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Hi, everyone.

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So in this video, we are going to discuss this question, finally, do some of the area using recursion

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so we can easily solve this problem with the help of for loop and why loop.

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But since we are learning recursion, so we will solve this problem with the help of recursion so that

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the functional brainteaser, we will return to some of the.

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And we will return at it.

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We will get that as input and we'll get how many elements are there as input.

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So we need to write the code for this function.

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So I told you how we will use it.

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So basically, we need to break our problem into smaller problem.

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And there are two ways to break the area.

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So the first rule of making this is what we will do.

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So I will make the idea like this the second way of breaking the arrays.

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I will break the array like this.

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So what I will do, I will call Dacogen.

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I have a qualification on this area.

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So this they will return the records and will return me the sum of this 80.

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So the question will be the some of the city of this military and what I will do, I will add this value,

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so I will add this value of zero.

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Simple now, a better way of solving this problem is basically I will call recursion on this very.

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So the question will give me the answer, it will give me some of this small area and I will add this

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value.

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So this is and minus one, so I will add and minus one.

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And that will be my final answer.

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So very simple, right.

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So first, let us write the code for this approach.

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So the name of the function is the name of the function is some of Eddie.

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So it will take ideas and put.

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And it will take how many elements are there?

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So basically this very simple.

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If.

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My area is empty, so if the size is zero, what will be the sum will be zero.

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So the base case is very simple.

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Now what we need to do.

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So I told you.

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Multivolume, I will call that equation.

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So I will call dedication on this.

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So this is a and this is a plus one and the number of elements and minus one, so the equation will

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give me the answer to your question, will give me some of this small area and I will add this value.

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So this value is Alpha zero, and that will be my final answer.

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So what is my final answer?

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They've done a zero.

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Plus, all this dysfunction, some of Harry.

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So the area which we want to give is this small area, so E-Plus one.

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And the number of elements and minus one.

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And that's all that we need to do.

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So let's call this function out some of very.

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We need to give Eddie.

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And a number of elements, five.

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So let's see.

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So the output is coming out to 15.

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So let's see whether 15 is right or wrong.

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So if you will add one plus two plus three plus four plus five.

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So this is the same as and when plus one by two, the value of it is five.

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So five to six Vido, so Tatebayashi two is 15, or you can write like this.

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So the output is 15 and 15 is the right output.

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So our approach is correct, and now let's see how it is working, let's write a novel called.

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So let's write a novel called So Let's take this example only.

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So I have one, two, three, four and five.

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The number of elements is five.

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So the number of elements, the site is not zero.

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So what I will do, I will collocation on this Mollari.

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So I will call the on the smaller two, three, four and five.

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The number of elements for so size is not zero, so call that equation the smaller I am calling the

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equation.

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I think this smaller and the number of elements, a number of elements, history and the elements are

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three, four and five.

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So, again, the size is not zero, so called the equation on smaller sizes, too.

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So again, the size is not zero.

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So call the equation smaller.

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The size is one.

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So again, the size is not zero.

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So collocation on smaller.

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So we'll call the ampitheater and size is zero.

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So it is empty and size zero.

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So if the sizes you know, I am returning zero, so this will return zero.

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So now this is getting zero.

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And what we are turning we are turning to some of the adding and plus 040.

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So this is the only element of this is we will return zero plus five.

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So I am returning five.

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So now.

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This area is returning fire, so this area is returning fire and I am getting zero, so I will wait

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for and are done, so I will return four plus five.

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So now this area is returning four plus five, which is nine.

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So I will add eight four zero.

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I will let you off zero and done so I will 80 and I will return to nine.

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Plus three is 12.

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So this area is returning to.

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I will add 84 zero and I will return Sawtell plus two is 14.

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So this area is returning 14 and I will add eight four zero.

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I will add zero and return to 14 plus minus 15.

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So I will return 15.

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And 15 is the right answer for this problem.

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Simple so that a way of solving this problem is basically what we will do.

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I will call that equation on this area.

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So starting this Arazi and a number of elements and minus one, so the question will give me the output

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for this Osmolarity equation, will give me the sum and I will add the last element.

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So aof and minus one.

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And that will be my answer.

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So let's write the code.

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So, teacher, let's copy the name of the function, some of very.

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To some of it, I will get it as input.

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And I will get how many elements are there.

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So this case will remain same.

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If it is empty in the cities, you know, the sun will be zero, so I will return zero.

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There is what we need to do, what will be our answer?

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So our answer will be the last next the last two half and minus one, and we will call this function

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some of the.

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Some of little I will give the area and I will give the number of elements.

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So now let's test dysfunctioning some of it to.

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Output should be 15.

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So the output is coming out to 15.

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So this is also working.

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And now let's see how it is working.

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So what I'm doing is.

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I am making my day like this.

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I am calling the occasion for this.

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So this is crazy and in number of elements isn't minus one.

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So the question, will you give me the output for this area?

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Because it will give me some indication, will give me some for this area.

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And I am adding the last element.

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So I am adding the value, I am adding this last element, and then I am returning the overall sum and

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then I am returning the.

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Let's take this example and let's see how it will work.

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One, two, three, four and five.

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So I have this.

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One, two, three, four, five.

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The number of elements is five.

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So size is not zero, so I will call on the smaller.

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I will call on one, two, three and four, the monofilament is four sizes, not zero.

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I will call on the smaller one, two, three sizes, three sizes in order to also call on the smaller

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one and to.

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Number of elements is still so still the size is not zero, so I will call on the smaller.

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So since the number of elements is one, it is not zero, so I will call on the empty address that is

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empty and the site is zero, so the size of zero zero seven zero.

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So basically this idea, what it will return the value which it is getting, plus the last value since

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there is only one element.

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So this is only the last value.

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So zero plus one, I will return.

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So basically this area is returning when the site is returning one.

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And I will add the last value which is to so zero plus one three one plus two is three.

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So I will return three.

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So basically, this area is redundantly, this area is turning, I will the last value, so last year

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values three, so three plus three is six.

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So this area is returning six over the last 12 months where the lost value and return.

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So last one is four six plus Foreston.

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So this area is returning.

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Then I will add the last value and return to last values 15 sodi the last values five five plus 10 15.

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So I will return 15 and 15 is the right answer.

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So that's how it is working.

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So there is one more way we can write the code.

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So currently what we are doing for example.

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So if I want to pass this area, I am passing a plus one and I am giving N minus one, I am passing

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eteplirsen and I am giving and minus one.

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So instead of changing the area, what we will do so instead of passing only this area.

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So one way of passing only this ad is basically changing writing like this, E-Plus one, the other

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way is basically what we will take.

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We will take our index.

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So it will take the next.

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The way he treated ordinary.

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So if the value of Isarel so that means this starting next year, the value of zero, that means I am

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passing the completely if the value of is one, that means I am passing.

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I'm not passing this Rohter element.

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I am passing the area starting from the first index.

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If the value of I used to, I will pass the starting from index to.

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If the value of iced tea, I will pass the idea starting from industry and so on, so basically if the

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value of AI is ND, then I am passing the idea starting from index and starting from index and Nixon

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does not exist.

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That means this is the condition venue that is empty.

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This is a condition for empathy, very simple.

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I'm repeating myself, if the value of I zero, I will pass the starting from zero.

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That means I am passing the completely.

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So that is the meaning of equal zero means.

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Pass the completed holiday.

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Pass the holiday.

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If the value of AI is one positive, starting from next one, if the value of I used to, I am passing

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the idea starting from next to the value of history.

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I am passing the area starting from index three.

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So this is the condition for the whole area.

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If the value of zero.

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So this is the condition for the empty.

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Very simple.

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So let's write the code using this index.

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So what I want to do, let's modify this code.

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I want to modify this code.

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Some of eighty three I will carry I will take a number of elements and I am taking one more, I am taking

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I index I so what is the condition?

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So this is a condition for Empty-headed, not a condition for Prairie's.

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Eye becomes.

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And so let's change the best case.

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So, Batiatus, if I is, and that means my heart is empty, so I am returning zero otherwise, but

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I will return, so I will call this function some of the three.

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There's no need to change the.

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The Namaroff elements will not change because I'm basically completely only the next will change, so

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I plus one.

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And similarly, this will be a.

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And that's all that we need to do.

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So now let's call dysfunction some of 83.

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We need to pass the value of which is zero.

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So let's see how it is working.

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So first, let us run our file and let's see whether it will work or not.

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So the output is coming out to 15, that means it is working.

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OK, so.

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This thing is working, I am passing the index and it is working, so let's see how it is working.

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So the approach is very simple, see?

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This is already.

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The value of AI is zero, so this is a the value of a zero and the size of the arrays and so you are

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taking I question no, then what they are doing.

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You are retaining Elfy.

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So this is Eddie.

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So Afie is Disvalue.

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So you are returning.

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If I, if I use this value you are calling some of.

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So we are calling recursion.

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I am giving Eddie so I am giving the complete Eddie the number of elemental remains him because I am

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giving this completely.

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I am giving this complete attitude equation and not the similarity, so I am giving this complete addy

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and not only this Mollari and then I'm giving a plus one.

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So the value of 5.0 now it will become one.

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So the value of I will become one.

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So if so, for this area.

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I am passing the computer.

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I'm still passing the completely, but since the value of AI is here now.

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And and is still the same, so and remains same, and we are passing the complete array, but we are

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using a variable.

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I do, I read over the area.

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So next time what will happen?

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You will pass the completely, but the value of five will become to show the value of.

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I will become to.

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This is the community will remain same.

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Again, you will pass the completely and the value of I will become three, so the value of I, I am

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using index.

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So this is current index I am using next to irate over the area.

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So let's put that in the school so that you can understand it better.

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Let's write in for this example, one, two, three, four and five.

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So my error is one, two.

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Three, four and five.

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Now, in this regulation, we are not breaking the ATM, we are passing the computer, but we are using

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this variable and next you can see at any minute same number of human remains same.

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So only this value is changing.

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So let's see how we can use the value of a.

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So I is at this position, so what is happening here, the number of elements is five.

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So what we will do so I the value of let's illustrate the value of the value of zero zero zero is not

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equal to five.

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So you will call that equation.

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So let's call that equation.

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You will pass the completely.

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I am passing the completed number of human remains same and I am passing the completely.

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Only the value of I will change, so the value of I will become when we are passing plus one.

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So one is not close to five again.

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I will pass the complete editorialization number of elements to him, only the value of I will change.

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So again.

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The value of is not the cost.

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And so I will pass the completely the value of these five.

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The value of any number of him and I used three, so three is not close to five.

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So again, I will pass the completely.

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Remain the same.

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The value of A for you can see we are passing the completely we are not changing any element because

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since we are passing the total, the value of N will not change and we are just doing a plus one.

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So I is not close to five, so I will pass the computer again.

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One, two, three, four, five.

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The number of elements are five and now the value of these five.

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So now the value of is five, so I started from here, then I use here, then I is here, then I is

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here, then I is here and now I becomes now I reaches here.

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Simple.

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So.

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I used basically so this is zero one, two, three, four and five, so I reaches the next five.

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So now you can see I end and they are equal.

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So if I am, then they are equal.

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I will return zero.

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So this area will return to.

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So I am getting zero and I am adding the value of elfy.

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So what is I I is pointing I is standing here so I will add five in return.

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I will add five zero and done so I will return five.

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So I am getting five from this area.

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I am getting five and I will if a what is if I if I is four.

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So if I entertain, so I will return nine.

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So no, and if I ended on whatever value you are getting, whatever value you are getting, and if I

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ever done so and if I try and return so, I will return to.

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So whatever value you are getting from Dacogen Guardian to and done so, I will return 14.

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So whatever value you are getting from the Guardian ad elfy and if I understand if I is one so I will

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return 15 and that's how we are getting 15.

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So basically first we are getting first we are getting the sum for this area, then we are getting the

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sum for this decided.

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Then we are getting the sum for this area, then we are getting the sum for this area and finally we

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will get the sum for the whole area.

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We will return aof.

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I will fight to this sum and we will return.

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So that's how it is working.

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So this index I so this approach is very useful and it is used.

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This technique is very useful.

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It is used at multiple places.

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So what I want you guys to do is make banin paper and try to flatten this code, try to find out how

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it is working.

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So just give it a try and you will be able to understand it very easily.

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So this is it from this video.

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I will see you in the next one.