Tries CS50 English Basque

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>> KEVIN SCHMID: Sometimes, when building a program, you might want to utilize a

>> KEVIN SCHMID: Batzuetan, sortzerakoan bat programa, agian garatu nahi duzun bat

data structure known as a dictionary.

Datu egitura hiztegi bat bezala ezagutzen.

A dictionary maps keys, which are usually strings, to values, ints,

Batek hiztegi mapak giltzak, diren Normalean kateak, balioei, ints,

chars, a pointer to some object, whatever we want.

karakteretan, objektu batzuk erakuslea, edozein dela ere nahi dugu.

It's just like ordinary dictionaries that map words through definitions.

Besterik hiztegiak arruntak bezala mapa duten hitzen definizioak bidez.

>> Dictionaries provide us with the ability to store information

>> Hiztegiak ematen gurekin batera informazioa gordetzeko gaitasuna

associated with something and look it up later.

zerbait lotutako eta geroago, itxura gora.

So how do we actually implement a dictionary in, say, C code that we can

Beraz, nola ez benetan ezartzeko dugu bat , esaten, C kodea hiztegi ahal dugun

use in one of our programs?

gure programa bat erabili?

Well, there are a lot of ways that we could implement a dictionary.

Beno, ez dira modu asko hiztegi bat martxan izan dugu.

>> For one, we could use an array that we dynamically re-size or we could use a

>> Bat, array bat erabili izan dugu dugun dinamikoki berriro tamaina edo bat erabili izan dugu

linked list, hash table or a binary tree.

lotutako zerrenda, hash taula edo zuhaitz bitar bat.

But whatever we choose, we should be mindful of the efficiency and

Baina edozein dela ere aukeratu dugu, behar dugu izan eraginkortasuna mindful eta

performance of the implementation.

ezartzeko errendimendua.

We should think about the algorithm used to insert and look up items into

Erabilitako algoritmoa buruz pentsatu behar dugu txertatzeko eta begiratu elementuak sartu

our data structure.

Gure datu-egitura.

>> For now, let's assume that we want to use strings as keys.

>> Oraingoz, Demagun dugun kateak teklak bezala erabili nahi.

Let's talk about one possibility, a data structure called a trie.

Dezagun aukera bat egin dezagun, Datu egitura bat trie bat deitu.

So here's a visual representation of a trie.

Hortaz, hona hemen bisuala ordezkaritza bat trie baten.

>> As the picture suggests, a trie is a tree data structure with

>> Irudian dioen bezala, trie zuhaitz datu-egitura bat da,

nodes linked together.

nodes lotuta elkarrekin.

We see that there's clearly a root node with some links extending to

Ikusten dugu ez dagoela argi erro bat lotura batzuk zabalduz Nodo

But what does each node consist of?

Baina zer datza nodo bakoitzean?

If we assume that we're storing keys with only alphabetic characters, and

Duten gakoak gordetzeko ari gara bere gain hartzen badugu karaktere alfabetiko bakarra, eta honekin

we don't care about capitalization, here's a definition of a node that

ez dugu kapitalizazio buruzko zaintzeko, hemen nodo baten definizio hori

nahikoa izango da.

>> An object whose type is struct node has two parts

>> Objektu bat bere motako struct da nodo bi zati ditu

called data and children.

datuak eta haurrak deitu.

We've left the data part as a comment to be replaced by a component

Datuen zatia utzi dugu iruzkin bat bezala haien tokia osagai batek

declaration when struct node is incorporated in a C program.

deklarazio denean egitura nodo da C programa batean sartu.

The data part of a node might be a Boolean value to indicate whether or

Datuak nodo baten zati bat izan liteke Balio boolearrak honakoa adierazten du: edo

not the node represents the completion of a dictionary key or it might be a

ez nodo amaitu adierazten hiztegi gako baten edo bat izango da agian

string representing the definition of a word in the dictionary.

katea definizioa ordezkari Hiztegian hitz baten.

>> We'll use a smiley face to indicate when data is present in a node.

>> Aurpegi alai bat erabiliko dugu adierazi datuak nodo bat presente dagoenean.

There are 26 elements in our children array, one index

Daude 26 elementu gure haurrak array, indize bat

per alphabetic character.

hizki bakoitzeko.

We'll see the significance of this soon.

Ikusiko dugu garrantzia hau laster neurtzen.

>> Let's get a closer look of the root node in our diagram, which has no data

>> Gaitezen erroa nodoaren hurbilago itxura bat Diagraman, zein datu ez du

associated with it, as indicated by the absence of the smiley face in the

horri lotuta, adierazten duen bezala aurpegieren aurpegia eza

The arrows extending from the parts of the children array represent non-node

Geziak atalen zabalduz haurrek array ez nodo irudikatzeko

pointers to other nodes.

beste nodo erakusleak.

For example, the arrow extending from the second element of children

Adibidez, gezi zabalduz haurrak bigarren elementua

represents the letter B in a dictionary key.

B gutunean adierazten hiztegi gako bat.

And in the larger diagram we label it with a B.

Eta handiago diagrama batean etiketatuko dugu B. batekin

>> Note that in the larger diagram, when we draw a pointer to another node, it

>> Kontuan handiagoa diagrama hori, noiz dugu nodo beste erakuslea bat marraztu, hura

doesn't matter where the arrowhead meets that other node.

ez du axola non gezi du beste nodo hori betetzen.

Our sample dictionary trie contains two words, that and zoom.

Gure lagina hiztegi trie dauka Bi hitz, hori eta zoom.

Let's walk through an example of looking up data for a key.

Goazen adibide baten bidez Datu gora begiratzen gako baten.

>> Suppose we wanted to look up the corresponding value for the key bath.

>> Suposatzen begiratu nahi izan dugu dagokion balioa gako bainu.

We'll begin our look up at the root node.

Gure begirada hasiko dugu sortu erroko nodoa.

Then we'll take the first letter of our key, B, and find the corresponding

Ondoren, gure lehenengo letra hartu dugu Giltza, B, eta dagokion jakiteko

spot in our children array.

gure seme array gelditzea.

Notice that there are exactly 26 spots in the array, one for each letter of

Nabarituko daudela zehazki 26 lekuak array, gutuna bakoitzeko bat in

And we'll have the spots represent the letters of the alphabet in order.

Eta izan dugu lekuak ordezkatzen alfabetoaren letrak ordenean.

>> We'll look at the second index then, index one, for B. In general, if we

>> Egingo bigarren indizearen begiratzen dugu, ondoren, indize bat, B. Oro har, eta badugu

have some alphabetic character C we could determine the corresponding spot

zenbait hizki C dugu dagokion lekua zehaztu ezin

in the children array using a calculation like this.

haurrak array erabiliz honen antzeko kalkulu bat.

We could have used a larger children array if we wanted to offer look up of

Haurrak handiago bat erabili ahal dugu begirada osatzen eskaini nahi array badugu

keys with a wider range of characters, such as the entire

karaktere sorta zabalago bat giltzak, esaterako osoan bezala

ASCII character set.

ASCII karaktere-jokoa.

>> In this case, the pointer in our children array at

>> Kasu honetan, erakuslea gure haurrei array

index one is not null.

indize bat da, ez da nulua.

So we'll continue looking up the key bath.

Beraz, bila jarraituko dugu Funtsezko bainu sortu.

If we ever encountered a null pointer at the proper spot in the children

Inoiz nulua erakuslea topo egin dugu bada haurrak in Leku egokia

array while we traversed the nodes, then we'll have to say that we

array nodoak zeharkatu dugun bitartean, Orduz dugula esan behar dugu

couldn't find anything for that key.

ezin gako horrentzako ezer aurkitu.

>> Now, we'll take the second letter of our key, A, and continue following

>> Orain, bigarren gutunean hartu dugu gure gakoa, A, eta jarraitu ondorengo

pointers in this way until we reach the end of our key.

modu horretan, erakusleak arte Gure funtsezko amaieran iritsiko.

If we reach the end of the key without hitting any dead ends, null pointers,

Gakoa amaieran iritsiko gara gabe bada muturretan hildako edozein sakatuz, null erakusleak,

as is the case here, then we only have to check one more thing.

gertatzen da hemen bezala, orduan guk bakarrik gauza bat gehiago begiratu behar.

Is this key actually in the dictionary?

Gako hau da, benetan hiztegian?

>> If so, we should find a value, well a smiley face icon in our diagram where

>> Hala bada, balio bat aurkitu beharko dugu, ongi bat aurpegia smiley gure diagrama ikono non

hitza bukatzen da.

If there is something else stored with the data, then we can return it.

Bada ez beste zerbait gordetzen da Datuak, ondoren, itzuli ahal izango dugu.

For example, the key zoo is not in the dictionary, even though we could have

Adibidez, funtsezko zoologiko ez da horretan hiztegia, nahiz eta izan dugu

reached the end of this key without ever hitting a null pointer, while we

Giltza honen amaieran iritsi inoiz gabe null erakuslea sakatuz, berriz dugu

iterate through the trie.

trie bidez batetik bestera joateko.

>> If we tried to look up the key bath, the second to last node's array index,

>> Funtsezko bainu aurkitu, saiatu ginen bada azken nodoaren array indizea bigarren,

corresponding to the letter H, would have held a null pointer.

letra H dagokiona, litzateke atxiki null erakuslea.

So bath is not in the dictionary.

Beraz, bainu ez dago hiztegian.

And so a trie is unique in that the keys are never explicitly stored in

Eta beraz trie bat berezia dela gakoak in dira inoiz esplizituki gordeta

the data structure.

Datuen egitura.

So how do we insert something into a trie?

Beraz, nola ez zerbait txertatu dugu trie batean?

>> Let's insert the key zoo into our trie.

>> Dezagun txertatzeko gakoa gure trie sartu zoo.

Remember that a smiley face at a node could correspond in code to a simple

Gogoratu nodo batean aurpegi alai bat duen kode in dagozkio soil batera

Boolean value to indicate that zoo is in the dictionary or it could

Balio boolearrak zoologiko duten adierazteko hiztegian edo izan liteke

correspond to more information that we wish to associate with the key zoo,

Informazio gehiago dagozkion dugu hemen gako zoologiko lotu nahi,

like the definition of the word or something else.

definizioa bezalako hitza edo beste zerbait.

In some ways, the process to insert something into a trie is similar to

Nolabait, prozesuan sartu trie batean zerbait antzekoa da

looking up something in a trie.

trie batean zerbait gora begiratzen.

>> We'll start with the root node again, following pointers corresponding to

>> Erroko nodoa hasiko gara berriro, honako erakusleak dagokion

the letters of our key.

Gure funtsezko hizkiak.

Luckily, we were able to follow pointers all the way until we reached

Zorionez, erakusleak jarraitu ahal izan dugu modu guztiak gara iritsi arte

the end of the key.

gakoa amaieran.

Since zoo is a prefix of the word zoom, which is a member of the

Geroztik Zoo hitzaren aurrizki bat da zoom, eta horrek kide da

dictionary, we don't need to allocate any new nodes.

hiztegi, ez dugu behar den edozein nodo berriak esleitzeko.

>> We can modify the node to indicate that the path of characters leading to

>> Nodoa aldatu ahal izango dugu, adierazten duten liderra karaktere bidea

it represents a key in our dictionary.

gure hiztegian gako bat irudikatzen du.

Now, let's try inserting the key BATH into the trie.

Orain, saiatu txertatu du Giltza trie sartu BATH.

We'll start at the root node and follow pointers again.

Egingo erroko nodoa etan hasiko gara eta erakusleak jarraitu berriro.

But in this situation, we hit a dead end before we're able to get to the

Baina egoera horretan, hildako bat hit dugu amaitzeko iristeko gai gara aurretik

end of the key.

gakoa amaieran.

Now, we'll need to allocate some new nodes will need to allocate one new

Orain, batzuk berriak esleitu behar dugu nodo berri bat esleitu beharko

node for each remaining letter of our key.

Gainerako bakoitzeko nodo gure teklaren hizkia.

>> In this case, we just need to allocate one new node.

>> Kasu honetan, behar besterik ez dugu nodo berri bat esleitu.

Then we'll need to make the H index reference this new node.

Gero H indizearen egin behar dugu nodo berri honi erreferentzia.

Once again, we can modify the node to indicate that the path of characters

Berriro ere, nodo aldatzeko dezakegu adierazten duten pertsonaiak bidea

leading to it represents a key in our dictionary.

da liderra adierazten batean gure hiztegi gakoa.

Let's reason about the asymptotic complexity of our procedures for these

Dezagun arrazoia asintotikoak buruzko gure hauentzako prozedurak konplexutasuna

two operations.

>> We notice that in both cases the number of steps our algorithm took was

>> Nabarituko dugu bi kasuetan kopuruaren Urratsak gure algoritmoa hartu zuten

proportional to the number of letters in the keyword.

kopuruaren proportzionala keyword letrak.

When you want to look up a word in a trie you just need to iterate through

Hitz bat bilatzeko batean nahi baduzu trie besterik bidez batetik bestera joateko behar duzun

the letters one by one until you either reach the end of the word or

letrak banan-banan arte bai Hitz amaieran edo iristeko

hit a dead end in the trie.

hildako amaiera hit trie batean.

>> And when you wish to insert a key value pair into a trie using the

>> Eta denean gako bat txertatu nahi duzu balioa bikotea trie batean erabiliz

procedure we discussed, the worst case will have you allocating a new node

prozedura aztertu ditugu, kasu txarrenean egingo nodoaren esleitzean duzu

for each letter.

letrak idazteko.

And we'll assume that allocation is a constant time operation.

Eta esleipena dela suposatuko dugu denbora etengabeko eragiketa bat da.

So if we assume that the key length is bounded by a fixed constant, both

Gako luzera dela suposatuko dugu hala bada konstante finkoa, bai mugatzen

insertion and look up are constant time operations for a trie.

txertatzeko eta begiratu etengabeak dira denbora trie baterako eragiketak.

>> If we don't make this assumption that the key length is bounded by a fixed

>> Ez badugu egin hipotesi hori gako luzera da finko bat mugatzen

constant, then insertion and look up, in the worst case, are linear in the

etengabea, eta gero txertatzeko eta begiratu, Kasu txarrenean, ari diren lineal

length of the key.

Gakoaren luzera.

Notice that the number of items stored in the trie doesn't affect the look up

Nabarituko elementu kopurua gordetzen trie batean ez du itxura eraginik sortu

or insertion time.

edo txertatzeko denbora.

It's only impacted by the length of the key.

Honez bakarrik eragin Gakoaren luzera.

>> By contrast, adding entries to, say, a hash table tends to make

>> Aitzitik, sarrerak gehituz, esan, hash taula bat egiteko joera

future look up slower.

etorkizunari begiratu motelagoa.

While this may sound appealing at first, we should keep in mind that a

Hau erakargarria soinu bitartean eta lehen, Kontuan hartu behar dugu mantentzeko a

favorable asymptotic complexity doesn't mean that in practice the data

aldeko asintotikoak konplexutasuna ez du esan nahi praktikan datuen

structure is necessarily beyond reproach.

egitura dela nahitaez reproach haratago.

We must also consider that to store a word in a trie we need, in the worst

Ere gorde kontuan hartu behar dugu bat trie bat behar dugu, txarrenean hitza

case, a number of nodes proportional to the length of the word itself.

kasuan, nodo kopurua proportzionala hitza bera luzera.

>> Tries tend to use a lot of space.

>> Saiatzen ohi espazio asko erabiltzeko.

That's in contrast to a hash table, where we only need one new node to

Duen hash taula bat kontrastea da, non soilik nodo berri bat behar dugu

store some key value pair.

Zenbait gako-balioa bikotea gordetzeko.

Now, again in theory, large space consumption doesn't seem like a big

Orain, berriro ere teorian, espazio handi kontsumoak ez du handi bat bezala dirudi

deal, especially given that modern computers have gigabytes and

aurre egiteko, are gutxiago, moderno ordenagailuak gigabyte eta

gigabytes of memory.

memoria gigabyte.

But it turns out that we still have to worry about memory usage and

Baina bihurtzen da hori oraindik ez dugu memoria erabilera eta kezkatu

organization for the sake of performance, since modern computers

mesedetan erakundea errendimendua, geroztik ordenagailuak modernoaren

have mechanisms in place under the hood to speed up memory access.

pean bildu diren mekanismoak izan kanpaia azkartzeko memoria sarrera.

>> But these mechanisms work best when memory accesses are made in compact

>> Baina mekanismo horiek lan onena memoria sarbideak dira trinkoa egin

regions or areas.

eskualde edo arloak.

And the nodes of a trie could reside anywhere in that heap.

Eta trie baten nodo bizi liteke zeure duen edozein lekutan.

But these are trade-offs that we must consider.

Baina horiek ez dira merkataritza-off duten kontuan hartu behar dugu.

>> Remember that, when choosing a data structure for a certain task, we

>> Gogoratu, Datuak bat aukeratzerakoan Zeregin jakin baterako egitura, dugu

should think about what kinds of operations the data structure needs to

pentsatu behar da zer motatako eragiketak datuak egitura behar

support and how much the performance of each of those

laguntza eta zenbat errendimendua horietako bakoitzaren

operations matters to us.

eragiketak gurekin gaietan.

These operations may even extend beyond just

Eragiketa horiek, are gehiago, baliteke besterik haratago hedatzen

basic look up and insertion.

oinarrizko look up eta txertatzeko.

Suppose we wanted to implement a kind of auto-complete functionality, much

Suposatzen moduko bat martxan jartzea nahi izan dugu auto-osoa funtzionaltasuna, askoz

like Google search engine does.

bezalako Google bilatzailea du.

That is, return all the keys and potentially values which

Hau da, itzultzeko tekla guztiak eta balioak potentzialki horrek

have a given prefix.

aurrizki jakin bat dute.

>> A trie is uniquely useful for this operation.

>> Trie bakarrean erabilgarria da eragiketa honetarako.

It's straightforward to iterate through the trie for each character of

Da erraza bidez batetik bestera joateko izaera bakoitzeko trie

Just like a look up operation, we could follow pointers

Just look up eragiketa bat bezala, erakusleak jarraitu ahal izan genuen

character by character.

pertsonaia by pertsonaia.

Then, when we arrive at the end of the prefix, we could iterate through the

Orduan, noiz iritsiko da amaieran dugu aurrizkia, bidez batetik bestera joateko genezake

remaining portion of the data structure since any of the keys beyond

Gainerako datuak egituraren zati giltzarrietako edozein haratago geroztik

this point have the prefix.

Puntu honetan izan aurrizkia.

>> It's also easy to obtain this listing in alphabetical order since the

>> Halaber Erraza da zerrenda honetan lortzea geroztik ordena alfabetikoan du

elements of the children array are ordered alphabetically.

haurrak array elementuak alfabetikoki ordenatuta daude.

So hopefully you'll consider giving tries a try.

Beraz, espero dugu kontuan hartu beharko duzu emanez saiatu saiatzen.

I'm Kevin Schmid, and this is CS50.

Naiz Kevin Schmid, eta hau da CS50.

>> Ah, this is the beginning of the decline.

>> Ah, hau hasiera da gainbehera.

>> Strike four.

Sorry for making the person who has to edit this go crazy.

Pertsonaren egiteko Barkatu nor editatzeko honetan joan crazy ditu.

>> SPEAKER 1: Well done.

>> HIZLARIA 1: Ongi egina.

That was really well done.

Benetan ondo egina zen.

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