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Hello everyone.



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So in this video I will explain you a question that you guys need to implement.



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Basically I want you guys to implement a Polynomial class.



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OK so you have to implement the polynomial now.



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So what is a polynomial.



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So in maths the example of a pilot may lose for example three X squared plus four X cube for X to the



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power five minus let's say extra the power seven.



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So this is the example of a polynomial limit.



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So a polynomial has two values.



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So one is the coefficient so when is convenient and the second one is third degree.



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Okay.



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So in class in the upper limit class we will store two things degrees and the coefficient.



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So this is the coefficient and this is the degree.



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This is the coefficient and this is the degree.



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So what we will do in the polemic class we will take.



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We will maintain an 80.



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Let's say the name of that is the coefficient.



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So how we will store for example if we want to store this polynomial so how we will store.



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Okay.



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So the maximum degree is seven.



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So it will do let's say we have an array of say seven



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so let's do t for five six and seven.



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Okay.



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Just a random size you can take the size of the error to be five and or ten thousand.



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Okay.



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So the size of that is like you can take anything.



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So let's say the size there is seven.



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So how we will store this polynomial.



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So what we will do for storing so go to index to and store three.



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So will the index to install three go to index five.



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And store food.



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So index five will store food go to index 7 and store 1.



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Sorry minus one.



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So index 7 it will store minus 1.



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The rest of the values will be 0 0 0 0 0 0.



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OK.



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So this is how we will store a polynomial.



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Okay so what we'll use we will use indexes as our degrees and the values we will use them as our coefficient.



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Okay so this will be our area.



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So in this way we will store our polynomial.



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Okay.



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And we will take one more data member.



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So just like the dynamic at glass we will keep a capacity also.



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So in this case the capacity of our arrays it okay the size of that is it.



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So in this way we will restore a polynomial.



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Okay.



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So let's discuss the function that you guys need to implement.



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Okay so you guys need to implement some basic basic functions so functions that you guys need to implement



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so the first function is default custom built again so first I'm writing the name of all the functions



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that you guys need to implement.



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So default then copy constructor



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and copy assignment operator



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Okay so what are default constructively to so we have to do the members as I work private field.



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So it will initialize the degree coefficient dairy and it will initialize our capacity let's say if



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you want the size to be 10 so that capacity will become 10 and degree of change will be new and then.



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Okay so our work is not finished here we have to do one more thing here.



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What we have to do we have to put zeros everywhere in the area we have to initialize this degree coefficient



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array with all the zeros.



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Okay so we have to initialized this degree of shown that if it all the zeros you can see here above.



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So 0 0 0.



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So initially this array initially this area will contain zero only.



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Okay then what do we do.



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We will read the polynomial and then we will feel the values.



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Okay.



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So initially that it contained zeros only okay.



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So you have to do two things inside the default constructor first initialize the degree coefficient



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that in the capacity area and then put all the zeros put zeros and the degree coefficient Daddy.



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Okay so now let us talk about copy constructor.



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Let us take an example so suppose my polynomial even looks something like this



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let's head to one zero minus 2 0 so 0 1 2 3 4 OK.



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So what does this polynomial.



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How can we get this polynomial.



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So three plus X minus two.



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Excuse me.



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Okay.



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So this is our polynomial so if I write if I'm creating another polynomial polynomial b2 b1.



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So what will happen.



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Copy constructor will get called.



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So essentially no copy constructor creates shallow copy.



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So this bill 2.0 that will point towards this area only.



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Okay so this is wrong.



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So inside the copy constructor we will what we will do we will create deep copy.



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We will create deep copy okay.



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Now let us talk about copy assignment operator.



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So if you will write B2 equals P1 what will happen.



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This will do will point towards this area only so we know copy assignment operator also creates shallow



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copy.



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Okay.



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So inside the copy assignment operator we will all audio operator equal.



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Operator we will overlord and we will create deep copy exactly the same function as the copy constructor.



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Okay.



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So after creating these three function let us talk about some more function that you have to implement.



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So brain function.



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So how you will bring the polynomial that you can see in the equation.



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I will explain in the question that in which format you have to like you have to print the polynomial.



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Okay.



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So after the brain function we we have to overload some operators which operator we will all load plus



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operator minus operator and multiply operator.



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Okay.



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So four plus operator we will write something like this.



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Tres B1 plus B2 okay.



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So this will go in this it will going argument and the return type will be a polynomial.



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So how do I do.



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Well normally so let's say the problem will be when is just like we used to do in maths.



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So for X minus two weeks the para five and we have another polynomial to so minus X plus let's say x



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squared plus X cube plus extra the powerful.



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Okay so B when plus Bill 2 What will happen if the degrees are c you can add them so simply three then



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minus X then degrees the same.



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So you can add them you can add the coefficient.



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So 5 x squared plus X cube plus extra the powerful and minus two extra the power five.



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Okay.



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So this will be given plus B2 which is B3 man what do you have to do.



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You have to like update this in the degree coefficient area off you have to update the degree coefficient



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area of P3.



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Okay so update the beginning of that of B3 accordingly and the same is the case.



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The same is the case for negative subtract.



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So be 3s B when minus B two.



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I hope you know how to subtract two but let me leave their degrees I assume you can separate the confident



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and for multiplication we have to do similar kind of stuff we will write B threes Bill and multiply



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b do so the multiplication will be a little bit tough it will be like a little bit tricky.



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So first like you can do it on pen and paper you can analyse how the things are working and then I will



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suggest you to write the code.



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Okay so this will be like a little more complex and a little bit complex.



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And now let us talk about the last function that you have to create.



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So we have to create.



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We have to implement a set coefficient function.



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So what this set conversion function really do.



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So this set coefficient function.



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Okay.



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So how we will write this so even Dart said coefficient so this search coefficient function will take



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two things as input.



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First one is the degree and the second one is the coefficient.



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So let's say B one is let's say the capacity is 6 0 1 2 3 4 and 5 and let's see the values are 1 0 minus



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2 again 0 1 and 0.



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Okay so we will call the function b one dart said coefficient and we will give degree and coefficient



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as input Okay so let's say the degrees 3 and the coefficient is 5.



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So what do we do.



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Go to index tree and make the coefficient 5 and let's say the values are degrees 4 and the coefficients



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then so go to index for make the coefficient and override the coefficient.



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Okay we have to override the coefficient.



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Now the problem will come here is let's say this size the capacity is 6.



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So the valid degrees are 0 to 5.



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Only okay if the capacity receives the value degrees of zero to five.



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And now if I do degrees 7 and let's say the coefficient is 20 so degrees 7 is not a valid index.



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Okay so what.



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So what is happening here is degree is greater than the capacity okay.



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Degrees good in the capacity.



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So in this case what we will do we will double the size of the array we work double the size of the



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area and then we will again check.



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We will check if their degree is less than the capacity then it's okay.



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Otherwise in the edit part we will again double the size of the 80 we will again double the size and



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we will again check.



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Then again double again check this will continue.



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Okay daily until we reach this condition.



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So in these two cases the degree is less than the capacity.



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So this is fine but in this case the degrees are good at any capacity.



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So just like in the dynamic at a class we will double the size.



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But here after doubling the size you have to continuously check if a degree is less than the capacity.



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Okay.



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For example.



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So initially the size is six.



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So let's say my value is 14.



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Let's say the value of degrees is 14.



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So I will double the size the size will become cool then I will check to L is less than 14 so I will



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again double the size.



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So 24.



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Now 14 is less than 24.



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So now we can override the values.



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We can override the coefficient.



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Okay so.



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And so these are all functions that you have to implement.



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Okay so let's see where the less structure have a code.



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So we have a class polynomial so inside the class polynomial we discussed that there will be two private



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properties first the dynamic Gary.



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So let's say the name is beginning coefficient and the second is the capacity.



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Okay.



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So these are the two private properties.



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And now what we have to do we have to create some functions so the first function is default constructor



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inside default constructor.



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We have to do two things we have to initialize negative coefficient initialize capacity and put zeros



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in the beginning coefficient Eddie then we need copy constructor why we need a copy constructor because



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we want to create deep copy then we need to copy assignment operator we have to overload copy assignment



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operator just like we did in the rich class in the dynamic edit class.



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Okay so copy assignment operator you have to overload so after that you have to right print function



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which would be very easy see the question to see what is the brand format and then you have to set competent



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function that will take two arguments.



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Sorry.



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Yes it will take two arguments degree and coefficient then you have to overload some operator so plus



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operator you have to overload negative operator you have to overload and then multiply operator you



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have to overload.



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So this will be our structure okay.



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So these are all functions you have to implement.



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Okay so I hope you understood this question.



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Good luck.



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Thank you.