Java Tutorial: Associativity of Operators in Java

Summary

This video covers essential topics related to operator precedence and associativity in Java, explaining how Java evaluates expressions. The speaker clarifies that, unlike mathematical BODMAS rules, Java relies on precedence (which operator is applied first) and associativity (the direction of execution). Through examples, they demonstrate how operators like multiplication, division, addition, and subtraction are evaluated in different contexts, helping viewers understand complex expressions. The video is highly relevant for students, interviewees, and anyone preparing for exams, offering a deep dive into an often misunderstood topic.

Takeaways

• 💻 The video focuses on explaining operator precedence and associativity in Java.
• 🔢 Java does not use the BODMAS rule, but instead follows precedence and associativity rules for operator evaluation.
• 🛠️ Operators like multiplication (*) and division (/) have higher precedence than addition (+) and subtraction (-).
• ⚖️ Associativity determines the order in which operators with the same precedence are evaluated (left to right or right to left).
• 📊 In Java, multiplication and division operators are left-associative, meaning they are evaluated from left to right.
• 🧮 Example: The expression '60 / 5 - 34 * 2' evaluates division first (60/5=12), then multiplication, and finally subtraction, resulting in -56.
• 📃 The instructor emphasizes using parentheses to avoid errors in complex expressions where multiple operators are involved.
• 🎓 The video includes a quadratic expression example, showing how operator precedence affects evaluation and how to correct it using parentheses.
• 📈 Operator precedence is critical in programming, especially during interviews or exams, as it affects how expressions are executed.
• ✅ The video encourages viewers to understand these concepts early on to avoid common mistakes in programming and interviews.

Q & A

What is operator precedence in Java?

Operator precedence in Java determines the order in which operators are evaluated in expressions. Operators with higher precedence are evaluated before those with lower precedence.

How does associativity affect the evaluation of expressions?

Associativity defines the direction in which operators with the same precedence are evaluated. Most operators in Java are left-to-right associative, meaning they are evaluated from left to right.

What is the difference between precedence and associativity?

Precedence determines which operator is evaluated first based on priority, while associativity resolves the order of evaluation for operators with the same precedence, dictating whether they are evaluated from left to right or right to left.

Why is the rule of BODMAS not used in Java?

Java uses precedence and associativity rules instead of the BODMAS rule for evaluating mathematical expressions. The precedence of operators in Java is defined by the language, not mathematical conventions like BODMAS.

How does Java evaluate the expression `6 * 5 - 34 / 2`?

In Java, `6 * 5` is evaluated first because multiplication has a higher precedence than subtraction. Then, `34 / 2` is evaluated because division also has higher precedence than subtraction. Finally, `30 - 17` is calculated, resulting in 13.

What happens when operators have the same precedence?

When operators have the same precedence, associativity determines the order of evaluation. For example, both division and multiplication have the same precedence, so Java evaluates them left to right.

How can parentheses change the order of evaluation?

Parentheses override the default precedence and associativity rules, forcing specific parts of an expression to be evaluated first. For example, `(6 - 5) * 2` will evaluate the subtraction before the multiplication, even though multiplication has higher precedence.

What happens if the denominator of an expression becomes zero?

If the denominator of an expression becomes zero, Java will throw an `ArithmeticException`, indicating a division by zero error. Division by zero is undefined in mathematics and causes an error in programming.

What is the significance of knowing precedence and associativity for interviews or exams?

Understanding operator precedence and associativity is crucial for writing and debugging Java code. It also helps in solving coding questions in interviews and exams where correct expression evaluation is necessary.

Why is it important to use parentheses in complex expressions?

Parentheses help clarify the intended order of evaluation in complex expressions, preventing unexpected results due to precedence and associativity rules. This makes code more readable and less prone to errors.

Outlines

00:00

🔧 Understanding Java Operator Precedence

The first paragraph introduces the topic of operator precedence in Java, which is important both in academic contexts and technical interviews. It explains that operators are applied and evaluated based on their precedence, and the video aims to cover this concept thoroughly. The speaker starts by naming the Java file and demonstrating an example of how precedence works in a Java expression. They highlight that precedence determines which operations are performed first, such as multiplication or division over addition or subtraction, and clarify that Java uses precedence and associativity rules instead of the traditional BODMAS rule.

05:01

🔄 Associativity in Java Operations

This paragraph expands on the concept of associativity, particularly how it resolves conflicts when operators have equal precedence, such as multiplication and division. Associativity determines the direction in which operations are evaluated—left-to-right or right-to-left. The speaker provides a practical example involving division and subtraction, and walks through how associativity impacts the final result. They stress that many students mistakenly apply the BODMAS rule, but in Java, associativity is key to determining the order of operations.

10:01

📝 Practical Example: Operator Precedence and Associativity in Expressions

The third paragraph introduces a 'quick quiz' for the audience, focusing on how to correctly write expressions based on the discussed concepts. The speaker gives examples of algebraic expressions like quadratic equations and walks through how to code them in Java, emphasizing the importance of precedence and associativity in getting the correct result. They also explain why using parentheses is recommended for complex expressions to avoid unintended evaluation orders, providing a detailed breakdown of how expressions like 'b² - 4ac / 2a' are evaluated in Java.

15:01

📊 Highest Precedence: The Role of Parentheses in Complex Expressions

In this paragraph, the speaker explains that parentheses have the highest precedence, meaning that any expression inside parentheses is evaluated first. They use this concept to further clarify how complex expressions, like those involving quadratic equations, should be handled in Java. The speaker also provides a mathematical rule that division by zero leads to undefined expressions, which can cause errors in programming. They conclude by encouraging viewers to understand these concepts early to avoid struggles during exams or interviews.

👍 Wrapping Up and Final Thoughts

The final paragraph provides a conclusion, summarizing the key points discussed in the video—operator precedence, associativity, and how to correctly evaluate expressions in Java. The speaker reflects on their personal experience of learning these concepts later in their career and emphasizes the importance of mastering them early. They also invite viewers to like the video, share it on social media, and stay tuned for future content. The speaker signs off by thanking the audience for watching.

Keywords

💡Operator Precedence

Operator precedence refers to the rules that determine the order in which different operations are evaluated in an expression. In the video, the speaker explains how operators like multiplication and division have higher precedence than addition and subtraction, meaning they are evaluated first. For example, in the expression `6 * 5 - 34 / 2`, multiplication and division are evaluated before subtraction.

💡Associativity

Associativity defines the direction in which operations of the same precedence level are evaluated. In Java, some operators are left-associative (evaluated from left to right), while others are right-associative. For example, multiplication and division share the same precedence, but are evaluated left to right when they appear together, such as in `60 / 5 * 2`, where division happens first.

💡BODMAS

BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) is a mathematical rule for the order of operations. However, the video emphasizes that Java does not strictly follow BODMAS but rather relies on operator precedence and associativity. This distinction is crucial for understanding how Java evaluates expressions differently than pure mathematical notation.

💡Expression

An expression in Java consists of operators and operands that are evaluated to produce a value. The speaker uses various examples like `int a = 6 * 5 - 34 / 2` to explain how expressions are evaluated based on precedence and associativity, showing how to correctly interpret the result using Java’s rules rather than mathematical intuition.

💡Multiplication and Division

Multiplication and division are two arithmetic operators that have higher precedence over addition and subtraction. In the video, the speaker uses the example `6 * 5 - 34 / 2` to show that these operations are performed first. Both operators share the same precedence but are left-associative, meaning they are evaluated from left to right when together in an expression.

💡Addition and Subtraction

Addition and subtraction are arithmetic operators that have lower precedence than multiplication and division. In the expression `6 * 5 - 34 / 2`, subtraction occurs after both multiplication and division are completed. The video highlights that the lower precedence of these operators impacts the final result of an expression.

💡Quadratic Formula

The quadratic formula `b^2 - 4ac / 2a` is used to solve quadratic equations. The speaker uses this as an example to demonstrate the importance of using parentheses to ensure the correct order of operations when writing expressions in Java. Without proper parentheses, the formula could yield incorrect results due to operator precedence and associativity.

💡Parentheses

Parentheses are used to override the default precedence and associativity rules in expressions. The speaker emphasizes their importance when dealing with complex expressions like the quadratic formula, ensuring that operations happen in the desired order. For example, placing parentheses around `b^2 - 4ac` ensures that this part of the expression is evaluated before dividing by `2a`.

💡Arithmetic Exception

An arithmetic exception occurs when an illegal arithmetic operation, such as division by zero, takes place. The speaker warns about the risk of encountering such an exception when the denominator in a division operation becomes zero, such as in the expression `b^2 - 4ac / 2a` when `a` is zero, leading to undefined behavior in programming.

💡Interview and Exam Preparation

The video repeatedly mentions that understanding operator precedence and associativity is crucial for success in academic exams and technical interviews. The speaker reflects on how mastering these concepts late in his career made him realize their importance, and now he wants to make them accessible early on for viewers preparing for Java-related assessments.

Highlights

Introduction to Java operator precedence and associativity, essential for both academic exams and job interviews.

Explanation of operator precedence: multiplication and division have higher precedence than addition and subtraction.

Example using the expression 'int a = 6 * 5 - 8 / 2', explaining how precedence leads to evaluating multiplication and division before addition and subtraction.

Clarification that Java does not follow the BODMAS rule but instead uses operator precedence and associativity.

Definition of associativity: when two operators have the same precedence, associativity (either left-to-right or right-to-left) determines the evaluation order.

Demonstration of left-to-right associativity using division and multiplication in an expression like '60 / 5 - 34 * 2'.

Difference between associativity of star (multiplication) and slash (division): both have equal precedence but are evaluated left-to-right.

Practical example: how left-to-right associativity in Java affects the result of a complex expression like '60 / 5 - 34 * 2'.

Use of comments in code to clarify which operations will be evaluated first based on precedence and associativity.

Explaining how parentheses can override default precedence and associativity in Java expressions.

Quadratic equation example: 'b^2 - 4ac / 2a', showcasing how operator precedence and parentheses affect expression evaluation.

Recommendation to use parentheses in complex expressions to ensure correct evaluation order and avoid programming errors.

Mention of potential programming errors, like arithmetic exceptions when the denominator becomes zero in division.

Personal note: the speaker reflects on their own late understanding of these concepts during their career, emphasizing the importance of learning early.

Encouragement to share and like the video, inviting viewers to tag the speaker on Instagram when sharing screenshots.

Transcripts

Guys, today's video will cover some important topics

like which thing is done first

Java compiler multiply will do first

divide will do first or then

subtract will do first or addition will do first

what is the precedence of our operator

what is the associativity of our operator

many questions are asked on these topics

whether you are from academics or

you are giving an interview for a corporate

this video is going to be very important for you

so in today's video we are going to discuss this thing

guys in this course of java we have talked a lot

in today's video we will talk about how precedence works of operator

because we have seen operators, types of operators

how expressions are there, we can write in java we have seen the types of operators what are the expressions we can write in java

we have seen all these things in detail

and you must have understood it well, we have done a lot of work on this

but I will do one thing here that I will make a file

and I am going to keep its name

I will keep its name according to the video number

so that whenever you are watching the video number, you will know which file it is

I have to give you a code, so I write here its name

09 underscore

and here I write cwh underscore

and chapter 2

operator precedence dot java

ok

and what is this problem, I think I have done something wrong, I can't write 09 in this

this is the problem, my class name can't start with 09

no problem, I will write cwh underscore 09

and see here, this is my class

I will minimize it, zoom in a little

let's put the main function here and we are good to go now

we can do our coding here

so I have told you about precedence in notes

precedence of operators

the operators are applied and evaluated based on precedence

so here according to precedence

your operators are applied like

less precedence of plus and minus than star divide

let's say i write an expression here

int a is equal to 6 multiplied by 5 minus a divided by 4

or 2 let us say

I do it like this and I shout it

I say print this

if you apply the rule of baud mass

apply the rule of baud mass, if the rule of mathematics is

6 multiplied by 5 will be 30

and 34 divided by 2 will be 17

so here 30-17 is 13

so this 13 will be the answer

you can see here I have run the wrong file

I have to right click and see here 13 is here

but what happens is that in java, baud mass is not used

in java, precedence and associativity is used

so what are these two things

today I will explain you well precedence and associativity so what are these two things today I will explain you

precedence and associativity

what is precedence?

precedence means

that I am bigger than you

so star means minus

that I am bigger than you

and minus means

that I am bigger than you

and the bigger one

is evaluated first the other will be evaluated first

the one who is bigger will be evaluated first

the one who is the most respected person will be evaluated first

and then the slash will be evaluated

now see why is this happening here

what is the precedence of associativity

the precedence is that star is bigger than minus

so it will be evaluated first

but what is associativity

and to explain associativity i will write an expression b

in which i will do a simple thing, i will put a slash and put a star

ok

ok i will tell you one thing

now tell me in which order it will be evaluated

earlier it was 6x5

then 34x2

and then this result and this result

but now we have to see its evaluation order

this is associativity

if your star is big

then it will be evaluated like this

let me put a comment here, multiline, and look at this carefully

you will not know this thing by chance

6 multiplied by 5 will be 30

minus then it will be 34 divided by 2

and after that it will be evaluated as 30 minus 17

and it will be equal to 13 this was our precedence but if I do the same thing for you

I do the same thing for B then you will see that what you think will not happen

there is a high chance that it will not happen

now there is a difference between star and slash

which one will be evaluated first

some people will say put a bodmask and do star

divide first and then multiply

no it doesn't work like that

here bodmask doesn't work

here we see associativity

so precedence is equal to slash and star

now when precedence is equal

star and slash are equal in precedence

so to break this tie we see associativity

associativity is like this, left to right, right to left

associativity of star and slash is left to right

so it will start to get evaluated like this

so 6 divided by 5 will be first

and I will make it 60

so that the expression will be correct

60 divided by 5 will be 12

and I will remove the rest of the expression

then you can see here

34 multiplied by 2 will be here

which is 68

so 12 minus 68 will be

and 12 minus 68 is

12 minus 68

is minus 56 so is equal to minus 56

so it will be minus 56

so let's print B

and let's print B here

I will run it here and see minus 56 is here

so 13 was here and minus 56 is here

so this is how our associativity works

so minus 56 minus 56 and 13

now many of you will think that how will we get associativity and how will we know

that what is the thing that we multiply first and divide

so to make this thing easy I have prepared an image for you

see here all the precedence, associativity

of all operators are written here

now many of you may not know about these operators

and you don't need to know about it, you just need to keep this list

you don't need to keep it, you just need to refer this table

whenever you will evaluate operators

then first of all you will see

who has the highest precedence here

this number is given to the precedence, highest precedence

so here if I want to see

which one will be evaluated first, let me zoom in

so in plus and star, you see here

the precedence of plus is less, the precedence of star is more

star has 12 precedence, plus minus has 11

so I will evaluate star first

but if star and slash come together

if I face both of them together

then I will use associativity

I will evaluate left to right

if there is slash in left then it will be evaluated first

if there is star then it will be evaluated first

like if I show you this expression

here 60 by 5 minus 34 into 2

so here slash is not being divided because the bodmass rule is running

that's why it is being evaluated first because it is in the left

associativity goes from left to right

this way your order of evaluation works

if you have a tie in the operators, if there is a tie in the precedence

so first of all associativity to break the precedence and tie, associativity is fine

so precedence and associativity work like this

so here I write, I make the comment very clear

that here, see, this star and slash, star was evaluated first

because its highest precedence of star and slash

and after that associativity was left to right

highest precedence goes to star and slash

they are then evaluated on the basis of left to right associativity

left to right associativity

after that they are getting evaluated

so they will get evaluated on the basis of left to right associativity

so here A's value is this B's value is this

and they are getting evaluated very easily

so I have written the same thing in notes for you

precedence of operators, operators are applied and evaluated based on precedence

ok, they are evaluated based on precedence

I have taken an example, there is less precedence of plus and minus

star and slash, so star and slash are evaluated first

and many students don't know that

that evaluation is done according to precedence and associativity

some people start applying baud mass here and say it is evaluated according to the precedence and associativity

some people start using the word board mask

and say that it is based on the board mask

some people say that it is a dangerous thing and we don't want to learn it

it is not dangerous, it is just an image

you have to look at the image carefully

and understand it

and this image will tell you

that what is the precedence of what and what is associativity

so here you have seen what is precedence and what is associativity

after that you can evaluate your expression

so here it is written about associativity that tells the direction of execution of operators

it can either be left to right or right to left ok

star slash is left to right

plus minus is left to right

plus plus right to left

plus plus or equal to right to left

like if you write something like this

a is equal to b is equal to c

equal to 45

so first b value will be 45

then a value will be equal to it

means it runs like this right to left

so it is not necessary that you have left to right

or associatively right to left

now here is a quick quiz for you

that how will you write these expressions

the expressions which I have written

on the basis of these concepts how will you write

so here x-y divided by 2

b square minus 4ac by 2

b square minus u square, a star b minus t

so if I want to write these expressions, I will write it here

quick quiz

so

here what I will do is

I will write this first

a x minus y by 2

so if I write x star Y by 2 here

suppose I wrote int k is equal to

and I will comment out all these above

because I don't want to disturb us

when we are coding below

so I will do this whole precedence associativity

this is a topic

I am commenting this topic completely

and you guys focus down, so I have put it here like this

no problem, no problem, here this comment is actually getting closed

so there is a problem, no problem, I will do it like this

I will comment it like this, you guys have understood

I have just explained it to you, so I have done k is it to you so k is equal to x

x into y is equal to 2

so if i do int x is equal to 5

int y is equal to 1

so what will be the value of this

5 multiplied by 1 is 5

and 5 divided by 2

let's make it 6

6 multiplied by 1 is 6

and divided by 2 is 3

so if i write it like this and 6 multiply by 1 will be 6 and divided by 2 will be 3

so if i write it like this

and system.out.printlnk

so what will be evaluated first

so it will be evaluated first and then divided by 2

so i don't have any risk of getting evaluated before y by 2

so i will write it like this

if i run it then I should get 3

and I am getting 3

so why should I put extra parenthesis

when my work is done without parenthesis

so this thing you should know

now along with that

if I talk to you

about another expression

b square minus 4ac upon 2a

which is your quadratic

quadratic equation the discriminant of quadratic equation

b square minus 4ac

and minus b plus minus under root b square minus 4ac upon 2a

which is the root of it

but b square minus 4ac upon 2a is our question

so if I comment this out and write

k is equal to

see square is nothing

you have to do b into b

and let me

comment out what is going on

so b square

minus 4

a c

and here I will write upon 2 a

and I have not given

value of b, a or c

so I will give that also so I will give here and I have not given value of b, a, c

so I will give that also here

so I will give value of expression here

int b is equal to 1

int c is equal to 4

and int a is equal to 5

like this

so I think I have already defined b and a

so I will comment out these

and this code that I am giving you I am giving you just to refer you it is not like I have defined it, so I will comment it out and this code that I am giving you

I am giving you to refer, it is not like I have distributed any software to you

so don't say that it is defined twice

so I am telling you, so according to that I have given

b is equal to 1 and c is equal to 4

we did, now what will happen first

what will be evaluated first, first these star will be evaluated, star and slash will be evaluated first first of all, these star and slash will be evaluated

in which order they will be evaluated, in this direction

so b square will be evaluated first

then 4, a, c will be evaluated

then it will be divided by 2

and whatever result will be there, it will be multiplied by a

here this is a mess, see the result will be multiplied by a

so a means it will come up

so no, I don't want a so what i will do

to correct this i will put parenthesis

here i will put parenthesis

and here i will put parenthesis

so now see what is the value

now value is coming

minus 7

and if i remove parenthesis then what will it come? then it will come separately

see what is coming here

then here minus 199 is coming

that means something else is happening

something else is happening now

so I want this value

ok

like this

so I put parenthesis

like this

so whenever you have a complicated expression

then parenthesis is recommended

because if you put parenthesis because you will not get any loss by putting parenthesis

but you should know about precedence and associativity

it is a very important concept

so you can write b2-4ac like this

what will it do first

the most precedence is of parenthesis

so parenthesis overwrites this thing

I will show you

highest 14 precedence

see this is of parenthesis

here parenthesis

here parenthesis will take maximum percentage

and after taking

here this value will be first

then this value will be first

then this b square will be first

then this divided by this and this will be minus

and your result will be here

so if i take b and a both as 0

here then my result

should be 0

and it will be 0, see

it will have to be 0

and if I take a as 0

then actually denominator is becoming 0

so I do one thing, I make it 10 and make c as 0

if denominator is 0 then you will get arithmetic exception

exception means that you will have some problem while evaluating your expression

now here it will be 0, see now it is zero

okay

so denominator should not be zero

there is a rule of mathematics that if your denominator is zero

then expression is undefined and undefined will give you trouble in programming languages

sometimes in the form of error

sometimes your program will misbehave

so you definitely don't want this

okay so this was about our operator of precedence, I hope I could explain you associativity,

I could explain you precedence, these two concepts are such that to be very honest

I will be very transparent with you, I also understood this concept very late in my career,

when I used to give exams, I did not understand this,

I want to be very transparent with you you but I understood when I came to know how expressions are evaluated

and that's why I have given priority to this topic and explained it to you

so earlier I used to put a board mask and all at one time

star slash and I used to get very worried about these topics

but time has gone and I understood these things

and today I am explaining to you too, so I want you to understand all these things in a very early stage

and these things become important from the point of view of interview, from the point of view of exam

from the point of view of exam, all these things become very important

so I will explain to you in this way that you should not face any problem

at least you should not face the problem that I have faced

so if you like the video then like it

and if you are taking screenshot of this video

and sharing it on instagram

then tag me so that I can put your story again

and if you like the video then like it

I am not just saying it

many of you like the video from the heart

so if you like the video from the heart then like it

I don't want to irritate you by saying

like it, like it,ate you if you like this video

then like the upcoming videos

thats it for now

thank you so much for watching this video

and i will see you next time Thank you for watching.