From 10dccbe7121b8b5df14f2084b5d46d6814a8deee Mon Sep 17 00:00:00 2001 From: Filip Znachor Date: Fri, 14 Apr 2023 00:29:41 +0200 Subject: [PATCH] =?UTF-8?q?P=C5=99id=C3=A1n=C3=AD=208.=20p=C5=99edn=C3=A1?= =?UTF-8?q?=C5=A1ky=20z=20PPA2?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- KIV PPA2/Prednaska08.md | 119 ++++++++++++++++++++++ KIV PPA2/_assets/implementace-tabulky.png | Bin 0 -> 185916 bytes 2 files changed, 119 insertions(+) create mode 100644 KIV PPA2/Prednaska08.md create mode 100644 KIV PPA2/_assets/implementace-tabulky.png diff --git a/KIV PPA2/Prednaska08.md b/KIV PPA2/Prednaska08.md new file mode 100644 index 0000000..5b7d420 --- /dev/null +++ b/KIV PPA2/Prednaska08.md @@ -0,0 +1,119 @@ +# Tabulka + +- vztah mezi množinou klíčů a množinou hodnot (jako například slovník) +- asociativní abstraktní datová struktura + +### Klíč + +- diskrétní datový typ: + - `int` + - `String` + - ne `double`! +- nejdůležitější vlastnost - možnost zjistit, zda jsou si dvě hodnoty rovny +- při vhodné implementaci vyhodnocení rovnosti může být klíčem i složitější struktura (např. množina čísel $\{0, 1, 2\}$ je shodná s $\{2, 0, 1\}$, může být tedy klíčem) + +### Hodnota + +- libovolný datový typ nebo reference na instanci + +### Vlastnosti + +- není určeno pořadí prvků +- některým klíčům nemusí být přiřazena žádná hodnota + +### Operace + +- přidání přiřazení (klíč + hodnota) +- získání hodnoty pro daný klíč +- zjištění existence hodnoty přiřazené danému klíči +- zrušení přířazení (odebrání klíče) +- získání všech klíčů s přiřazenou hodnotou + +Ideálně by měly mít všechny (kromě všech klíčů) složitost $\Theta(1)$ + +### Implementace tabulky + +**Tabulka s přímým adresováním** +- pole, kde index je klíč +- problém: + - často neznáme rozsah možnách klíčů + - počet přípustných klíčů může být velmi velký nebo nekonečný + - neřeší složitější klíče +- výhoda: splňuje $\Theta(1)$ + +**Reprezentace absence prvku** +- pomocí obalovací třídy (např. `Element`) +- ta obsahuje `value` s daty +- odlišíme tak neexistující klíč od `null`, `-1`, ... + +**Rozptylová tabulka** (hash table) +- hashovací funkce + - vstup: *klíč*, výstup: *index v poli* + - vlastnosti: + - hodnota 0 až délka pole -1 + - pro různé hodnoty různé klíče + - nelze vždy, počet klíčů může být větší než délka pole + - pro stejný klíč vrátí stejný index + +**Kolize** +- vložíme hodnotu s klíčem $k_1$, uloží se na index $H(k_1)$ +- vložíme další hodnotu s takovým klíčem $k_2$, že $H(k_1) = H(k_2)$ +- pozice v poli už je obsazena +- nedá se jim dost dobře bránit, musí se řešit + - do pole uložíme spojové struktury + - každý záznam v poli obsahuje hodnotu i klíč + - záznam bude obsahovat `next`, kam se dá případný další klíč s hodnotou + +![](implementace-tabulky.png) + +### Implementace operací + +- přidání prvku + - vložíme jej na začátek spojové struktury (nemusíme jí celou procházet) +- získání prvku + - procházíme `while` cyklem + - porovnáváme klíče - jeho instance musí být schopna rozhodnout o své významové shodnosti (`.equals()`) + +### Výpočetní složitost + +- přidání prvku: $\Theta(1)$ +- vybrání a odebrání prvku závisí na délce spojové struktury + - přidáno bylo $n$ prvků + - používá se pole o délce $m$ + - složitost tedy je $\Theta(n/m) = \Theta(n)$ + - **řešení**: + - omezit poměr $n/m$ (např. $n/m < 10$) + - po překročení limitu se data přesunou do větší struktury + - průměrná složitost je poté $\Theta(1)$ + +**Rozložení klíčů** +- známe-li rozložení klíčů, je potřeba mu přizpůsobit hashovací funkci +- pokud ne, funkce by měla záviset na všech částech klíče + - ne jen na prvním písmenu, poslední číslici, ... + +### Implementace v Javě + +- třída `HashMap` +- typové parametry `` (klíč) a `` (hodnota) + +**Metody** +- `void put(K key, V value)` +- `V get(K key)` +- `boolean containsKey(K key)` +- v průměrném případě $\mathcal O(1)$ + +**Rozptylová funkce** +- používá se `public int hashCode() {...}` na datovém typu +- výsledek může být libovolné číslo (java se postará o namapování na indexy pole) + +**Rovnost klíčů** +- používá se `boolean equals(Object o) {...}` + +Při implementaci `equals` a `hashCode` musíme dbát na jejich konzistenci! +- když `a.equals(b) == true`, pak `a.hashCode() == b.hashCode()` + - naopak to neplatí +- `a.equals(a)` musí vracet `true` +- když `a.equals(b) == true`, potom musí `b.equals(a) == true` + +**Třída `HashSet`** +- má pouze klíče - hodí se k efektivnímu nalezení duplicit \ No newline at end of file diff --git a/KIV PPA2/_assets/implementace-tabulky.png b/KIV PPA2/_assets/implementace-tabulky.png new file mode 100644 index 0000000000000000000000000000000000000000..db4b9bebce43370782c6793b1e1ca206dd5578c1 GIT binary patch literal 185916 zcmeFYWl&sg&^9;&g9Il8NN@`f2o~JkZE%7I3GOa~CTP%L!JWY&xD#B0ySvNaGT6uS zJl|WpwY9ZX`)_}2S4~aTsXnJp^?kbU?(4elFtCy|CK?eM006+0m61>d0Fa0P07PX} zgqJIPQgKG>4b^r4NCNN?V0{|2NSqV{fkF=v@cOSi;Y2>w=ze~-Mac0EC 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