Stepping Through Iterative Fibonacci Function Khan Academy English Estonian

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So we can make sure we really understand what's happening in this little iterative Fibonacci function

Me saame kindlaks teha kas me saame aru mis toimub selles väikses korduvas fibonacci funktsioonis.

that I wrote, I'm going to step through it with a particular example.

Ma läbin ühe näite samm-sammult

So we're going to assume that this function is called with the argument 5.

Oletame, et see funktsioon on kutsutud argumendiga 5.

So we want the fifth term in the Fibonacci sequence

Me tahame 5. tingimust fibonacci jadas.

starting at where we're indexing things starting at 0.

Alustades kus indeks on 0.

So the 0th term will be really sometimes what you would imagine the first term to be.

0. tingimus on... tegelikult... vahepeal te peate ette kujutama milline esimene tingimus on.

We'll start at the 0th term.

Me alustame 0. tingimusest.

So we're assuming that Fibonacci of 5 is called.

Me oletame, et on välja kutsutud fibonacci(5).

So we want the fifth term starting at the 0th term. So we just want the fifth one.

Me tahame 5. tingimust. Alustades 0. tingimusega ning me tahame 5.

And so when we go into this program, terms is defined as this list right here

Kui me lähme programmi siis tingimused algavad... on defineeritud selles listis siin.

that just has two elements, 0 and 1.

Sellel on 2 elementi: 0 ja 1.

So what I've done here is, I'm going to really focus on what happens in this loop.

Mis ma siin tegin on: Ma keskendun sellel mis siin korduses toimub,

So as we enter into this loop, the first time that we enter into this loop, terms

et kui me lähme sellesse loop'i siis esimene kord kui me siseneme siia loop'i

is referring to a list that has just 0 and 1 in it.

tingimused viitavad listile milles on ainult 0 ja 1.

And we did that because, by definition, those are the first two terms of the Fibonacci sequence.

Me tegime seda, sest definitsiooni järgi need on esimesed kaks tingimust fibonacci jadas

And then also entering into the loop, we define i as being equal to 2.

ning sisenedes loop'i me defineerisime i võrdsena... i võrdsena 2

And we do that, because we've already defined the 0th term and the first term.

ning me tegime seda kuna me juba defineerisime 0. ja 1. tingimuse

And so now we want to, as we enter the loop,

ja nüüd me tahame loop'i sisenedes... alustada... me tahame lisada...

we want to add the second term as we go into the loop.

Me tahame lisada teise tingimuse kui me lähme loop'i

And then we say, while i is less than or equal to n.

ja siis vaatame kas i on väiksem või võrdne n.

Well, we already know that n is 5.

Me teame et n on 5.

So in the scope of this function, while we are running it, the variable n is 5.

Selle funktsiooni piires kui me seda jooksutame on n muutuja 5.

And so clearly i is less than or equal to 5, so we will run this code right over here.

Selgelt on i väiksem või võrdne kui 5 nii et me käivitame selle koodiosa siin

And we're appending to terms. So we're going to append something.

ja me lisame tingimustele nii et me lisame midagi.

So entering into this clause, this is what i, in terms,

Sisenedes sellesse osalausesse on see milline i tingimus välja näeks.

look like. But it looks like we're going to append something to terms. So terms is going to look like-- terms is going to be 0 and 1. And then we're going to add something.

aga näeb välja nagu me lisaks midagi tingimustele nii et tingimused näevad välja nagu... Tingimused on 0 ja 1 ning me lisasime sinna midagi...

We're going to add something right over here to terms.

Me lisame midagi siit tingimustele

And what is that thing we're going to add?

ja mis on see mida me lisame?

Well, we're going to add whatever this business over here is.

Me lisame misiganes see asi siin on.

It seems complicated, but when you break it down, it actually doesn't look too bad.

See näeb keeruline välja, kuid kui see osadeks laiali võtta siis see ei ole väga raske.

In this situation, what is i minus 1?

Mis on i miinus 1 selles olukorras?

Well, i is 2, so in this situation, i minus 1 is going to be 1, and i minus 2 is

I on 2 nii et selles olukorras i miinus 1 on 1 ja i miinus 2 on 0

going to be 0, as we go through this iteration.

kui me läbime seda iteratsiooni.

The first term in terms, the first term, so this is the 0th term.

Nii et tingimused... esimene tingimus tingimustes... esimene tingimus on 0. tingimus.

This is the first term.

See on esimene tingimus.

So the first term in terms is literally a 1.

Nii et esimene tingimus tingimustes on lihtsalt 1.

So this whole thing is 1. And the 0th term in terms, remember terms, the 0th term

Nii et kogu see asi on 1 ja 0. tingimus tingimustes. Pidage meeles... tingimused... 0. tingimus tingimustes.

in terms-- actually I should write it this way.

tegelikult ma peaksin selle kirjutame niimoodi.

The list is called terms.

0. tingimus... listi nimi on tingimused(terms).

The 0th term in terms-- this is what term looks like right

0. tingimus tingimustes. See on see milline tingimus näeb välja praegu ja see on 0.

now-- is going to be 0. So this whole thing is going to be 0, as well.

Nii et kogu see asi siin on ka 0.

So it's 1 plus 0, which is 1. And that's what we're appending to terms.

Nii et see on 1 pluss 0 mis on 1 ja selle me lisame tingimustele.

So we're going to append a 1 over here. And then we say i is equal to i plus 1.

Me lisame 1 siit ja siis me ütleme et i on võrdne i plus 1.

Well i is, right now, equal to 2. So you're going to add 2 plus 1 is 3. And that's going to be the new value for i.

I on nüüd 2 nii et me lisame 2 pluss 1 mis on 3 ja see on meie uus väärtus. Uus väärtus i.

And then we go back, we loop back up to the beginning of the while loop.

Siis me lähme tagasi. Me lähme tagasi while loop'i algusesse

And we say while i is less than or equal to n.

ja me vaatame kas i on väiksem või võrdne n.

Well, now i is a little bit closer to n. It's 3 now. But it's still less than or equal to 5.

Nüüd on i natuke lähemal n väärtusele. See on nüüd 3, aga see on ikkagi väiksem või võrdne 5.

So now we evaluate this again.

Arvutame selle väärtuse uuesti.

So once again, entering into the loop,

taaskord me siseneme loop'i.

terms now looks like this-- 0, 1, 1.

Tingimused näeb välja nüüd selline: 0, 1, 1.

I looks like this-- 3.

I näeb välja selline, 3.

It's really the same values we had exiting the loop.

Need on samad väärtused mis meil olid loop'ist väljudes

And now we evaluate right over here.

ja nüüd me arvutame siin.

We're going to add something to terms.

Me lisame midagi tingimustele.

So terms right now is 0, 1, 1. We're going to add something to it.

Nii et tingimused praegu on: 0, 1, 1 ja me lisame midagi sellele.

And what is that something?

Mis see midagi on?

It's going to be the i minus 1th term of terms.

See on i miinus 1. tingimus tingimustes.

So what's the i?

I over here is 3. 3 minus 1 is 2.

I on siin 3. 3 miinus 1 on 2.

So this right over here is now going to be 2.

Nii et see siin on nüüd 2.

So it's going to be the second indexed term in terms. So this is the 0th, the first, the second.

Nii et see on teine indekseeritud tingimus tingimustes nii et see on 0. see 1. ja see 2.

So this over here is going to evaluate to 1, plus i minus 2.

Nii et selle väärtus siin on 1 pluss i miinus 2.

Well, i is now 3. 3 minus 2 is 1. So plus the first term in terms.

I on nüüd 3. 3 miinus 2 on 1. Nii et pluss esimene termin terminites.

This is the 0th term and the first term. So this is also going to be a 1 over here.

Nii et see on 0. tingimus 1. tingimuses nii et selle väärtus tuleb siin ka 1.

This is going to be 1 plus 1, or 2.

Nii et see tuleb 1 pluss 1 mis on 2.

So we're going to append a 2 to terms.

Me lisame 2 tingimustele.

That's what this does over here. And then we take whatever i was, which is i, in this iteration, i is 3, and we're going to add 1 to it and redefine i to be that.

See siin teebki seda ning me võtame selle misiganes i oli mis praegu siin on 3. Me lisame sellele 1 ja määrame i ümber selleks.

So 3 plus 1 is 4. And that's the new i.

3 pluss 1 on 4 ja see on meie uus i väärtus.

Then we go again to the beginning of the loop. While i is less than or equal to n.

Siis me läheme tagasi loop'i algusesse ja vaatame kas i on väiksem või võrdne n.

Well, i is now 4. n is is still 5.

I on praegu 4, n on alati ning ikka 5.

4 is less than or equal to 5. So we run this again.

4 on väiksem või võrdne kui 5 nii et me käivitame selle uuesti

And once again, we need to figure out what terms of i minus 1 are.

ja taaskord me peame arvutama mis tingimused i miinus 1 on.

Let me write it over here, since this is getting kind of messy.

Las ma kirjutan selle siia. See on päris segane.

Let me actually clear this up, because I

Võib-olla ma peaks selle puhtaks tegema, sest ma tahan et te saaks seda selgesti lugeda.

want to be able to read it clearly.

Las ma teen selle puhtaks.

So let me clear this. So now in this loop, let's just think

Nüüd selles loop'is.

about what-- so now, let me write it over here.

Mõtleme mis... nüüd... Las ma kirjutan selle siia.

Entering the loop now, i is equal to 4--

Sisenedes loop'i, i on nüüd 4.

I'm going to do that same orange color-- entering into the loop

Ma teen selle sama oranži värviga.

i is equal to 4. And the terms has now been-- it now has four elements in it-- 0, 1, 1, and 2.

Sisenedes loop'i on i väärtus 4 ja tingimused... tingimused on nüüd... Tingimustel on nüüd 4 elementi: 0, 1, 1 ja 2.

And now 4 is still less than or equal to 5, so we do this,

4 on ikka väiksem või võrdne 5 nii et me teeme seda

and we have to figure out what terms of i minus 1 is.

ja me peame arvutama mis tingimused i miinus 1 on.

Well, now i minus 1 is 3, right?

Nüüd i miinus 1 on 3. Õigus?

4 minus 1 is 3, so terms of-- not terms of.

4 miinus 1 on 3 nii et tingimused... õigemini 3. element....

I should say the third element in terms is 0, 1, 2, 3.

Mitte element. Ma peaks ütlema et kolmas element tingimustes on 0, 1, 2, 3.

So it's going to be-- this whole thing

Nii et see on kõik see asi siin.

is going to be this 2 right over here.

See on see 2 siin.

So we're going to take that 2-- I

Nii et me võtame selle 2. Ma tean et te saate seda lugeda.

know you can't read that-- we're going to take this 2, and we're going to add it to terms, the i minus 2th terms.

Me võtame selle 2 siit... Me lisame selle kahe tingimustele, i miinus kaks tingimustest.

I is 4, 4 minus 2 is 2. The second term in terms is 0, 1, 2.

I on 4. 4 miinus 2 on 2. teine tingimus tingimustes on 0, 1, 2.

It's this 1 right over here.

See on see üks siin.

So we're adding this 2 plus this 1 to now get 3.

Nii et me lisame selle 2 pluss see 1 ja saame 3 ning me võtame...

And we're taking-- so this whole thing-- when you add it it's 3. And we are appending it to terms.

Kogu see asi... kui te lisate 3 ja me lisame selle tingimustele.

So terms was 0, 1, 1, 2. But now we are appending a 3 to the end of it. We're appending a 3 to the end of it.

Nii et tingimused olid: 0, 1, 1, 2, aga nüüd me lisame 3 selle lõppu

And then we're saying i is equal to i plus 1.

ning siis me ütleme, et i on võrdne i pluss 1.

I was 4, 4 plus 1 is 5, so that is what i is equal to now.

I oli 4. 4 pluss 1 on 5 millega see nüüd ka võrdub.

It's equal to 5.

Then we go the beginning of the loop.

Siis me lähme tagasi loop'i algusesse.

i is now going to be equal to 5.

I on nüüd 5. tingimused.

Terms-- let me write in that same color for consistency--

Las ma kirjutan selle sama värviga järjepidevuse mõttes.

terms are now 0, 1, 1, 2, and 3. And then we say, well i is less than or equal to n. n is 5.

Tingimused on nüüd: 0, 1, 1, 2 ja 3 ning me vaatame kas i on väiksem või võrdne n.

Well, 5 is still less than or equal to 5.

N on 5. 5 on ikka väiksem või võrdne 5.

It's equal to 5, so this still is true. So we will execute this clause.

See võrdub 5 nii et see on ikkagi tõene mistõttu me käivitame selle osalause

And now we have to figure out-- let me clear this out

ja me peame nüüd arvutama...

again-- now we have to figure out what is terms of i, well, what is the i minus 1th term in terms?

Las ma teen selle tühjaks jälle. Nüüd me peame selgeks saame mis on tingimused i... mis on i miinus 1. tingimus tingimustes.

So now i is 5. So it's 5 minus 1. So it's the fourth term in terms.

Nüüd i on 5. Nii et see on 5 miinus 1. Nii et see on 4. tingimus tingimustes.

So 0, 1, 2, 3, 4. So it is this term right over here. It is the 3.

See on 0, 1, 2, 3, 4. nii et see on see tingimus siin. See on 3.

So this over here is 3 now. And then we have to think about-- let

Nii et see 3 siin ja siis meil on... ja siis me peame mõtlema...

me do this in another color-- and then we

Las ma teen selle teise värviga.

have i minus 2. i is 5 now. 5 minus 2 is 3. The third term in terms 0, 1, 2, 3 is this over here.

Meil on i miinus 2. I on 5 nüüd. 5 miinus 2 on 3. Kolmas tingimus tingimustes: 0, 1, 2, 3 on see siin.

So this over here is 2.

Nii et see siin on 2.

So you evaluate this-- you'll notice we're just adding the last two terms that we had so far.

Te arvutate nüüd selle. Te panete tähele, me lihtsalt liidame viimast kahte tingimust mis meil siiamaani on olnud.

This is how we build our Fibonacci sequence.

Nii me ehitame üles meie fibonacci jada

And so 3 plus 2 is 5. So we're going to append the 5 to the end of terms.

ja nii 3 pluss 2 on 5 ning me lisame 5 tingimuste lõppu.

So terms is going to be 0, 1, 1, 2, 3, and then we are going to append a 5 to it. And then we say i is equal to i plus 1.

Nii et tingimused on: 0, 1, 1, 2, 3 ja siis me lisame... Me lisame 5 sellele ning seejärel me määrame i väärtuseks i pluss 1.

So i is equal to 5 plus 1, or 6.

I võrdub 5 pluss 1 mis on 6. I on nüüd 6.

i is equal to 6 now. We go to the beginning of the loop,

Kui me lähme tagasi loop'i algusesse mis seab tingimuse

and it says, while i is less than or equal to n.

kui i on väiksem või võrdne n.

Well, now i is 6, and n has been 5. 6 is not less than or equal to 5. So this is false, So we do not-- we break out of the loop,

I on nüüd 6 ja n on... see on alati olnud 5. 6 ei ole väiksem ega võrdne 5 nii et see on väär. Nii et me ei tee... Me peatame loop'i ja me lähme...

and we go to, I guess, we stopped running it. And then we go to return the nth term in terms. So remember n was 5.

Ma arvan et me lõpetasime selle jooksutamise ja me lähme nüüd väljastamise juurde... väljasta n kohal tingimus tingimustes. Jätke meelde. N oli 5.

So what's the fifth term if we start at 0?

Mis on 5. tingimus. Kui me alustasime 0.

So this is the 0th term, first term, second term, third term, fourth term, fifth term, and we are done.

See on 0. tingimus, 1. tingimus, 2. tingimus, 3. tingimus, 4. tingimus, 5. tingimus.

And hopefully that gives you an understanding

Ja me oleme lõpetanud.

of why this worked. And also a little bit of the logic of how we wrote it.

Loodetavasti see annab teile arusaama miks see töötab ja ka natuke loogikat

It's literally building up the Fibonacci sequence the way

kuidas me selle kirjutasime. See on sõna otseses mõttes fibonacci jada ülesehitamine eelduse järgi.

you would expect to. It started with the first two terms by definition, and then each time we went to the loop,

See alustas esimese kahe tingimusega definitsiooni järgi ning iga kord me läksime loop'i juurde

and it added another term and said, hey, the new term is just going to be the sum of the last term,

ning lisasime uue tingimuse. See ütles et uus tingimus on summa mille liidetavad on viimane tingimus

right now, and the second to last term. And add them together, and then that will be the new term,

ja viimasele eelnev tingimus ning see on meie uus tingimus

and you keep doing that. You keep doing that until you have, essentially, until you've added that nth term.

ning kui seda seda edasi teha siis te saate vajaliku tingimuse kui teil on lisatud numbriga n tingimus.

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