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| author | Doni Pracner <quinnuendo@gmail.com> | |
| Sat, 7 Nov 2015 20:25:16 +0000 (21:25 +0100) | ||
| committer | Doni Pracner <quinnuendo@gmail.com> | |
| Sat, 7 Nov 2015 20:25:16 +0000 (21:25 +0100) |
18 files changed:
| Hash/Gadjanje.java | [new file with mode: 0644] | patch | blob |
| Hash/InfoTip.java | [new file with mode: 0644] | patch | blob |
| Hash/Kancelarija.java | [new file with mode: 0644] | patch | blob |
| Hash/OHashSet.java | [new file with mode: 0644] | patch | blob |
| Hash/Set.java | [new file with mode: 0644] | patch | blob |
| Hash/TestHash.java | [new file with mode: 0644] | patch | blob |
| Hash/XO.java | [new file with mode: 0644] | patch | blob |
| Hash/hash.pdf | [new file with mode: 0644] | patch | blob |
| Hash/hash.txt | [new file with mode: 0644] | patch | blob |
| Hash/kancelarije/t0.txt | [new file with mode: 0644] | patch | blob |
| Hash/kancelarije/t1.txt | [new file with mode: 0644] | patch | blob |
| Hash/kancelarije/t2.txt | [new file with mode: 0644] | patch | blob |
| Hash/mete/t0.txt | [new file with mode: 0644] | patch | blob |
| Hash/mete/t1.txt | [new file with mode: 0644] | patch | blob |
| Hash/mete/t2.txt | [new file with mode: 0644] | patch | blob |
| Hash/xo/t0.txt | [new file with mode: 0644] | patch | blob |
| Hash/xo/t1.txt | [new file with mode: 0644] | patch | blob |
| Hash/xo/t2.txt | [new file with mode: 0644] | patch | blob |
diff --git a/Hash/Gadjanje.java b/Hash/Gadjanje.java
--- /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
--- /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
--- /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
--- /dev/null
+++ b/Hash/OHashSet.java
@@ -0,0 +1,185 @@
+/**\r
+ * ADT skup realizovan otvorenih hashovanjem\r
+ * \r
+ * Modifikovana verzija za ilustracije i test program\r
+ */\r
+public class OHashSet<T> implements Set<T> {\r
+\r
+ private static final int DEFAULT_TABLE_SIZE = 101;\r
+\r
+ private static class Node {\r
+ Object value;\r
+ Node next;\r
+\r
+ public Node(Object value) {\r
+ this.value = value;\r
+ }\r
+ }\r
+\r
+ private Node[] table;\r
+\r
+ private int count;\r
+ private int[] tableCount;\r
+\r
+ public OHashSet() {\r
+ this(DEFAULT_TABLE_SIZE);\r
+ }\r
+\r
+ public OHashSet(int size) {\r
+ if (size <= 0)\r
+ throw new IllegalArgumentException(\r
+ "Velicina hash tabele ne moze biti negativna");\r
+\r
+ table = new Node[size];\r
+ tableCount = new int[size];\r
+ count = 0;\r
+ }\r
+\r
+ private int hash(T o) {\r
+ if (o == null)\r
+ throw new IllegalArgumentException(\r
+ "Hash funkcija se ne moze racunati za null objekat");\r
+\r
+ return Math.abs(o.hashCode()) % table.length;\r
+ }\r
+\r
+ /**\r
+ * Pretrazuje listu kolizija za datu vrednost hash funkcije (drugi argument\r
+ * metoda) trazeci element (prvi argument metoda).\r
+ * \r
+ * Metod vraca null ukoliko element ne postoji u tabeli, ili niz od dve\r
+ * reference: 1. prva referenca je referenca na trazeni element 2. druga\r
+ * referenca je referenca na element ispred trazenog elementa\r
+ */\r
+ private Node[] searchColissionChain(T element, int hashValue) {\r
+ Node current = table[hashValue];\r
+ Node prev = null;\r
+\r
+ while (current != null) {\r
+ if (current.value.equals(element)) {\r
+ Node[] ret = new Node[2];\r
+ ret[0] = current;\r
+ ret[1] = prev;\r
+ return ret;\r
+ }\r
+\r
+ prev = current;\r
+ current = current.next;\r
+ }\r
+\r
+ return null;\r
+ }\r
+\r
+ public boolean add(T element) {\r
+ int hashValue = hash(element);\r
+ Node[] n = searchColissionChain(element, hashValue);\r
+ if (n != null) {\r
+ return false;\r
+ }\r
+\r
+ Node newElement = new Node(element);\r
+ newElement.next = table[hashValue];\r
+ table[hashValue] = newElement;\r
+\r
+ count++;\r
+ tableCount[hashValue]++;\r
+ return true;\r
+ }\r
+\r
+ public boolean remove(T element) {\r
+ int hashValue = hash(element);\r
+ Node[] n = searchColissionChain(element, hashValue);\r
+ if (n == null)\r
+ return false;\r
+\r
+ if (n[0] == table[hashValue]) {\r
+ table[hashValue] = table[hashValue].next;\r
+ } else {\r
+ n[1].next = n[0].next;\r
+ }\r
+\r
+ count--;\r
+ tableCount[hashValue]--;\r
+ return true;\r
+ }\r
+\r
+ public boolean contains(T element) {\r
+ return searchColissionChain(element, hash(element)) != null;\r
+ }\r
+\r
+ public void print() {\r
+ for (int i = 0; i < table.length; i++) {\r
+ System.out.print("HashCode = " + i + ": ");\r
+\r
+ Node head = table[i];\r
+ if (head == null) {\r
+ System.out.println(" empty");\r
+ } else {\r
+ while (head != null) {\r
+ System.out.print("[" + head.value + "]");\r
+ head = head.next;\r
+ }\r
+ System.out.println();\r
+ }\r
+ }\r
+ }\r
+\r
+ public String toString() {\r
+ return "OHashSet; br elemenata " + getCount();\r
+ }\r
+\r
+ public int getCount() {\r
+ return count;\r
+ }\r
+\r
+ public int size() {\r
+ return getCount();\r
+ }\r
+\r
+ public double getChiSquare() {\r
+ double chi = 0.0;\r
+\r
+ if (count > 0 && table.length > 0) {\r
+ double avg = (double) count / table.length;\r
+ for (int i = 0; i < tableCount.length; i++) {\r
+ chi += (tableCount[i] - avg) * (tableCount[i] - avg) / avg;\r
+ }\r
+ }\r
+ return chi;\r
+ }\r
+\r
+ public double getPercentFull() {\r
+ if (tableCount.length == 0) {\r
+ return 0;\r
+ }\r
+\r
+ int filled = 0;\r
+\r
+ for (int i = 0; i < tableCount.length; i++) {\r
+ if (tableCount[i] > 0)\r
+ filled++;\r
+ }\r
+\r
+ return filled * 100.0 / tableCount.length;\r
+ }\r
+\r
+ public void printStats() {\r
+ System.out.printf("Elements : %3d%n", getCount());\r
+ System.out.printf("Percent full: %6.2f %n", getPercentFull());\r
+ System.out.printf("Chi square : %8.4f %n", getChiSquare());\r
+ System.out.printf("'Columns' : %3d%n", table.length);\r
+ }\r
+\r
+ @SuppressWarnings("unchecked")\r
+ public T someElement() {\r
+ if (count > 0) {\r
+ for (int i = 0; i < table.length; i++) {\r
+ Node head = table[i];\r
+ if (head != null) {\r
+ return (T) head.value;\r
+ }\r
+ }\r
+ }\r
+ return null;\r
+ }\r
+}\r
diff --git a/Hash/Set.java b/Hash/Set.java
--- /dev/null
+++ b/Hash/Set.java
@@ -0,0 +1,25 @@
+/**\r
+ * Specifikacija ADT skup\r
+ * \r
+ * @author svc\r
+ */\r
+public interface Set<T> {\r
+\r
+ /**\r
+ * Dodaje element u skup. \r
+ * Vraca false ukoliko element vec postoji u skupu \r
+ */\r
+ boolean add(T element);\r
+ \r
+ /**\r
+ * Brise element iz skupa. \r
+ * Vraca false ukoliko element ne postoji u skupu.\r
+ */\r
+ boolean remove(T element);\r
+ \r
+ /**\r
+ * Proverava da li je element u skupu.\r
+ */\r
+ boolean contains(T element);\r
+}\r
+\r
diff --git a/Hash/TestHash.java b/Hash/TestHash.java
--- /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<Object> 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<InfoTip> 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<InfoTip> 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
--- /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 (file)
index 0000000..4a1249a
Binary files /dev/null and b/Hash/hash.pdf differ
index 0000000..4a1249a
Binary files /dev/null and b/Hash/hash.pdf differ
diff --git a/Hash/hash.txt b/Hash/hash.txt
--- /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
--- /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
--- /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
+Dragic 89
+Maletkovic 41
+Milovanovic 19
+Ivanic 64
+Ognjenovic 52
+Maletkovic 69
+Milic 12
+Budimirovic 81
+Pejakov 88
+Radovic 19
+Radovic 86
+Milovanovic 52
+Malinovic 81
+Pavlovic 50
+Horvat 70
+Savic 47
+Milic 49
+Miloradovic 66
+Milanovic 70
+Stojkovic 56
+Kacanski 31
+Malinovic 52
+Avramovic 62
+Nikolic 78
+Tanaskovic 9
+Meseldzija 10
+Brkic 54
+Meseldzija 9
+Novakovic 50
+Popadic 13
+Kovac 10
+Djukic 57
+Stojkovic 20
+Radovic 36
+Francisko 88
+Popadic 47
+Radovic 18
+Milanovic 31
+Rodic 89
+Lazarevic 34
+Stojanovic 75
+Stojkovic 49
+Rodic 7
+Malinovic 38
+Lazarevic 93
+Preradovic 1
+Jugovic 76
+Markovic 20
+Milovanovic 90
+Kacanski 13
+Tarabic 98
+Meseldzija 44
+Pavicevic 2
+Pavlovic 29
+Djukic 24
+Jovovic 54
+Jovovic 74
+Tanaskovic 5
+Popovic 7
+Jovanovic 41
+Lazarevic 9
+Lazarevic 42
+Mandic 33
+Malinovic 82
+Rasomon 71
+Dragic 81
+Ognjenovic 59
+Orlovic 49
+Popovic 45
+Savic 79
+Ristic 36
+Ostojic 85
+Ostojic 66
+Radovic 49
+Meseldzija 63
+Avramovic 20
+Vidovic 100
+Ostojic 9
+Pejakov 29
+Jovovic 45
+Miloradovic 91
+Gilam 66
+Popadic 8
+Ognjenovic 32
+Jovovic 36
+Nikolic 8
+Nikolic 72
+Nemanjic 45
+Pavlovic 86
+Milovanovic 5
+Milanovic 93
+Mandic 56
+Pavlovic 49
+Dejanovic 17
+Rasomon 23
+Milic 10
+Nedeljkov 10
+Milovanovic 58
+Ostojic 96
+Milovanovic 98
+Milic 15
+Marjanovic 100
+Popadic 73
+Pejakov 8
+Dejanovic 44
+Savic 66
+Gilam 13
+Kovacevic 45
+Milovanovic 68
+Maletkovic 94
+Popovic 3
+Brkic 76
+Kacanski 3
+Gilam 40
+Kovac 20
+Jeftic 75
+Radovic 71
+Maletkovic 43
+Pejic 34
+Dragic 55
+Lazarevic 79
+Maric 75
+Marjanovic 62
+Stojkovic 11
+Ivanic 5
+Jovovic 72
+Horvat 87
+Rodic 81
+Pejakov 64
+Preradovic 17
+Ognjenovic 63
+Milic 34
+Rasomon 26
+Savic 58
+Orlovic 20
+Markovic 94
+Francisko 83
+Meseldzija 24
+Filipovic 65
+Ristic 37
+Brkic 100
+Avramovic 60
+Tanaskovic 16
+Malinovic 59
+Novakovic 33
+Ostojic 100
+Rodic 78
+Vidovic 56
+Avramov 90
+Stojanovic 20
+Vidovic 35
+Milic 21
+Meseldzija 24
+Papic 17
+Jeftic 33
+Kacanski 60
+Djukic 45
+Filipovic 65
+Mandic 1
+Gregorovic 31
+Stojanovic 80
+Ristic 93
+Jovovic 21
+Maric 98
+Kovac 41
+Jovovic 57
+Kovac 54
+Tarabic 23
+Ostojic 78
+Savic 47
+Nemanjic 95
+Malinovic 92
+Nemanjic 52
+Jovovic 68
+Nemanjic 51
+Pejakov 57
+Gregorovic 42
+Brkic 80
+Ognjenovic 19
+Mandic 77
+Papic 37
+Nikolic 81
+Vidovic 49
+Jugovic 65
+Avramov 30
+Maletkovic 41
+Miloradovic 70
+Jeftic 1
+Nedeljkov 97
+Milanovic 39
+Meseldzija 53
+Gregorovic 76
+Brkic 39
+Pavlovic 77
+Milovanovic 76
+Stojkovic 64
+Ognjenovic 100
+Loncar 69
+Ognjenovic 85
+Rodic 23
+Popadic 54
+Milovac 27
+Tanaskovic 79
+Francisko 71
+Vidovic 24
+Stojkovic 56
+Jugovic 24
+Filipovic 66
+Nedeljkov 95
+Loncar 69
+Milic 73
+Stojkovic 61
+Nikolic 28
+Pap 56
+Pejic 46
+Stojanovic 85
+Gregorovic 95
+Tarabic 1
+Maric 81
+Tarabic 73
+Vidovic 1
+Novakovic 66
+Gregorovic 95
+Dejanovic 81
+Jovanovic 2
+Milovanovic 15
+Horvat 70
+Tarabic 66
+Pap 39
+Dragic 31
+Curcic 95
+Pavlovic 14
+Jeftic 65
+Pavicevic 80
+Milic 53
+Dragic 64
+Popovic 16
+Milanovic 46
+Budimirovic 88
+Savic 62
+Jovanovic 32
+Stojkovic 52
+Gilam 58
+Nedeljkov 13
+Pavicevic 79
+Loncar 8
+Rasomon 17
+Brkic 36
+Tanaskovic 80
+Kovacevic 47
+Loncar 18
+Avramovic 88
+Ostojic 57
+Jeftic 54
+Papic 75
+Milic 16
+Milovac 46
+Loncar 50
+Nikolic 54
+Loncar 2
+Kovac 78
+Horvat 37
+Ognjenovic 83
+Tanaskovic 9
+Ognjenovic 85
+Rasomon 90
+Lazarevic 25
+Jugovic 69
+Brkic 36
+Orlovic 45
+Loncar 13
+Vidovic 93
+Maletkovic 86
+Avramovic 23
+Gregorovic 9
+Dejanovic 51
+Pavicevic 54
+Avramov 45
+Budimirovic 50
+Vidovic 98
+Radovic 42
+Milic 30
+Kacanski 10
+Novakovic 2
+Maric 1
+Avramovic 52
+Jovovic 17
+Pejic 7
+Milic 29
+Stojanovic 95
+Loncar 40
+Orlovic 82
+Papic 22
+Maric 65
+Mandic 85
+Kacanski 66
+Rasomon 84
+Markovic 86
+Gilam 96
+Rodic 76
+Kovacevic 32
+Jovanovic 8
+Pavlovic 32
+Jovovic 7
+Ristic 84
+Miloradovic 56
+Nikolic 38
+Ognjenovic 96
+Popovic 61
+Marjanovic 95
+Ostojic 33
+Djukic 27
+Djukic 20
+Loncar 34
+Pejic 27
+Maric 11
+Marjanovic 38
+Preradovic 26
+Pejic 58
+Orlovic 57
+Radovic 13
+Savic 52
+Francisko 56
+Radovic 69
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\ No newline at end of file
diff --git a/Hash/kancelarije/t2.txt b/Hash/kancelarije/t2.txt
--- /dev/null
+++ b/Hash/kancelarije/t2.txt
@@ -0,0 +1,10000 @@
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\ No newline at end of file
diff --git a/Hash/mete/t0.txt b/Hash/mete/t0.txt
--- /dev/null
+++ b/Hash/mete/t0.txt
@@ -0,0 +1,10 @@
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\ No newline at end of file
diff --git a/Hash/mete/t1.txt b/Hash/mete/t1.txt
--- /dev/null
+++ b/Hash/mete/t1.txt
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diff --git a/Hash/mete/t2.txt b/Hash/mete/t2.txt
--- /dev/null
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\ No newline at end of file
diff --git a/Hash/xo/t0.txt b/Hash/xo/t0.txt
--- /dev/null
+++ b/Hash/xo/t0.txt
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\ No newline at end of file
diff --git a/Hash/xo/t1.txt b/Hash/xo/t1.txt
--- /dev/null
+++ b/Hash/xo/t1.txt
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diff --git a/Hash/xo/t2.txt b/Hash/xo/t2.txt
--- /dev/null
+++ b/Hash/xo/t2.txt
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