Precedence and Associativity of Operators

Precedence of Python Operators

 A valid expression is a  combination of literal values, variables, operators, and functions.

Example:

 

>>> 2 + 3

5

 

Here 2 + 3  is an expression.  Let take another expression

>>> 2 + 3 * 4

14

​​​​​​​An expression can have  more than one operator. The  above expression can be evaluated in two ways

Method 1

Step 1      2 +  3  =  5

Step 2     5  * 4    = 20

 

Method 2

Step 1      3  *  4  =  12

Step 2      2 + 12  = 14

In the above expression there are two operators + and *.  To solve the expression the order is decided by the precedence. It guides the order in which these operations are carried out, since * has higher precedence  3 * 4 is evaluated first and 2 is added to 12 ( 3  * 4).

Here is the table of operator precedence.

The operator precedence in Python is listed in the following table. It is in descending order (upper group has higher precedence than the lower ones).

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

 

Example

 2 * 3 ** 2

​​​​​​​Here ** has higher precedence than * , The 3 **2  is evaluated first  3 **2 = 9

and 2*  9 = 18 which is the outcome of the expression

Output

2 * 3 ** 2  = 18

Example

 (2 * 3 ) ** 2

Here () has higher precedence , the (2 * 3) will be evaluated first,  (2*3) = 6, now the expression is  6**2  which is 36

Output

(2 * 3) ** 2  = 36

Example

 True and not False

The not has higher precedence  first  not False is evaluated which is True , True and True  is True

Output

True  and  not False

Associativity of Python Operators

When two operators have the same precedence, associativity helps to determine the order of operations.

Associativity is the order in which an expression is evaluated that has multiple operators of the same precedence. Almost all the operators have left-to-right associativity.

Let take another example

Example

 10000 / 100 * 100 // 10 % 10

When  the operators  have same precedence Operator Associativity is used to determine the order of evaluation. It can either be Left to Right or from Right to Left.

The associativity is the order in which Python evaluates an expression containing multiple operators of the same precedence.

Left to Right Associtivity means the expression is evaluated from Left to right The  Right to  Left Associtivity is where the expression is evaluated from Right to Left

Note: Almost all operators, except the exponent (**) support the left-to-right associativity.

Example

 2 ** 3 ** 2

The above expression has two exponent operator  these are evaluated from left to right, first 3 **2  is evaluated here expression become  2**9  which id 512

Output

2 ** 3 ** 2  = 512

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