Precedence and Associativity of Operators in Python

In this article, you’ll learn:

1. What are precedence and associativity of operators in python

2. How they affect the order of operations (with examples)

3. Need of precedence and associativity of operators

4. How do you remember operator precedence in python? (short trick)

So, Let’s get started!

Before we move further,

Let’s have a quick look on some important terms, so that you’ll understand all the upcoming concepts easily and feel confidence as you move forward.

And, the terms which I’m talking about are: Expressions, and Evaluation of an expression.

Expression: An Expression is a sequence or combination of values, variables, operators and function calls that always produces or returns a result value.

If you type an expression on the IDLE or on the command line, the interpreter evaluates it and displays the result.

Example: x = 5, y = 3, z = x + y

In the above example x, y and z are variables, 5 and 3 are values, = and + are operators.

So, the first combination x = 5 is an expression, the second combination y = 3 is an another expression and at last, z = x + y is also an expression.

Evaluation of an expression: It simply means that, to calculate or to solve the value of something. Such as in the above example: z = x + y, which is equivalent to z = 5 + 3. So, here we are calculating the value of z. and, hence, z = 8.

Sorry! (for taking your more time)

But, I want you to understand every single stuff better.

So, May I ask two rapid question!

Question 1: What will be the output of this expression: 2 + 3

Your answer is 5, right…?

Ya, you are correct. That’s so simple.

Now,

Question 2: Guess the output of the expression given below?

Done?

What is your answer?

Is it 4 or is it 14?

If your answer is 4, then you are correct, and if your answer is 14, then you are wrong.

I know, I know… the person who got the answer 14 might be wondering that why 14 is wrong and why 4 is correct.

Explanation: 14 is wrong because, those who got 14 then, he/she must have solved the expression according to the following way:

He/she definitely added 6 and 4 first, then subtracted the result (i.e., 6 + 4 = 10) by 3 and at last multiplied the result (i.e., 10 - 3 = 7) by 2. Which will give 14 as an output.

But, the answer is wrong. Why? – because, it has not been evaluated according to the order as like the operators are evaluated in python.

And, to overcome this problem, Precedence of operators comes into picture.

So,

When an expression contains more than one operator, then we need to decide which operator will be evaluated first.

The set of rules which gives the priority (precedence) of operators while evaluating an expression is known as operator precedence.

So, There is a rule of precedence (priority) in python which gives the order/sequence in which various operation are performed in an expression according to the priority of operators is known as hierarchy of operations or operator precedence.

Precedence rules decides the order in which different operators are applied in an expression.

The operators at the higher level of precedence are evaluated first.

? The following table summarizes the operator precedence in Python. It is in descending order (upper group has higher precedence than the lower ones). Operators in the same box have the same precedence.

Python operator precedence table:

Operator	Description (Meaning)
(expressions... ) [expressions...], {key: value...}, {expressions...}	Parenthesized expression, list display, dictionary display, set display
x[index], x[index:index], x(arguments...), x.attribute	Subscription, slicing, call, attribute reference
await x	Await expression
**	Exponent
+x, -x, ~x	Unary plus (positive), Unary minus (minus), bitwise NOT
*, @, /, //, %	Multiplication, Matrix multiplication, Division, Floor division, Modulus
+, -	Addition, Subtraction
<<, >>	Bitwise left shift, Bitwise right shift
&	Bitwise AND
^	Bitwise XOR
|	Bitwise OR
in, not in, is, is not, <, <=, >, >=, !=, ==	Membership, identity and Comparison (Relational) operators
not	Logical NOT
and	Logical AND
or	Logical OR
if - else	Conditional expression
lambda	Lambda expression
:=	Assignment operators

So, from the above table we can see that,

⚉ Parentheses has the highest precedence in python.

Since, expressions in parentheses are evaluated first, 3 * (5-2) is 9.

⚉ Exponentiation has the next highest precedence, so 2 + 3**3 is 29, not 125.

⚉ Multiplication and Division have higher precedence than Addition and Subtraction.

So, 3*4-2 is 10, not 6, and 5+6/2 is 8, not 5.2

⚉ Assignment operator has the lowest precedence in python.

⚉ Operators with the same precedence are evaluated from left-to-right (except exponentiation). So in the expression degrees / 2 * pi, the division happens first and the result is multiplied by pi. To divide by 2*pi, you can use parentheses or write degrees / 2 / pi.

Let’s have a look at some of the examples:

Examples 1:

1. Precedence of arithmetic operators:

An arithmetic expression without parentheses will be evaluated from left-to-right using the rules of precedence of operators.

There are two distinct priority levels of arithmetic operators in Python:

⚉ High priority: *, /, //, %

⚉ Low priority: +, -

The basic evaluation procedure includes ‘two’ left-to-right passes through the expression.

During the first pass, the high priority operators (if any) are applied as they are encountered. During the second pass, the low priority operators (if any) are applied as they are encountered.

Consider the following evaluation of an expression:

9 - 12 / 3 + 3 * 2 - 1

The above expression is evaluated as follows:

First pass

Step1: 9 - 124/3 + 3 * 2 -1 = 9 - 4 + 3 * 2 -1 (Here, division has the highest priority. so, division between 12 and 3 happens first.)

Step2: 9 - 4 + 6 - 1 (Then, multiplication between 3 and 2)

Second pass

Step3: 5 + 6 - 1 (evaluated from left-to-right. because, + and – have the same priority, so addition between 5 and 6 happens first)

Step4: 11 - 1 (evaluated from left-to-right)

Step5: 10

However, the order of evaluation can be changed by introducing parentheses into an expression.

Consider the same expression (which we have taken in the above example) with parentheses as shown below:

9 - 12 / (3 + 3) * (2 - 1)

Whenever parentheses are used, the expressions within parentheses is suppose to highest priority.

If two or more sets of parentheses appear one after another as shown above, the expression contained in the left-most set is evaluated first and the right-most in the last.

The new steps are:

First pass

Step1: 9 - 12 / 6 * ( 2 - 1)

Step2: 9 - 12 / 6 * 1

Second pass

Step3: 9 - 2 * 1 (Multiplication between 2 and 1 happens first. because, it has higher precedence than subtraction)

Step4: 9 - 2

Third pass

Step5: 7

This time, the procedure consists of three left-to-right passes. However, the number of evaluation steps remains the same as 5 (i.e., equal to the number of arithmetic operators).

Parentheses may be nested, and in such cases, evaluation of the expression will begin outward from the innermost set of parentheses.

Points to be noted:

Every opening parenthesis has a matching closing parenthesis.

For example: 9 - (12 / (3 + 3) * 2) - 1 = 4

Whereas, 9 - ((12 / 3) + 3 * 2) - 1 = -2

Advantages of using parentheses in an expression:

– Parentheses makes an expression easier to read and understand.

Example: As in (minute * 100) / 60, even if it doesn’t change the result.

– Parentheses can be used to force an expression to evaluate in the order you want.

– Parentheses allow us to change the order of priority.

Example 2:

2. Precedence of operators (belonging to two or more different groups):

Let’s take a conditional statement: if(x == 10 + 15 and y < 5)

The precedence rules say that the addition operator has a higher priority than the logical operator (and) and the relational operators (== and <).

Therefore, the addition of 10 and 15 is evaluated first.

This is equivalent to: if(x == 25 and y < 5)

The next step is to determine whether x is equal to 25 and y is less than 5. If we assume a value of 18 for x and 4 for y, then

x == 25 is FALSE

y < 5 is TRUE

And, as we already know that == and < operator has the same priority and evaluated from left-to-right, so, x == 25 is tested first and then y< 5 is tested.

Finally we get: if(FALSE and TRUE)

And, In and operator, if one of the condition is FALSE, then the complex condition is also FALSE.

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Associativity of Python Operators:

If you look at the above precedence table, then you’ll find that more than one operator lies (exist) in the same box (group) or we can say they have same level of precedence.

Example: *, /, //, % are in the same box, which means that all these operators have the same precedence or same level of precedence.

Now, one question will definitely arises in your mind, that if all these operators (*, /, //, %) has the same priority and if they all are encountered in a same expression, then which operator will be evaluated first.

To overcome this problem, Associativity of operators comes into picture.

So, Associativity of operators comes into picture when two or more operators have the same precedence and we need to decide which operator will be evaluated first.

Associativity rule decides the order in which multiple occurrences of the same level or we can say operator with same precedence are applied in an expression.

Associativity is the order/sequence in which an expression is evaluated that has two or more than two operators of the same precedence.

It can either be left-to-right or right-to-left.

But, here – What does left-to-right or right-to-left mean?

It simply means that, evaluation of an expression takes place from left-to-right hand side or right-to-left hand side.

Associativity of all operators is from left-to-right (except for exponentiation and assignment operators which groups from right-to-left).

Example 1:

1. Associativity of arithmetic operator:

Let’s say: x = 6 % 4 * 14 // 9 / 3

Now, what will be the value of x?

Ans: x = 1

Explanation: As we can see that the above expression (i.e., x = 6 % 4 * 14 // 9 / 3) contains all the operators (arithmetic operators) of same precedence.

And, we all know that arithmetic operators with the same precedence are evaluated from left-to-right. So in the expression: x = 6 % 4 * 14 // 9 / 3, the modulo division (%) happens first then the result is multiplied by 14 then after multiplying by 14 the result is divided (floor division) by 9 and at last divided by 3.

Which will give 1 as an output.

Example 2:

2. Associativity of exponent operator:

Exponent operator (**) has right-to-left associativity in python.

Now, Guess the output of: 3 ** 2 ** 2

Output of the above expression (i.e., 3 ** 2 ** 2) is: 81

Explanation: As we already know, that exponent has right-to-left associativity. So in the expression: 3 ** 2 ** 2, 2 raise to the power of 2 happens first then the result (i.e., 4) is again raise to the power of 3.

Which will give 81 as an output.

So, we can say that 3 ** 2 ** 2 is equal to 3 ** (2 ** 2).

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Non associative operators

As the name indicates, Non associative operators are those operators which do not have associativity in python.

Or, you can say, Those operators which do not follow the associativity rules of python are called non associative operators.

Assignment operators and comparison operators comes under this category.

There are specific rules for ordering of this type of operator and cannot be expressed as associativity.

Example 1:

Let’s say: x = 5, y = 4 and z = 3

And, If you write a conditional expression like this: x > y > z. Then, It neither means (x > y) > z nor x > (y > z).

Rather, x > y > z is equivalent to x > y or y > z, and is evaluated from left-to-right.

Example 2:

Let’s say: x = y = z = 1 {Assigning a single value (1) to multiple variables (x, y and z)}.

And, If you assign a single value to multiple variables in python, then it is a valid expression.

But,

x = y = z+= 5 is not a valid expression. This expression will give an error.

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How do you remember operator precedence in python? (short trick)

Have you heard about BODMAS rule in mathematics?

I know your answer. It’s definitely gonna be YES!

BODMAS stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction. This rule gives the order in which an expression can be evaluated when different arithmetic operators are encountered in an expression.

Similarly,

If you look at the above precedence table, you’ll find that the priority of operators follow the following sequence/order:

– Parentheses
– Exponentiation
– Multiplication
– Division
– Addition
– Subtraction

And, The short form of this rule is PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction), Which is the synonym of BODMAS.

A funny and short trick to remember this rule would be “Puppy, Eat My Dish and Sleep”.

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Conclusion:

So, from this article we learned:

Rules of Precedence and Associativity

– Precedence rules decides the order in which different operators are applied in an expression.

– Associativity rule decides the order in which multiple occurrences of the same level or we can say operator with same precedence are applied in an expression.

I hope this article helped you a lot.

Now, It’s your turn!

If you have any question, feel free to ask in the comment section below right now.

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