Variables, Expressions and Statements

Operator Precedence

When you deal with operators in Python, it is essential to understand the concept of Python operator precedence and associativity. It is because they determine the priorities of the operator otherwise we will have unexpected outputs.

operator precedence

Operator Precedence

We use this in an expression that has more than one operator with difference precedence to determine which operation must be performed first.

Example

Solve 25 + 10 * 20

25 + 10 * 20 is calculated as 25 + (10 * 20)

and not as (25 + 10) * 20

Code:

Python3

                    

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# Precedence of '+' & '*'

expr = 25 + 10 * 20

print(expr)

Output:

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Precedence of Python Operators

We term the combination of values, variables, operators, and function calls as an expression. The Python interpreter can evaluate a valid expression. For instance:

>>> 3 – 8

-5

Over here, 3 – 8 is an expression. Thus, there can be more than one operator in an expression. Moreover, in order to evaluate these kinds of expressions, there is a rule of precedence in Python. In other words, it guides the order in which these operations carry out.

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

For instance, multiplication has higher precedence than subtraction.

                    

# Multiplication has higher precedence

# than subtraction

>>> 10 - 4 * 2

2

 

However, we can change this order by making use of parentheses () as it has higher precedence than multiplication.

                    

# Parentheses () has higher precedence

>>> (10 - 4) * 2

12

 

If you look at the operator precedence in Python in the table mentioned above, you will see it is in descending order. In other words, the upper group has higher precedence than the lower ones.

Example

To understand this better, we will take a look at some examples:

Suppose that you are constructing an if…else block which runs if when breakfast is either cereal or toast and only if money is more than or equal to 2.

                    

# Precedence of or & and

meal = " cereal "

money = 0

if meal == " cereal" or meal == " toast" and money >= 2:

print("Breakfast  being delivered")

else:

print("Can't deliver breakfast ")

Output

                    

Breakfast  being delivered

Associativity of Python Operators

The table makes it clear that more than one operator is present in the same group. In other words, these operators have the same precedence. Thus, when two operators have the same precedence, associativity assists in determining the order of operations.

Further, we see that associativity refers to the order in which an expression is assessed that has multiple operators of the same precedence. Similarly, almost all the operators have left-to-right associativity.

For instance, multiplication and floor division have the same precedence. Therefore, if both of them exist in an expression, the left one will be evaluated first.

                    

# Left-right associativity

# Output: 3

print(5 * 2 // 3)

# Shows left-right associativity

# Output: 0

print(5 * (2 // 3))

Output

Note: Exponent operator ** has right-to-left associativity in Python.

                    

# Shows the right-left associativity of **

# Output: 512, Since 2**(3**2) = 2**9

print(2 ** 3 ** 2)

# If 2 needs to be exponated first, need to use ()

# Output: 64

print((2 ** 3) ** 2)

We can see that 2 ** 3 ** 2 is equivalent to 2 ** (3 ** 2).

Non Associative Operators

Some operators like assignment operators and comparison operators do not have associativity in Python. Thus, we have separate rules for sequences of this kind of operator and we cannot express them as associativity.

For instance, x < y < z neither means (x < y) < z nor x < (y < z). x < y < z is equivalent to x < y and y < z, and is evaluated from left-to-right.

In addition, while chaining of assignments like x = y = z = 1 is perfectly valid, x = y = z+= 2 will result in error.

                    

# Initialize x, y, z

x = y = z = 1

# Expression is invalid

# (Non-associative operators)

# SyntaxError: invalid syntax

x = y = z+= 2

Output

                    

File "", line 8

x = y = z+= 2

^

SyntaxError: invalid syntax

FAQ on Operator Precedence

Question 1: Which is the order of precedence in Python?

Answer 1: Python follows the same precedence rules for its mathematical operators just like mathematics. Further, parentheses have the highest precedence we can use them to force an expression to evaluate in the order one wants. Moreover, as we evaluate expressions first in parentheses, 3 * (2-1) is 3, and (1+1)**(5-2) is 8.

Question 2: What is the precedence of logical operators?

Answer 2: The order of precedence is logical complements ( Not ) are performed first. After that, logical conjunctions ( And ) are performed next. Finally, logical disjunctions ( Or ) are performed at the end.

Question 3: What is the order of operations in Python?

Answer 3: PEMDAS is P, E, MD, AS; multiplication and division have the same precedence, and the same applies for addition and subtraction. Further, when a division operator appears before multiplication, division goes first. Thus, the order Python operators are executed in is governed by the operator precedence, and it follows the same rules.

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