with the same precedence level are evaluated. Most of the operators in Python have **left-to-right** associativity, meaning that they are evaluated from left to right when they have the same precedence level.

Examples of operators with left-to-right associativity are *arithmetic*, *bitwise*, *comparison*, and *logical operators*.

#### 3.1.1 Examples

**Example 1:** Left-to-right associativity in arithmetic operations

result = 5 - 3 + 2 # (5 - 3) + 2, 2 + 2, the result is 4

Explanation:

- Subtraction:
**5 - 3**evaluates to**2** - Addition:
**2 + 2**evaluates to**4**

**Example 2:** Left-to-right associativity in comparison operations

result = 10 < 15 > 12 # (10 < 15) > 12, True > 12, the result is False

Explanation:

- Comparison:
**10 < 15**evaluates to**True** - Comparison:
**True > 12**evaluates to**False**(In this case,**True**is treated as**1**)

**Example 3:** Left-to-right associativity in bitwise operations

result = 7 | 4 & 3 # (7 | 4) & 3, 7 & 3, the result is 3

Explanation:

- Bitwise OR:
**7 | 4**evaluates to**7**(binary:**111 | 100 = 111**) - Bitwise AND:
**7 & 3**evaluates to**3**(binary:**111 & 011 = 011**)

**Example 4:** Left-to-right associativity in logical operations

result = True or False and not False # (True or False) and not False, True and not False, # the result is True

Explanation:

- Logical OR:
**True or False**evaluates to**True** - Logical NOT:
**not False**evaluates to**True** - Logical AND:
**True and True**evaluates to**True**

These examples demonstrate how **left-to-right** associativity works for operators with the same precedence level in Python.

### 3.2 Right-to-Left Associativity

Some operators in Python have **right-to-left** associativity, meaning that they are evaluated from right to left when they have the same precedence level.

The operators with right-to-left associativity in Python are exponentiation ****** and unary operators like unary plus **+**, unary minus **-**, and bitwise NOT **~**.

#### 3.2.1 Examples

**Example 1:** Right-to-left associativity in exponentiation

result = 2 ** 3 ** 2 # 2 ** (3 ** 2), 2 ** 9, the result is 512

Explanation:

- Exponentiation (right-to-left):
**3 ** 2**evaluates to**9** - Exponentiation (right-to-left):
**2 ** 9**evaluates to**512**

**Example 2:** Right-to-left associativity in unary operators

result = -3 ** 2 # -(3 ** 2), -9, the result is -9

Explanation:

- Exponentiation (right-to-left):
**3 ** 2**evaluates to**9** - Unary minus (right-to-left):
**-9**evaluates to**-9**

**Example 3:** Right-to-left associativity with bitwise NOT

result = ~5 + 3 # (~5) + 3, -6 + 3, the result is -3

Explanation:

- Bitwise NOT (right-to-left):
**~5**evaluates to**-6**(binary:**~0101 = 1010**, decimal:**-6**) - Addition (left-to-right):
**-6 + 3**evaluates to**-3**

These examples demonstrate how **right-to-left** associativity works for operators with the same precedence level in Python, such as exponentiation and unary operators.

### 3.3 Non-Associativity Operators

**Non-associativity** operators are those that do not have any specific order of evaluation when they appear in a sequence with the same precedence level.

In Python, non-associativity operators include comparison chaining operators like **==**, **!=**, **<**, **>**, **<=**, and **>=**. Using these operators in a chain can lead to ambiguous or unintended results, so it's better to avoid such constructs or use parentheses to clarify the intended order of evaluation.

#### 3.3.1 Examples

**Example 1:** Non-associativity in comparison chaining

result = 5 < 10 > 3 # This is equivalent to (5 < 10) and (10 > 3), # the result is True

Explanation:

- Comparison chaining:
**5 < 10 > 3**evaluates to**True**because both**5 < 10**and**10 > 3**are**True**

**Example 2:** Non-associativity with equality and inequality operators

result = 5 == 5 != 3 # This is equivalent to (5 == 5) and (5 != 3), # the result is True

Explanation:

- Comparison chaining:
**5 == 5 != 3**evaluates to**True**because both**5 == 5**and**5 != 3**are**True**

However, it is important to note that using non-associative operators in a chain can lead to **ambiguity**, and it is better to clarify the intended order of evaluation using **parentheses**. Here's an example of how ambiguity can arise:

**Ambiguous example:**

result = 5 < 10 < 7 > 3 # This can be interpreted as (5 < 10) < 7 > 3 # or 5 < (10 < 7) > 3, which is ambiguous

In such cases, it is recommended to use **parentheses** to clarify the intended order of evaluation:

**Clear example:**

result = (5 < 10) and (10 < 7) and (7 > 3) # The result is False

These examples demonstrate how non-associativity works for comparison chaining operators in Python and the importance of using parentheses to avoid ambiguity.

## Section 4: Mixing Precedence and Associativity

### 4.1 Understanding Complex Expressions

When working with complex expressions involving operators with different precedence levels and associativity, it's essential to understand how these factors impact the evaluation order of the expression. In this section, we'll examine examples involving a mix of operators with different precedence and associativity to understand the evaluation order.

**Example 1:** Mixing arithmetic and comparison operators

result = 2 * 3 + 4 < 5 * 2 # (2 * 3) + 4 < 5 * 2, 6 + 4 < 10, 10 < 10, # the result is False

Explanation:

- Multiplication (left-to-right):
**2 * 3**evaluates to**6** - Addition (left-to-right):
**6 + 4**evaluates to**10** - Multiplication (left-to-right):
**5 * 2**evaluates to**10** - Comparison (left-to-right):
**10 < 10**evaluates to**False**

**Example 2:** Mixing arithmetic, comparison, and logical operators

result = 2 + 3 * 4 > 5 and 6 / 2 < 4 # (2 + 3 * 4) > 5 and (6 / 2) < 4, # (2 + 12) > 5 and (3) < 4, # 14 > 5 and 3 < 4, the result is True

Explanation:

- Multiplication (left-to-right):
**3 * 4**evaluates to**12** - Addition (left-to-right):
**2 + 12**evaluates to**14** - Comparison (left-to-right):
**14 > 5**evaluates to**True** - Division (left-to-right):
**6 / 2**evaluates to**3** - Comparison (left-to-right):
**3 < 4**evaluates to**True** - Logical AND (left-to-right):
**True and True**evaluates to**True**

In complex expressions like the ones above, it's crucial to keep track of the precedence and associativity rules to understand how the expression will be evaluated. When in doubt, use **parentheses** to clarify the intended order of evaluation and make the code more readable.

### 4.2 Tips to Simplify Expressions and Improve Code Readability

When working with complex expressions that involve multiple operators with different precedence and associativity, it's essential to **simplify** the expressions to improve code readability. Here are a few tips to help with that:

**Use parentheses:**Using parentheses to group expressions can clarify the intended order of evaluation and make the code easier to read.**Break down complex expressions:**Splitting a complex expression into smaller parts using intermediate variables can make it more manageable and easier to understand.**Add comments:**When dealing with complex expressions, adding comments to explain the logic can help other developers understand your code.**Consistent formatting:**Using consistent formatting and whitespace can improve the readability of your code.

### 4.3 Examples with Mixed Precedence and Associativity

**Example 1:** Mixing arithmetic, comparison, and logical operators with parentheses

result = (2 * 3 + 4) < (5 * 2) and (6 / 2) < 4 # (6 + 4) < 10 and 3 < 4, 10 < 10 and 3 < 4, the result is False

Explanation:

- Multiplication, addition, and comparison expressions are enclosed in
**parentheses**to clarify the intended order of evaluation. - Logical AND is applied to the results of the two comparison expressions.

**Example 2:** Breaking down a complex expression using intermediate variables

a = 2 * 3 b = 4 c = 5 * 2 d = 6 / 2 result = (a + b) < c and d < 4 # (6 + 4) < 10 and 3 < 4, 10 < 10 and 3 < 4, the result is False

Explanation:

- The complex expression is broken down into smaller parts using
**intermediate variables**, making it more manageable and easier to understand. - The final result is calculated using the intermediate variables and logical AND.

These examples demonstrate how to simplify complex expressions involving **mixed precedence** and **associativity**. By following the tips provided, you can improve the readability and maintainability of your Python code.

## Section 5: Using Parentheses to Clarify Expressions

Using **parentheses** in expressions can help clarify the intended order of evaluation and improve code readability. By explicitly specifying the order in which operations are performed, you can prevent potential errors due to misunderstanding of precedence and associativity rules. Let's look at some examples that demonstrate the usage of parentheses.

**Example 1:** Using parentheses to clarify arithmetic expressions

result = (2 + 3) * (4 - 1) # (2 + 3) * 3, 5 * 3, the result is 15

Explanation:

- Parentheses are used to
**group**addition and subtraction operations before multiplication. - The addition and subtraction operations are evaluated first, followed by the multiplication.

**Example 2:** Using parentheses to clarify mixed expressions

result = (3 * 4 > 5) and not (2 + 2 == 4) # (3 * 4) > 5 and not (2 + 2 == 4), # 12 > 5 and not True, the result is False

Explanation:

- Parentheses are used to
**group**arithmetic and comparison operations, making the intended order of evaluation explicit. - The result of the grouped comparisons is then combined using the logical AND and NOT operators.

**Example 3:** Using parentheses to avoid ambiguity in chaining comparisons

result = (5 < 10) and (10 < 7) and (7 > 3) # True and False and True, the result is False

Explanation:

- Parentheses are used to
**group**each comparison operation to avoid ambiguity and clarify the intended order of evaluation. - The result of the grouped comparisons is then combined using the logical AND operator.

By using parentheses to **group operations** and clarify the order of evaluation, you can create more readable and maintainable Python code. This practice helps prevent potential errors due to misinterpretation of precedence and associativity rules.

## Section 6: Best Practices for Precedence and Associativity

### 6.1 Using Parentheses for Readability

Utilize parentheses to enhance readability and clarity in your code, especially when dealing with complex expressions that involve multiple operators. By explicitly specifying the order of operations, you can avoid potential errors due to misunderstanding precedence and associativity rules.

### 6.2 Avoiding Non-Associative Operator Ambiguity

Some operators in Python, like comparison operators, are non-associative. This means that they cannot be chained directly without causing ambiguity. When working with non-associative operators, use parentheses to group operations and clearly define the intended order of evaluation.

### 6.3 Ensuring Correct Evaluation of Expressions

To ensure the correct evaluation of expressions, always be mindful of operator precedence and associativity rules. If you are unsure of the evaluation order, use parentheses to clarify the order in which the operations should be performed. This can help prevent potential errors and ensure that your code behaves as intended.

### 6.4 Ensuring Code Readability and Maintainability

Maintaining readable and maintainable code is essential for long-term success in any software project. By consistently using parentheses to group operations, following consistent formatting and whitespace rules, breaking down complex expressions into smaller parts, and adding comments to explain the logic, you can ensure that your Python code remains easy to understand and maintain.

By following these best practices for operator precedence and associativity, you can create clean, readable, and maintainable Python code that is less prone to errors and easier for others to understand.

## Section 7: Conclusion

In this article, we discussed the concepts of **operator precedence** and **associativity** in Python, covering their importance and how they affect the evaluation of expressions. We examined different types of operators, including arithmetic, comparison, logical, and bitwise operators, and learned how they relate to one another in terms of precedence and associativity.

To ensure correct evaluation and improve the readability of your code, we recommended the following best practices:

- Use parentheses to clarify the intended order of evaluation.
- Be mindful of non-associative operators and use parentheses to avoid ambiguity.
- Break down complex expressions into smaller parts to make them more manageable.
- Maintain consistent formatting and add comments to explain your logic.

By understanding and applying these principles, you can create Python code that is not only more readable and maintainable but also less prone to errors caused by misunderstandings of operator precedence and associativity rules.

We encourage you to continue learning and exploring the Python programming language, as well as its many libraries and frameworks. As you become more proficient in Python, you will undoubtedly find these concepts and best practices invaluable in developing efficient, reliable, and easily understandable code.

I hope you found this article helpful.

Cheers!

Happy Coding.

About the AuthorThis article was authored byANKIT SINGH. Verified byRawnak.