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Hi, everyone.

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So in this lesson, we are going to solve this question, find the smallest elements.

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So the input is basically in an area and I integer key, so we have to find the key smallest elements.

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So, for example, what are the key smallest elements here?

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So this is zero one five and six.

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So these are the four smallest elements.

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President in this area.

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So since the value of Gaisford, so say I will take four, so I have to find the smallest element.

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Now the first and the basic approach is basically what you will lose or you will apply the sorting algorithm.

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So if you are deciding now, what do I look like?

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So this is zero, then one, then five, six.

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So it will become eight.

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Then nine, then 10.

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And then 12.

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And then they have to do so, you have to find fast food, so take the first four elements and this

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is your answer.

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So this is your smallest elements now with the complexity of the solution.

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So that time complexities and low end because you have to sort the area and then after sorting the area,

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you can take the first four elements and basically the first key elements.

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You will take the first key elements, and that will be your answer.

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Now, this was the first way using Starting Now the time complexity for using Sardinians and Logan.

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But I want to solve this question in a longer time complexity.

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Now, this is long and this is logoff.

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So Loki's much, much less than Laugavegur because and it's basically the number of elements present

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in the area and will be very small.

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So basically, it is much, much less than in.

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So that's why lockyear will be much, much smaller than log often.

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So I want to solve this question in this much time complexity.

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Now let's discuss how we can solve this question.

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So basically, what I will do, I will create a maximum priority queue.

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So what I'm going to do, I will create a maximum priority queue and I will push for key elements so

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the value of Gaisford, so I will first push.

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So this is my original idea before sorting the inventory.

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So I will first push the key elements to the value of Gaisford.

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So push the first four elements into your maximum priority.

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So this is eight, then five, then 12 and then 10.

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Simple now consider elements one by one, so zero now.

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So basically the zero element is less than the largest element.

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So the maximum pressure to give you can only access the largest element.

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So zero is less than 10.

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So what I will do, I will slap 10 with zero.

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Now, this is my priority.

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Give it five.

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OK, so the maximum limit rostral, the maximum limit was 12.

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So zero will get slapped with 12.

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So 12 will come hit.

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So zero will come around the system.

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Now, the next element is one.

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So when you compare one with the largest element to the largest element is 10, because in the mix protect

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you, you only have access to the largest element using the top function to compare one with Pennsylvania's

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less than 10.

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So what I will do, I will strap.

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So this is eight five zero and then we will pop out done.

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And we will push one bob then and push one.

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So when now the next element is six.

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So six and what is the largest element, the largest element is currently eight now six is less than

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eight.

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So we will pop it and we will push six six five zero and one.

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The next element is nine.

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So campaign nine with the largest element to the largest element is six.

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So nine is bigger than six to do nothing.

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So do nothing.

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And the still remains him six, five, zero and one.

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And now basically we will reach the end of the year.

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So what is my answer?

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So this is my answer.

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The elements present in the mix and produce my answer.

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You can compare.

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See, the elements are correct.

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Six five 091 Now, since this is a dequeue so it will pop out elements, then the elements will come

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in the order.

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So first six will come, then five will come, then one will come and then zero will come.

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This is the Maksym element, so that's where it will come out first, so this will be an order, it

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will pop out the element from the MAKSYM priority you.

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If you want to retain the Olympics in started with what you will do, you will just reverse the elements.

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So after reversing, this will become zero one five and six and then you can print or you can do anything

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you want.

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So with the help of Maksym, where we can reconcile this question and local time and local time, because

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you can see what is the size of the mix compared to you.

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So it is containing key elements.

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So that's why the insert function and the function they will take.

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So basically they push and delete is actually pop.

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So push and pop, they will take log of their time.

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Simple, so let's take one more example to.

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I understand this question better.

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So let's say my area is said this is my area.

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Five, then six, then nine, then later.

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Well, then let's say three, then let's say 13 and then let's say two.

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And let's say the valley of KS three.

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I want to find out three smallest, smallest element.

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So again, I will create a maximum priority queue and I will push the first key elements.

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So push the first key elements.

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That is first three elements into to make priority.

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So this is five, then I have six and then I have nine now elementally so compared well with the largest

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elements that I just listen to a little girl then I do nothing.

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Now the next element is three now compared three with the largest element.

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So three is actually less than nine.

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So it will do pop nine and push three.

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So five, six, three.

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Now the next element is 13.

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So 13 the largest element in the mix and produce six.

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I don't lundie mix impractical.

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We only have access to the topmost element that is the largest element.

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So 13 will be 13 is good and six do nothing.

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Now, the next element is to show two, and the largest element is six, total is less than six, but

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will push through.

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We will pop six and we will push two.

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So this is we are five, then two and three.

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So this is the content of the priority.

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You and then I will reach the end of the area.

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So what is my answer?

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This is my answer.

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So the three smallest elements are five, two and three.

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And if you will pop out the elements, first of all, five will come, then three will come and then

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two will come.

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So these are the three smallest element present in this area.

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So with the help of maximum priority queue, you can easily solve this question.

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So if you are ready now, let us right the called.

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So let's say I want to return a vector of integers.

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And let's say the name of the function is Geissman list or before, let's say let's printhead only,

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we will not return, we will just print and we have to print Casemore list elements.

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So Casemore list, it will take areas and put.

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So it will take the size and it will also take the value of.

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So what we have to do is, first of all, I have to create a maximum priority to.

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So this is the syntax for creating a mix, in particular vintages, then I have to pop, I have to push

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first gay elements.

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So I am pushing.

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The first key elements into my priority given to my Maksym verdict also be Cadart Bush.

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Now, after pushing what we have to do.

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So they decided over.

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So this time I would start trading from next.

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I placeless, sorry, Ellerston and I placeless.

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Now, what we have to do, so we have to combat the element to the current element, so if Elfy is basically

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less than the topmost element of the priority, you sort of must element is actually.

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Your daughter up, so if my current element is less than the maximum present in the mix in particular,

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then what you can do to pop out the maximum elements would be good pop.

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You'll call the function pop.

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And they will push the current elements will be Art Bush.

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Elfy.

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And that's.

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And that's all that we have to do, so for printing the answer no.

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So it's time to bring it down, so I have my answer stored in the priority queue, so let us bring those

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elements.

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So while priority queue is not empty.

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What they have to do.

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You will take one by one and you will bring that element.

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So I only have access to the topmost element.

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So bigger and bigger, not Bob.

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And now let us pass let us create an integrated.

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Let's say the elements are.

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Five, six, nine.

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Well, let's say three.

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Let's say 13 and let's go to.

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So I have to call this function is my list.

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So I have to pass.

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What is the number of elements or one, two, three, four, five, six and seven?

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So seven elements are there.

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And lastly, I want to find out the smallest elements of the value of Kastari.

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The use prior to whatever have to you have to include prior to you or you can simply write.

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So if you do not want to write this, what you have to do this, it is actually implemented in July,

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so you have to include hash included QUE.

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So I think this much more will work.

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So let us test our program.

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So my answer is five, three and two.

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And I wouldn't say it's 100 percent correct because they had the same input that we give.

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We discussed here, so five to two was our answer, and they are also coming out to be five, three

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and two.

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So basically our goal is working fine.

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Now, let us discuss the time, complexity.

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So the size of my priority is actually key.

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And I am pushing key elements of their time, complexity for this party scale, Skalak.

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Again, this will run and minus good times and I am popping the element and pushing the elements, so

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again, lockyear times when and minus Killock and the size of the Prada Gucci.

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So I am popping out elements of Killock again, if you will, at this time complexity.

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So your time will come out to be alloca.

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Which is the desired time complexity.

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OK, so this way you will be able to find out the smallest elements so you can write the code in Davíð

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also, for example, what I'm doing here.

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So I'm comparing and then I'm pushing or popping the elements.

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But instead of this campaign, I pushed the elements and popped the element.

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So let me take an example.

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So let us take this example.

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Only five, six, nine.

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So what I want to show you.

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So finally, what do we want?

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So let's take an example first of the five, six, then let's say nine, then to 12, three, 13 and

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two and the value of case three.

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So finally, what will happen?

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Our maximum priority queue.

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So the size of the maximum vertical will be key because it will contain key elements.

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Correct.

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So finally, the size of a maximum priority is going to be key.

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So what we will do, we will maintain the size.

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So I maintain the size what I want to say.

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So you push the first element size is less then, correct?

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Less than I requested.

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Now push the next element.

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The size is two and the maximum size allowed is three, correct, because the next element nine.

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So the size is three and the maximum size allowed is three.

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Correct push the fourth element.

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Now the size is equal.

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Sorry, now the size is for the sizes four and the maximum size allowed is three.

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So what you will do, you will pop one element and which element we can bob.

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Obviously the maximum vertical so we can only possibly largest element.

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So I will.

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Popplewell Correct.

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Now push three.

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So Bush three.

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So, again, this is greater than the maximum size allowed, so you will pop the maximum element, what

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is the maximum element?

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Nine, so nine will get popped.

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So currently this is going to make symbiotically five six entry.

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So the next element is tradin so Bush starting now again, the has become forth, but this is not allowed.

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So make some element.

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So today we'll get Bob.

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Now, to add insult to again, the size becomes four to.

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So, Bob, did I just say, well, Bob, the largest element and this is the content of the mix in particular

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to five and three, and if you will eliminate one by one, so five will come first, then three will

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come first and then two will come first.

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So five, three, two.

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So in this way, you can also write the code.

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So we just have to maintain the size of the prior.

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So if you want, I can write this code for you.

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So, OK, so let me write this code for you so that you can understand it.

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But the logic is same, just the way of writing will be different.

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So what we have to do, let's comment about this called.

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So what I am saying, you have to create a protocol that is correct, so after creating the protocol,

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let's start inserting elements one by one.

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So I equals zero.

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I listen in, I placeless.

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I will just maintain the size of my mixing protocol.

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Symbol.

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So let's push the element, so let's push elements or picador push.

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If I am pushing the element and after pushing the limit, let's check the size so I have function to

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be good size, so the maximum size allowed is gey.

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So if the size becomes a gudinski.

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That makes them say the loudest, if the sides become bigger, then you will just pop.

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So Picador Pop.

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And that's all so what I'm doing.

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If the size becomes bigger than the size of the priority has to be key because our priority will contain

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key elements finally, so the size becomes bigger than you can basically pop and then you can just print

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the content of your priority queue.

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So while.

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The product is not empty.

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So I'm just writing the same code, you can copy paste this line.

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So bigger and bigger.

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ARTPOP.

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OK, so we are just getting over the.

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I am pushing every element and if the size becomes bigger, then you will pop the element which element

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will be popped.

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So the largest element will be popped out first.

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So largest element.

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Will be deleted.

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Correct, and then finally, the size of your priority queue, it is containing key elements and now

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let us push, not a sprint.

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Those key elements seem so here.

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Also, your answer was containing key elements.

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Inside your priority, you insider makes Embraer dequeue.

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So this court will also work fine, just like the Boven, if you want, I can run this court for you.

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So the output is going out to resolve this one, five, three and do so same.

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The output is coming out three, five, three and two.

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So let's run our program.

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So you can see the output is coming out to be five, three and two, and what is the time, complexity

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of the solution?

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So this solution is exactly the same as the previous one, but just the way of writing is different.

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So, again, this loop is running and times and I am doing logi work, so this will take a long time.

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So the time, complexities and Locky.

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And for this, the time, complexity, scale.

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OK, so again, if you will add these to the time complexity is going to be and logi so everything the

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same time, complexity, space, complexity.

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OK, so the space complexity is big off key because.

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My hope will contain key elements at any point of time, so this is the time and the space complexity,

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I'm repeating myself.

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The above me of writing the code and the below of writing the code.

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The logic is seem exactly the same logic, but the way of writing is different.

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And again, the time and the space complexity, the same for both the solutions.

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So in the next video, what will do so in the next video, we will discuss how we can use our inbuilt

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medium priority.

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So this is actually an example I would take you in the next video.

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We will discuss how to create how to use the inbuilt minimum priority protocol.

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I will see you there.

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Bye bye.