From: Doni Pracner Date: Sat, 7 Nov 2015 20:25:16 +0000 (+0100) Subject: Hash funkcije, materijal za test X-Git-Url: http://svarog.pmf.uns.ac.rs/gitweb/?p=spa2-materijali.git;a=commitdiff_plain;h=5f68f3621816a1c64afb491f08c669903553165a Hash funkcije, materijal za test --- diff --git a/Hash/Gadjanje.java b/Hash/Gadjanje.java new file mode 100644 index 0000000..549fe0d --- /dev/null +++ b/Hash/Gadjanje.java @@ -0,0 +1,84 @@ +import org.svetovid.io.SvetovidReader; + +/** + * Gadjanje mete + * + * Prosiruje InfoTip samo zbog jednostavnosti u TestHash, nema razloga inace. + */ +public class Gadjanje extends InfoTip { + private int[] rezultati; + private static int MAX_DUZ = 20; + + public Gadjanje(String linija) { + String[] delovi = linija.replaceAll(" ", " ").split(" "); + if (delovi.length > 0) { + try { + int br = Integer.parseInt(delovi[0]); + rezultati = new int[br]; + for (int i = 0; i < br; i++) { + rezultati[i] = Integer.parseInt(delovi[i + 1]); + } + } catch (Exception ex) { + throw new RuntimeException(ex); + } + } else + throw new RuntimeException("Pogresan broj argumenata u redu"); + } + + public Gadjanje() { + // prazan konstruktor potreban za test program + } + + public boolean equals(Object o) { + // Objekat je identican + if (this == o) { + return true; + } + // Null je uvek razlicit + if (o == null) { + return false; + } + // Ako su klase razlicite, objekti ne mogu bili jednaki + if (getClass() != o.getClass()) { + return false; + } + + Gadjanje o2 = (Gadjanje) o; + if (o2.rezultati.length == rezultati.length) { + for (int i = 0; i < rezultati.length; i++) { + if (o2.rezultati[i] != rezultati[i]) + return false; + } + return true; + } + return false; + } + + @Override + public int hashCode() { + int rez = 0; + for (int i = 0; i < rezultati.length; i++) { + rez = (rez + rezultati[i] * (MAX_DUZ + 1 - i)) * 7; + } + return rez; + } + + @Override + public InfoTip ucitaj(SvetovidReader r) { + Gadjanje rez = new Gadjanje(); + int br = r.readInt(); + rez.rezultati = new int[br]; + for (int i = 0; i < br; i++) { + rez.rezultati[i] = r.readInt(); + } + return rez; + } + + public String toString() { + String str = "Gadjanje (" + rezultati.length + "):"; + for (int i : rezultati) { + str += " " + i; + } + return str; + } +} diff --git a/Hash/InfoTip.java b/Hash/InfoTip.java new file mode 100644 index 0000000..fc251f3 --- /dev/null +++ b/Hash/InfoTip.java @@ -0,0 +1,11 @@ +import org.svetovid.io.SvetovidReader; + +/** + * Ova klasa nam sluzi samo zato da pojednostavimo menjanje tipa u TestHash. + * + * Inace uopste nije neophodno da tipovi prosiruju ovu klasu da bi se koristili + * u OHashSet. + */ +public abstract class InfoTip { + abstract public InfoTip ucitaj(SvetovidReader r); +} diff --git a/Hash/Kancelarija.java b/Hash/Kancelarija.java new file mode 100644 index 0000000..372fb7d --- /dev/null +++ b/Hash/Kancelarija.java @@ -0,0 +1,68 @@ +import org.svetovid.io.SvetovidReader; + +/** + * Koriscenje kancelarija + * + * Prosiruje InfoTip samo zbog jednostavnosti u TestHash, nema razloga inace. + */ +public class Kancelarija extends InfoTip { + private String prezime; + private int broj; + + public Kancelarija(String line) { + String[] delovi = line.replaceAll(" ", " ").split(" "); + if (delovi.length == 2) { + try { + prezime = delovi[0]; + broj = Integer.parseInt(delovi[1]); + } catch (Exception ex) { + throw new RuntimeException(ex); + } + } else + throw new RuntimeException("Pogresan broj argumenata u redu"); + } + + public Kancelarija(String prezime, int broj) { + this.prezime = prezime; + this.broj = broj; + } + + public Kancelarija() { + }; + + public boolean equals(Object o) { + // Objekat je identican + if (this == o) { + return true; + } + // Null je uvek razlicit + if (o == null) { + return false; + } + // Ako su klase razlicite, objekti ne mogu bili jednaki + if (getClass() != o.getClass()) { + return false; + } + + // pretvaramo objekat u kancelariju + Kancelarija k2 = (Kancelarija) o; + // poredimo polja + if (prezime.equals(k2.prezime) && broj == k2.broj) { + return true; + } + + return false; + } + + public int hashCode() { + return prezime.hashCode() * broj; + } + + @Override + public InfoTip ucitaj(SvetovidReader r) { + String prez = r.readToken(); // citamo jednu "rec" + int br = r.readInt(); + InfoTip rez = new Kancelarija(prez, br); + return rez; + } +} diff --git a/Hash/OHashSet.java b/Hash/OHashSet.java new file mode 100644 index 0000000..52f8952 --- /dev/null +++ b/Hash/OHashSet.java @@ -0,0 +1,185 @@ +/** + * ADT skup realizovan otvorenih hashovanjem + * + * Modifikovana verzija za ilustracije i test program + */ +public class OHashSet implements Set { + + private static final int DEFAULT_TABLE_SIZE = 101; + + private static class Node { + Object value; + Node next; + + public Node(Object value) { + this.value = value; + } + } + + private Node[] table; + + private int count; + private int[] tableCount; + + public OHashSet() { + this(DEFAULT_TABLE_SIZE); + } + + public OHashSet(int size) { + if (size <= 0) + throw new IllegalArgumentException( + "Velicina hash tabele ne moze biti negativna"); + + table = new Node[size]; + tableCount = new int[size]; + count = 0; + } + + private int hash(T o) { + if (o == null) + throw new IllegalArgumentException( + "Hash funkcija se ne moze racunati za null objekat"); + + return Math.abs(o.hashCode()) % table.length; + } + + /** + * Pretrazuje listu kolizija za datu vrednost hash funkcije (drugi argument + * metoda) trazeci element (prvi argument metoda). + * + * Metod vraca null ukoliko element ne postoji u tabeli, ili niz od dve + * reference: 1. prva referenca je referenca na trazeni element 2. druga + * referenca je referenca na element ispred trazenog elementa + */ + private Node[] searchColissionChain(T element, int hashValue) { + Node current = table[hashValue]; + Node prev = null; + + while (current != null) { + if (current.value.equals(element)) { + Node[] ret = new Node[2]; + ret[0] = current; + ret[1] = prev; + return ret; + } + + prev = current; + current = current.next; + } + + return null; + } + + public boolean add(T element) { + int hashValue = hash(element); + Node[] n = searchColissionChain(element, hashValue); + if (n != null) { + return false; + } + + Node newElement = new Node(element); + newElement.next = table[hashValue]; + table[hashValue] = newElement; + + count++; + tableCount[hashValue]++; + return true; + } + + public boolean remove(T element) { + int hashValue = hash(element); + Node[] n = searchColissionChain(element, hashValue); + if (n == null) + return false; + + if (n[0] == table[hashValue]) { + table[hashValue] = table[hashValue].next; + } else { + n[1].next = n[0].next; + } + + count--; + tableCount[hashValue]--; + return true; + } + + public boolean contains(T element) { + return searchColissionChain(element, hash(element)) != null; + } + + public void print() { + for (int i = 0; i < table.length; i++) { + System.out.print("HashCode = " + i + ": "); + + Node head = table[i]; + if (head == null) { + System.out.println(" empty"); + } else { + while (head != null) { + System.out.print("[" + head.value + "]"); + head = head.next; + } + System.out.println(); + } + } + } + + public String toString() { + return "OHashSet; br elemenata " + getCount(); + } + + public int getCount() { + return count; + } + + public int size() { + return getCount(); + } + + public double getChiSquare() { + double chi = 0.0; + + if (count > 0 && table.length > 0) { + double avg = (double) count / table.length; + for (int i = 0; i < tableCount.length; i++) { + chi += (tableCount[i] - avg) * (tableCount[i] - avg) / avg; + } + } + return chi; + } + + public double getPercentFull() { + if (tableCount.length == 0) { + return 0; + } + + int filled = 0; + + for (int i = 0; i < tableCount.length; i++) { + if (tableCount[i] > 0) + filled++; + } + + return filled * 100.0 / tableCount.length; + } + + public void printStats() { + System.out.printf("Elements : %3d%n", getCount()); + System.out.printf("Percent full: %6.2f %n", getPercentFull()); + System.out.printf("Chi square : %8.4f %n", getChiSquare()); + System.out.printf("'Columns' : %3d%n", table.length); + } + + @SuppressWarnings("unchecked") + public T someElement() { + if (count > 0) { + for (int i = 0; i < table.length; i++) { + Node head = table[i]; + if (head != null) { + return (T) head.value; + } + } + } + return null; + } +} diff --git a/Hash/Set.java b/Hash/Set.java new file mode 100644 index 0000000..6f1b0e3 --- /dev/null +++ b/Hash/Set.java @@ -0,0 +1,25 @@ +/** + * Specifikacija ADT skup + * + * @author svc + */ +public interface Set { + + /** + * Dodaje element u skup. + * Vraca false ukoliko element vec postoji u skupu + */ + boolean add(T element); + + /** + * Brise element iz skupa. + * Vraca false ukoliko element ne postoji u skupu. + */ + boolean remove(T element); + + /** + * Proverava da li je element u skupu. + */ + boolean contains(T element); +} + diff --git a/Hash/TestHash.java b/Hash/TestHash.java new file mode 100644 index 0000000..607d3b1 --- /dev/null +++ b/Hash/TestHash.java @@ -0,0 +1,101 @@ +/** + * Test program za hash funkcije i equals funkciju + * + * Napravljen je da prikazuje rezultate ubacivanja istog fajla u tabele + * razlicitih velicina. + * + * Takodje se lako moze promeniti tip podataka koji se ubacuje promenama dve + * promenljive na pocetku klase. Medjutim da bi to radilo tipovi treba da + * prosiruju klasu InfoTip i da imaju ili prazan konstruktor ili da se nekako + * drugacije inicijalizuje objekat `element` u ovoj klasi. + */ +public class TestHash { + + // treba promeniti tip ovog objekta i folder u kome su adekvatni + // podaci da bi se radilo sa drugim podacima + private InfoTip element = new Kancelarija(); + private String folder = "kancelarije"; + + // Na primer ovako treba podesiti za Gadjanje mete + // private InfoTip element = new Gadjanje(); + // private String folder = "mete"; + + // a ovako za XO + // private InfoTip element = new XO(); + // private String folder = "xo"; + + /* + * Pravi praznu mapu i ispisuje je + */ + public void emptyTest() { + OHashSet hash = new OHashSet<>(); + hash.printStats(); + } + + /* + * ucitava podatke iz datog fajla u tabelu date velicine, pri cemu su podaci + * datog tipa, te ispisuje na kraju statistike o tabeli. + */ + public void infoTest(String fajl, int size, InfoTip i) { + OHashSet hash = new OHashSet<>(size); + if (Svetovid.testIn(fajl)) { + while (Svetovid.in(fajl).hasMore()) { + hash.add(i.ucitaj(Svetovid.in(fajl))); + } + Svetovid.closeIn(fajl); + } + hash.printStats(); + } + + /* + * Testira ubacivanje i izbacivanje elemenata iz tabele, cime se dodatno + * proverava da li hash/equals rade kako treba + */ + public void addRemoveTest(String fajl, int size, InfoTip i) { + OHashSet hash = new OHashSet<>(size); + if (Svetovid.testIn(fajl)) { + while (Svetovid.in(fajl).hasMore()) { + hash.add(i.ucitaj(Svetovid.in(fajl))); + } + Svetovid.closeIn(fajl); + } + hash.printStats(); + InfoTip it = hash.someElement(); + if (!hash.add(it)) { + System.out.println("success: not added again"); + } else { + System.out.println("fail: added again!"); + } + if (hash.remove(it)) { + System.out.println("success: removed"); + } else { + System.out.println("fail: not removed!"); + } + if (hash.add(it)) { + System.out.println("success: added back in"); + } else { + System.out.println("fail: not added back in"); + } + } + + public void run() { + // emptyTest(); + + String fajl = "/t2.txt"; + + infoTest(folder + fajl, 101, element); + Svetovid.out.println(); + infoTest(folder + fajl, 503, element); + Svetovid.out.println(); + infoTest(folder + fajl, 997, element); + Svetovid.out.println(); + + // add remove radimo na manjem fajlu + addRemoveTest(folder + "/t0.txt", 101, element); + + } + + public static void main(String[] args) { + new TestHash().run(); + } +} diff --git a/Hash/XO.java b/Hash/XO.java new file mode 100644 index 0000000..38be212 --- /dev/null +++ b/Hash/XO.java @@ -0,0 +1,61 @@ +import org.svetovid.io.SvetovidReader; + +/** + * Igra XO + * + * Prosiruje InfoTip samo zbog jednostavnosti u TestHash, nema razloga inace. + */ +public class XO extends InfoTip { + public static final int DIM = 3; + private int[][] tabla = new int[DIM][DIM]; + + public XO() { + } + + @Override + public InfoTip ucitaj(SvetovidReader r) { + XO rez = new XO(); + for (int i = 0; i < DIM; i++) { + for (int j = 0; j < DIM; j++) { + rez.tabla[i][j] = r.readInt(); + } + } + return rez; + } + + public boolean equals(Object o) { + // Objekat je identican + if (this == o) { + return true; + } + // Null je uvek razlicit + if (o == null) { + return false; + } + // Ako su klase razlicite, objekti ne mogu bili jednaki + if (getClass() != o.getClass()) { + return false; + } + XO o2 = (XO) o; + for (int i = 0; i < DIM; i++) { + for (int j = 0; j < DIM; j++) { + if (o2.tabla[i][j] != tabla[i][j]) { + return false; + } + } + } + return true; + } + + @Override + public int hashCode() { + int rez = 0; + for (int i = 0; i < DIM; i++) { + for (int j = 0; j < DIM; j++) { + rez += tabla[i][j]; + } + } + return rez; + } + +} diff --git a/Hash/hash.pdf b/Hash/hash.pdf new file mode 100644 index 0000000..4a1249a Binary files /dev/null and b/Hash/hash.pdf differ diff --git a/Hash/hash.txt b/Hash/hash.txt new file mode 100644 index 0000000..75e8cc7 --- /dev/null +++ b/Hash/hash.txt @@ -0,0 +1,534 @@ +% Hash funkcije - pripremni materijal +% SPA2, DMI-PMF-UNS, www.dmi.rs +% 2015 + +Heš kod i jednakost u programskom jeziku Java +============================================= + +U programskom jeziku Java u svakoj klasi mogu (i često i trebaju) da +postoje metodi + + public int hashCode() + public boolean equals(Object o) + +Oni omogućavaju vrlo efikasne operacije nad velikim skupovima +objekata, ali je bitno da uzajamno imaju konzistentno ponašanje. + +Tačnije, ako su dva objekta jednaka u skladu sa `equals` tada im i heš +vrednost koju vraća `hashCode` mora biti ista. Obrnutno ne mora da važi, +odnosno može postojati neograničeni broj različitih objekata koji +imaju isti heš kod. Isto tako ako dva objekta imaju različih heš, tada +oni ne bi smeli biti jednaki kad se pita `equals`. No i ovde ne važi +obrnuto, odnosno ako su dva objekta različiti, heš kod im ne mora biti +različit. + +Zbog ovih podrazumevanih odnosa je jako bitno da se ova dva metoda +pišu zajedno, odnosno da se ne menja samo jedan bez promena u drugom. + +U opštem slučaju ako se ovo ponašanje ne promeni reimplementacijom +ovih metoda, objekti u Javi će za ova dva metoda da vraćaju vrednosti +koje se odnose na sam pokazivač u memoriji. Odnosno dva objekta su +isti samo ako se bukvalno isti objekat u memoriji, bez obzira na to da +li imaju isti sadržaj. Isto tako će sam heš kod biti generisan od +vrednosti samog pokazivača, a ne od sadržaja objekta. Jako često ovo +nije poželjno ponašanje, te se zbog toga moraju pisati svoji metodi. + +Heš kod je uvek poželjno pisati tako da se dobija što više različitih +vrednosti za različite instance objekata. U idealnom slučaju bi se za +svaki različit objekat dobijao različit heš kod, međutim to u praksi +često nije moguće. + +Klasa `String` ima redefinisana oba ova metoda. Heš kod koji se dobija +za ovu klasu je veoma kvalitetan i uglavnom se vredi osloniti na njega +za polja ovog tipa. + + +Ocene kvaliteta funkcije +======================== + +Kvalitetna heš funkcija ravnomerno raspoređuje elemente po celoj tabeli, +odnosno dobijamo podskupove sličnih veličina. + +Za poređenje kvaliteta heš funkcija se mogu koristi različite mere. Prva je +procentualna popunjenost tabele -- odnosno procenat podskupova (listi) +u kojima postoji bar po jedan element. + +Nešto komplikovanija mera je $\chi^2$ \emph{(hi-kvadrat)} test. +\begin{equation} + \chi ^2 = \sum_{i=1}^{n} \frac{(K_i - E)^2}{E} +\end{equation} + +gde je $K_i$ - broj elemenata u podskupu $i$, a $E$ - očekivan broj +elemenata u podskupu, odnosno idealna vrednost koja je jednaka +količniku ukupnog broja elemenata i broja skupova. + +Iako deluje relativno komplikovano, ovo nam zapravo daje dobru ocenu +koliko su (ne)ravnomerno raspoređeni elementi. U idealno slučaju bi +sve $K_i$ vrednosti bile jednake sa $E$ i imali bi da je vrednost +testa nula. U opštem slučaju se naravno javljaju odstupanja od +proseka, a pošto kvadriramo udaljenosti, $\chi^2$ brzo raste ukoliko +ima većih anomalija. + +Pri pisanju heš funkcije treba ciljati na što veću procentualnu +popunjenost tabele, idealno je to 100\% za veću količinu podataka. + +Sa druge strane, $\chi^2$ test predstavlja ravnomernost duzina listi, +te bi trebao ostajati relativno konzistentan. Kod dobrih heš funkcija +koje ravnomerno rasporedjuju elemente ovaj test često daje niže +vrednosti tek za veći broj ubačenih elemenata, pošto tek onda dolaze +do izražaja statističko ravnomerno raspoređivanje. + +Dobre vrednosti za ovaj test za heš funkciju zavise od podataka sa +kojima se radi, ali u opštem slučaju treba ciljati da budu niže od +broja podskupova. + + +Primeri +======= + +U sledećim primerima će se razmatrati različiti tipovi podataka i kako +se oni efikasno mogu skladištiti u heš tabelama. Uglavnom će se +razmatrati ideje heš tabele koja ima tačno određen broj podskupova i +pratiti njihovu pokrivenosti i hi kvadrat meru. Tipično će se +razmatrati razlitiče veličine ovih tabela, na primer 101, 503 i 997 +radi bolje ilustracije uticaja veličine na lošije heš funkcije. + + +Korišćenje kancelarija +---------------------- + +Treba da čuvamo podatke o korišćenju kancelarija u toku jednog dana i +da omogućimo što bržu proveru da li je neka konkretna osoba koristila +neku konkretnu kancelariju. Podaci vezuju prezimena za identifikacione +brojeve soba. Naravno moguće je da više ljudi koristilo istu +kancelariju, a moguće je i da je neko više puta koristio istu -- ovo +će se u tabeli skladištiti samo jedan put, pošto nas samo zanima ko je +bio unutra, a ne koliko puta. + +Uzmimo sledeću definiciju klase + +```Java + class Kancelarija { + private int broj; + private String prezime; + .... + } +``` + +U datim fajlovima nema više od~100 prostorija, a i postoji samo +oko~60 različitih prezimena (tj zaposlenih). + +Broj sobe tipa `int` i deluje kao "očigledan" kandidat za heš kod. +Validno bi bilo da se ova informacija vraća kao heš kod: + +```Java + public int hashCode() { + return broj; + } +``` + +Pogledajmo primere učitavanja većeg broja podataka u heš tabele sa +različitim brojem podskupova, ako imamo tako definisanu heš funkciju: + +Elements : 4885 +Percent full: 99.01 +Chi square : 67.3081 +'Columns' : 101 + +Elements : 4885 +Percent full: 19.88 +Chi square : 19778.4749 +'Columns' : 503 + +Elements : 4885 +Percent full: 10.03 +Chi square : 44000.6551 +'Columns' : 997 + +Budući da ima samo 100 soba, primećujemo da vrednosti nisu +zadovoljavajuće čim imamo veće tabele, odnosno imamo manje od 20\% pokrivenosti +tabele sa 503 mesta i oko 10\% za 997 mesta. + +Slično važi i za prezimena, budući da ih ima samo šestdesetak, bez +obzira na koliko je dobar heš kod u klasi `String`, možemo imati samo +šestdesetak različitih rezultata, odnosno dobijamo još gore rezultate, +čak i za relativno malu tabelu sa 101 podskupom. + +```Java + public int hashCode() { + return prezime.hashCode(); + } +``` + + +Elements : 4885 +Percent full: 49.50 +Chi square : 6320.7484 +'Columns' : 101 + +Elements : 4885 +Percent full: 11.53 +Chi square : 39251.8342 +'Columns' : 503 + +Elements : 4885 +Percent full: 5.72 +Chi square : 85190.9396 +'Columns' : 997 + +Očigledno je potrebno kombinovati ove dve vrednosti. Možemo ih +jednostavno samo sabrati: + +```Java + public int hashCode() { + return prezime.hashCode() + broj; + } +``` + +Dobijamo dosta bolje rezultate u testovima: + +Elements : 4885 +Percent full: 100.00 +Chi square : 20.7468 +'Columns' : 101 + +Elements : 4885 +Percent full: 100.00 +Chi square : 720.2837 +'Columns' : 503 + +Elements : 4885 +Percent full: 99.00 +Chi square : 1341.3007 +'Columns' : 997 + +Množenje će tipično dati bolje vrednosti nego sabiranje kad imamo +vrednosti koje su jako blizu jedne drugima (što brojevi kancelarija +koji idu zaredom jesu), pošto pomaže u "raspipanju" vrednosti na većem +opsegu. + +Na primer + +```Java + public int hashCode() { + return prezime.hashCode() * broj; + } +``` + +Elements : 4885 +Percent full: 100.00 +Chi square : 78.8864 +'Columns' : 101 + +Elements : 4885 +Percent full: 100.00 +Chi square : 483.8686 +'Columns' : 503 + +Elements : 4885 +Percent full: 99.10 +Chi square : 951.0727 +'Columns' : 997 + +Iz rezultata se vidi da se konzistentno dobijaju dobre vrednosti sa +ovakvom heš funkcijom. Naročito je bitno što nam vrednost hi kvadrat +testa govori da imamo odstupanje u veličinama podskupova u proseku +manje od jedan. + +Istovremeno je bitno da se i `equals` definiše da koristi ista polja. +Metod zahteva da parametar bude tipa `Object`, pa uvek moramo da krenemo +od toga. Najjednostavnija varijanta zahteva da proverimo da li je +prosledjeno nešto što je iste klase kao i naš objekat, pa tek +onda možemo da menjamo tip i da poredimo polja. + +```Java + public boolean equals(Object o) { + // proveravamo da li je objekat sa + // kojim se poredimo Kancelarija + if (o instanceof Kancelarija) { + // pretvaramo objekat u kancelariju + Kancelarija k2 = (Kancelarija) o; + // poredimo polja + if (prezime.equals(k2.prezime) && broj == k2.broj) { + return true; + } + } + return false; + } +``` + +Međutim potpuna verzija `equals` metoda treba da proveri da li je u +pitanju baš ista klasa kao naša (moguće da je neki naslednik koji +tehnički ne mora biti isti), te da tu uzme u obzir i da je moguće da +nam je prosleđen `null` što nikako ne može biti isto kao i naš +objekat. Dalje se može ubrzati postupak proverom da li su u pitanju +pokazivači na isto mesto pošto nema potrebe za proverama onda. + +Potpuna verzija bi izgledala ovako: + +```Java + public boolean equals(Object o) { + // Objekat je identican + if (this == o) { + return true; + } + // Null je uvek razlicit + if (o == null) { + return false; + } + // Ako su klase razlicite, objekti ne mogu bili jednaki + if (getClass() != o.getClass()) { + return false; + } + + // pretvaramo objekat u kancelariju + Kancelarija k2 = (Kancelarija) o; + // poredimo polja + if (prezime.equals(k2.prezime) && broj == k2.broj) { + return true; + } + + return false; + } +``` + +Razmotrimo sledeću modifikaciju klase: recimo da se i dalje želi samo +pratiti u tabeli ko je bio u kojoj kancelariji, ali da su negde već +definisani objekti u kojima se skladišti i vreme poslednjeg +pristupanja, ili recimo neki dodatni opis zašto je neko bio u +kancelariji. + +```Java + class KancelarijaVreme { + private int broj; + private String prezime; + + private int pristupDan, pristupSat; + + private String komentar; + } +``` + +Budući da za naše potrebe nije bitno kad je pristupano niti zbog čega, +i dalje bi trebali da koristimo iste kodove za `equals` i za +`hashCode` pošto nam je dosta da ubacimo samo jedan objekat za svako +pojedinačno korišćenje. Negde druge se naravno oni mogu koristiti za +detaljije zapise, ali nas to trenutno ne interesuje. + + +Gadjanje mete +------------- + +Potrebno je da čuvamo podatke o rezultatima gadjanja mete. U nizu se +nalazi do 20 brojeva izmedju i uključujući 0 i 10. + +Recimo da je klasa definisana na sledeći način: + +```Java +public class Gadjanje { + private int[] rezultati; + private static int MAX_DUZ = 20; + ... +} +``` + +Pošto je moguće (i vrlo verovatno zapravo) da neko nije gađao svih 20 +puta, u podacima će biti nizovi različitih dužina. U skladu sa tim je +i format za unos takav da je prvi broj u redu zapravo broj gađanja, +koji određuje veličinu niza. + +Funkcija jednakosti bi izgledala ovako: + +```Java + public boolean equals(Object o) { + // Objekat je identican + if (this == o) { + return true; + } + // Null je uvek razlicit + if (o == null) { + return false; + } + // Ako su klase razlicite, objekti ne mogu bili jednaki + if (getClass() != o.getClass()) { + return false; + } + + Gadjanje o2 = (Gadjanje) o; + if (o2.rezultati.length == rezultati.length) { + for (int i = 0; i < rezultati.length; i++) { + if (o2.rezultati[i] != rezultati[i]) + return false; + } + return true; + } + return false; + } +``` + +"Očigledno" rešenje je samo sabrati sve ove vrednosti i vratiti broj. +Međutim ovakvo rešenje daje maksimalno 200 različitih vrednosti i dosta +loše vrednosti u tabeli: + +Elements : 9049 +Percent full: 100.00 +Chi square : 314.5114 +'Columns' : 101 + +Elements : 9049 +Percent full: 27.63 +Chi square : 34841.7383 +'Columns' : 503 + +Elements : 9049 +Percent full: 13.94 +Chi square : 77947.1553 +'Columns' : 997 + +U ovakvoj strukturi, pozicija u nizu bi trebalo da bude značajna za +krajnje heš vrednosti. Da bi se to postiglo jedan pristup je množenje +brojeva sa svojim pozicijama ili različitim (prostim) brojevima. + +Za ovaj primer u kome je dužina niza raznolika i ima više "početnih" +elemenata je dodatno pogodno da se težine primenjuju unazad, pa recimo +možemo uvesti da prvi element ima težinu 21, a poslednji u nizu od 20 +elemenata težinu 2. Dodatno to možemo unaprediti množenjem prostim +brojem pri svakom sabiranju, tako da se ta množenja akumuliraju na +prvim elementima. + +```Java + public int hashCode() { + int rez = 0; + for (int i = 0;i < rezultati.length; i++) { + rez = (rez + rezultati[i] * (MAX_DUZ+1-i)) * 7; + } + return rez; + } +``` + +Elements : 9084 +Percent full: 100.00 +Chi square : 101.7743 +'Columns' : 101 + +Elements : 9084 +Percent full: 100.00 +Chi square : 415.1915 +'Columns' : 503 + +Elements : 9084 +Percent full: 100.00 +Chi square : 981.2660 +'Columns' : 997 + + +Tabla za igru XO +---------------- + +Zadatak nam je da efikasno čuvamo podatke o pozicijama u igri XO, +odnosno matrice 3x3, u kojima su vrednosti -1 za "X", 0 za prazno +polje i 1 za "O". + +Npr: +``` + 1 0 -1 O _ X + 1 1 -1 O O X +-1 0 1 X _ O +``` +predstavlja poziciju u kojoj je ``O'' pobedio/la. + +Polja klase bi se mogla definisati na sledeći način: + +```Java +public class XO { + public static final int DIM = 3; + private int[][] tabla = new int[DIM][DIM]; +.... +} +``` + +Poredjenje ovakvih objekata bi naravno trebalo da pojedinačno ispituje +elemente matrice, na primer: + +```Java + public boolean equals(Object o) { + // Objekat je identican + if (this == o) { + return true; + } + // Null je uvek razlicit + if (o == null) { + return false; + } + // Ako su klase razlicite, objekti ne mogu bili jednaki + if (getClass() != o.getClass()) { + return false; + } + XO o2 = (XO) o; + for (int i = 0; i < DIM; i++) { + for (int j = 0; j < DIM; j++) { + if (o2.tabla[i][j] != tabla[i][j]) { + return false; + } + } + } + return true; + } +``` + +Za ovaj primer vredi prvo razmotriti da neke relativno očigledne +tehnike nisu efikasne: sumiranje ovakve matrice daje vrednosti do plus +ili minus 9, odnosno ima samo 19 različitih vrednosti, što bi +predstavljalo jako lošu pokrivenost tabele. Dodatno, vrlo često će +rezultat biti 0 i uopšteno će biti više tablica koje su bliže +"sredini" rezultatom, što opet dovodi do loše ravnomernosti +raspoređivanja elemenata. + +Dakle ovako definisan metod za heš će davati dosta loše rezultate: + +```Java + public int hashCode() { + int rez = 0; + for (int i = 0; i < DIM; i++) { + for (int j = 0; j < DIM; j++) { + rez += tabla[i][j]; + } + } + return rez; + } +``` + +Elements : 4424 +Percent full: 9.90 +Chi square : 87664.1198 +'Columns' : 101 + +Elements : 4424 +Percent full: 1.99 +Chi square : 454193.0719 +'Columns' : 503 + +Elements : 4424 +Percent full: 1.00 +Chi square : 904604.2717 +'Columns' : 997 + +Efikasnost se u ovakvoj strukturi dobija davanjem "težine" +elementima. Odnosno ne treba gledati jednako ako je "1" u gornjem +levom uglu i u sredini. Npr u jednostavnijim varijantama se može zbir +iz svakog reda množiti različitim brojem. Još bolji rezultati se +dobijaju uvodjenjem još detaljnijih "težina": pri sumiranju reda +množiti različito, ili čak imati specijalne proste brojeve za svako +polje ili uvoditi dodatne operacije. + +Takodje treba uzeti u obzir i to da sabiranje pozitivnih i negativnih +vrednosti može da dovede do "međusobnog poništavanja", te da nula +vrednosti ne pomažu zbiru, naročito kad se uvedu težine koje se množe +sa vrednostima polja. Jedan način da se ovo uradi u konkretnom slučaju +je da se pri računanju heša vrednosti u matrici sabiraju sa 2, pa time +imamo 1,2,3 umesto -1,0,1, što dovodi do veće različitosti. + +Kombinovanjem ovih ideja se mogu napraviti `hashCode` metodi koji će +rezultovati sa hi kvadrat vrednostima manjim od broja podskupova +("kolona"), što se ostavlja za samostalnu vežbu. + diff --git a/Hash/kancelarije/t0.txt b/Hash/kancelarije/t0.txt new file mode 100644 index 0000000..1d159cb --- /dev/null +++ b/Hash/kancelarije/t0.txt @@ -0,0 +1,5 @@ +Pavicevic 84 +Orlovic 32 +Brkic 76 +Loncar 52 +Rodic 84 \ No newline at end of file diff --git a/Hash/kancelarije/t1.txt b/Hash/kancelarije/t1.txt new file mode 100644 index 0000000..79be2e1 --- /dev/null +++ b/Hash/kancelarije/t1.txt @@ -0,0 +1,1000 @@ +Popadic 9 +Nemanjic 3 +Pejic 100 +Jovovic 59 +Milanovic 97 +Jovovic 36 +Milovanovic 90 +Tanaskovic 77 +Gilam 24 +Kovacevic 76 +Popovic 28 +Djukic 20 +Orlovic 87 +Budimirovic 48 +Radovic 68 +Ivanic 95 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+Jovanovic 18 +Marjanovic 63 +Novakovic 63 +Curcic 19 +Dragic 91 +Maletkovic 44 +Marjanovic 4 +Kacanski 31 +Orlovic 46 +Vidovic 4 +Preradovic 39 +Ristic 12 +Novakovic 38 +Popadic 99 +Gregorovic 51 +Radovic 51 +Ognjenovic 55 +Novakovic 5 +Lazarevic 17 +Pap 69 +Dragic 60 +Ognjenovic 9 +Marjanovic 53 +Jovovic 67 +Maletkovic 69 +Preradovic 5 +Brkic 61 +Pap 2 +Dejanovic 66 +Pap 47 +Loncar 91 +Avramovic 4 +Pavicevic 18 +Popadic 48 +Rodic 3 +Savic 9 +Francisko 12 +Maletkovic 45 +Jugovic 94 +Rodic 75 +Ristic 33 +Savic 17 +Francisko 7 +Mandic 29 +Maletkovic 87 +Horvat 48 +Nemanjic 46 +Maric 91 +Horvat 68 +Meseldzija 30 +Tarabic 59 +Avramovic 44 +Markovic 12 +Rodic 12 +Miloradovic 83 +Maletkovic 45 +Savic 26 +Jugovic 29 +Papic 15 +Ognjenovic 57 +Stojanovic 67 +Kacanski 5 +Popovic 74 +Meseldzija 63 +Lazarevic 48 +Lazarevic 97 +Papic 19 +Ostojic 36 +Nedeljkov 84 +Rodic 89 +Stojkovic 60 +Rodic 79 +Miloradovic 39 +Gilam 88 +Ristic 92 +Milovac 44 +Gilam 59 +Milovac 100 +Pap 97 +Avramov 100 +Pavlovic 51 +Tanaskovic 14 +Pavicevic 53 +Pavicevic 32 +Radovic 35 +Milovac 33 +Jovovic 73 +Ristic 1 +Avramovic 92 +Markovic 84 +Pejakov 45 +Tanaskovic 32 +Rodic 2 +Jugovic 3 +Gilam 37 +Popadic 38 +Nedeljkov 16 +Kacanski 73 +Orlovic 43 +Orlovic 93 +Stojkovic 13 +Jovovic 12 +Milovac 30 +Jugovic 81 +Popadic 50 +Milic 23 \ No newline at end of file diff --git a/Hash/kancelarije/t2.txt b/Hash/kancelarije/t2.txt new file mode 100644 index 0000000..05ffe3c --- /dev/null +++ b/Hash/kancelarije/t2.txt @@ -0,0 +1,10000 @@ +Orlovic 79 +Brkic 64 +Rasomon 2 +Horvat 26 +Kacanski 60 +Mandic 36 +Nemanjic 96 +Rodic 35 +Lazarevic 92 +Tarabic 25 +Filipovic 44 +Horvat 65 +Jugovic 91 +Milovanovic 88 +Tanaskovic 47 +Jugovic 95 +Popovic 80 +Nikolic 1 +Brkic 99 +Pavlovic 50 +Brkic 68 +Brkic 6 +Kovac 43 +Vidovic 63 +Malinovic 96 +Ivanic 73 +Orlovic 2 +Mandic 52 +Pap 58 +Dragic 74 +Tanaskovic 15 +Kovacevic 36 +Milic 20 +Orlovic 42 +Pejic 90 +Dejanovic 14 +Pavlovic 61 +Markovic 92 +Pejakov 82 +Stojkovic 13 +Budimirovic 41 +Ivanic 72 +Pavicevic 92 +Maric 90 +Ristic 24 +Djukic 98 +Avramov 74 +Jugovic 4 +Avramov 39 +Horvat 79 +Nikolic 69 +Avramov 62 +Stojanovic 80 +Meseldzija 12 +Francisko 77 +Malinovic 8 +Nikolic 70 +Tarabic 88 +Jovovic 48 +Vidovic 38 +Gregorovic 75 +Pap 90 +Pejakov 51 +Budimirovic 95 +Brkic 20 +Avramov 28 +Djukic 7 +Meseldzija 67 +Maric 52 +Milic 53 +Pavlovic 68 +Budimirovic 89 +Milovac 32 +Nedeljkov 47 +Nedeljkov 69 +Kovacevic 85 +Popadic 48 +Filipovic 88 +Jovanovic 38 +Milic 26 +Ognjenovic 64 +Rasomon 29 +Vidovic 52 +Ognjenovic 65 +Savic 44 +Vidovic 70 +Pejic 16 +Gregorovic 27 +Maletkovic 27 +Pejakov 3 +Kacanski 72 +Tanaskovic 18 +Gilam 79 +Maletkovic 58 +Avramovic 11 +Jeftic 9 +Kovacevic 3 +Milic 70 +Vidovic 65 +Pejakov 11 +Tanaskovic 19 +Nikolic 21 +Stojanovic 68 +Budimirovic 31 +Dragic 11 +Malinovic 14 +Milanovic 35 +Avramovic 50 +Jovanovic 12 +Kacanski 27 +Pap 83 +Pejakov 3 +Popadic 57 +Loncar 31 +Dragic 96 +Rodic 85 +Tarabic 18 +Preradovic 73 +Djukic 84 +Nemanjic 28 +Tanaskovic 28 +Radovic 90 +Jugovic 48 +Pejakov 69 +Ristic 6 +Mandic 47 +Kovac 73 +Horvat 40 +Jugovic 97 +Horvat 64 +Milic 47 +Popadic 4 +Novakovic 77 +Jeftic 45 +Nikolic 73 +Milic 51 +Pejakov 41 +Horvat 77 +Pavicevic 99 +Radovic 5 +Mandic 46 +Markovic 9 +Pavlovic 9 +Pejakov 66 +Avramovic 16 +Milovanovic 93 +Markovic 2 +Ostojic 36 +Ognjenovic 3 +Dragic 51 +Pavlovic 58 +Gregorovic 84 +Popadic 23 +Stojkovic 2 +Tanaskovic 58 +Popadic 69 +Ognjenovic 100 +Jeftic 63 +Miloradovic 71 +Ognjenovic 6 +Radovic 63 +Tanaskovic 43 +Francisko 20 +Pap 60 +Milic 10 +Curcic 94 +Ognjenovic 47 +Dragic 26 +Kacanski 18 +Dragic 84 +Miloradovic 23 +Francisko 39 +Tanaskovic 24 +Avramovic 60 +Gilam 36 +Vidovic 22 +Orlovic 15 +Avramovic 48 +Stojanovic 33 +Pavlovic 13 +Papic 60 +Novakovic 22 +Pejic 80 +Maletkovic 61 +Dragic 10 +Novakovic 97 +Kovacevic 41 +Pejic 43 +Pavlovic 77 +Ristic 72 +Pejic 27 +Jugovic 18 +Preradovic 35 +Kacanski 29 +Nedeljkov 5 +Tarabic 50 +Jugovic 94 +Gregorovic 51 +Meseldzija 70 +Maletkovic 86 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+Ognjenovic 92 +Curcic 96 +Stojanovic 41 +Avramovic 10 +Nikolic 92 +Miloradovic 75 +Avramovic 92 +Dejanovic 98 +Papic 61 +Stojkovic 98 +Mandic 44 +Tanaskovic 49 +Brkic 58 +Maletkovic 54 +Stojanovic 90 +Mandic 34 +Stojkovic 87 +Pejakov 37 +Preradovic 70 +Gilam 29 +Tarabic 78 +Ognjenovic 91 +Novakovic 37 +Popovic 6 +Nedeljkov 50 +Budimirovic 92 +Rasomon 25 +Avramovic 13 +Filipovic 27 +Markovic 43 +Horvat 29 +Miloradovic 53 +Ognjenovic 20 +Markovic 64 +Popadic 13 +Milovac 55 +Orlovic 19 +Stojkovic 79 +Loncar 70 +Kovacevic 75 +Dejanovic 16 +Miloradovic 11 +Marjanovic 83 +Stojanovic 71 +Nikolic 82 +Jovovic 67 +Orlovic 92 +Rodic 42 +Stojkovic 51 +Tarabic 23 +Lazarevic 39 +Avramov 10 +Milovac 28 +Ognjenovic 92 +Pavicevic 14 +Kovacevic 85 +Maletkovic 6 +Papic 87 +Nemanjic 74 +Mandic 99 +Malinovic 93 +Markovic 25 +Francisko 38 +Curcic 22 +Stojanovic 89 +Meseldzija 82 +Pejic 48 +Jovanovic 68 +Loncar 11 +Pejakov 61 +Kacanski 86 +Milic 48 +Pejic 92 +Rodic 81 +Popadic 65 +Miloradovic 22 +Milovanovic 58 +Novakovic 42 +Rasomon 86 +Pejakov 9 +Kovacevic 17 +Kovac 80 +Maletkovic 11 +Milovanovic 23 +Gregorovic 19 +Djukic 99 +Tanaskovic 94 +Preradovic 93 +Papic 55 +Francisko 24 +Nedeljkov 30 +Tanaskovic 62 +Tanaskovic 93 +Radovic 98 +Nemanjic 83 +Radovic 36 +Pavicevic 31 +Vidovic 62 +Gregorovic 62 +Tanaskovic 74 +Tanaskovic 97 +Markovic 61 +Milic 89 +Malinovic 2 +Pavicevic 74 +Francisko 73 +Nemanjic 63 +Savic 48 +Rasomon 72 +Maric 76 +Stojanovic 74 +Pavicevic 5 +Vidovic 76 +Budimirovic 79 +Dejanovic 59 +Stojanovic 49 +Filipovic 15 +Jeftic 8 +Kovac 53 +Papic 20 +Mandic 5 +Jeftic 76 +Maric 49 +Rasomon 84 +Stojanovic 29 +Jeftic 88 +Ostojic 75 +Meseldzija 57 +Francisko 75 +Pejakov 60 +Lazarevic 15 +Vidovic 43 +Lazarevic 36 +Novakovic 23 +Milic 60 +Pavlovic 100 +Stojanovic 5 +Pap 100 +Tarabic 80 +Lazarevic 82 +Ristic 71 +Malinovic 15 +Savic 85 +Kacanski 61 +Popovic 32 +Budimirovic 8 +Stojkovic 97 +Budimirovic 42 +Marjanovic 8 +Jeftic 39 +Horvat 95 +Jugovic 80 +Radovic 80 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4 +Budimirovic 1 +Lazarevic 3 +Malinovic 7 +Tarabic 7 +Malinovic 50 +Radovic 85 +Savic 22 +Nemanjic 8 +Vidovic 88 +Gregorovic 27 +Milovac 63 +Loncar 57 +Ostojic 28 +Kovac 28 +Pejic 29 +Lazarevic 67 +Jugovic 73 +Maletkovic 75 +Ivanic 22 +Jugovic 32 +Curcic 49 +Tanaskovic 81 +Lazarevic 19 +Gilam 29 +Tanaskovic 34 +Marjanovic 98 +Pejakov 70 +Jovanovic 4 +Stojkovic 62 +Brkic 76 +Djukic 46 +Vidovic 75 +Papic 86 +Pavicevic 94 +Papic 23 +Radovic 11 +Stojanovic 10 +Loncar 29 +Popadic 75 +Lazarevic 26 +Savic 67 +Kovac 94 +Jugovic 5 +Tanaskovic 84 +Francisko 51 +Pavicevic 93 +Stojanovic 8 +Orlovic 97 +Dejanovic 68 +Ognjenovic 62 +Markovic 80 +Milanovic 45 +Savic 65 +Kovacevic 8 +Tarabic 24 +Pejakov 46 +Nikolic 50 +Lazarevic 49 +Avramovic 42 +Orlovic 13 +Stojanovic 28 +Novakovic 98 +Popovic 91 +Gilam 9 +Dragic 47 +Maric 77 +Jovanovic 43 +Avramovic 77 +Marjanovic 73 +Tanaskovic 1 +Francisko 40 +Kovacevic 2 +Curcic 33 +Markovic 64 +Popovic 92 +Dragic 62 +Gilam 49 +Meseldzija 49 +Gregorovic 49 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