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Jun 14, 20120 likes159 views

9.1 Algoritmizace úlohy, vlastnosti algoritmu
Žák dovede:
vysvětlit pojem algoritmus a jeho základní vlastnosti;
algoritmizovat jednoduchou úlohu.

Algoritmus je :
Algoritmus je přesný návod či postup, kterým lze vyřešit daný typ úlohy. Pojem algoritmu se nejčastěji
objevuje při programování, kdy se jím myslí teoretický princip řešení problému (oproti přesnému zápisu v
konkrétním programovacím jazyce). Obecně se ale algoritmus může objevit v jakémkoli jiném vědeckém
odvětví. Jako jistý druh algoritmu se může chápat i např. kuchařský recept. V užším smyslu se slovem
algoritmus rozumí takové postupy, které splňují některé silnější požadavky:

Vlastnosti algoritmů
Konečnost (finitnost)
Každý algoritmus musí skončit v konečném počtu kroků. Tento počet kroků může být
libovolně velký (podle rozsahu a hodnot vstupních údajů), ale pro každý jednotlivý vstup
musí být konečný. Postupy, které tuto podmínku nesplňují, se mohou nazývat výpočetní
metody. Speciálním příkladem nekonečné výpočetní metody je reaktivní proces, který
průběžně reaguje s okolním prostředím. Někteří autoři však mezi algoritmy zahrnují i
takovéto postupy.
Obecnost (hromadnost, masovost, univerzálnost)
Algoritmus neřeší jeden konkrétní problém (např. „jak spočítat 3×7“), ale obecnou třídu
obdobných problémů (např. „jak spočítat součin dvou celých čísel“), má širokou množinu
možných vstupů.
Determinovanost
Každý krok algoritmu musí být jednoznačně a přesně definován; v každé situaci musí být
naprosto zřejmé, co a jak se má provést, jak má provádění algoritmu pokračovat, takže
pro stejné vstupy dostaneme pokaždé stejné výsledky. Protože běžný jazyk obvykle
neposkytuje naprostou přesnost a jednoznačnost vyjadřování, byly pro zápis algoritmů
navrženy programovací jazyky, ve kterých má každý příkaz jasně definovaný význam.
Vyjádření výpočetní metody v programovacím jazyce se nazývá program. Některé
algoritmy ale determinované nejsou, pravděpodobnostní algoritmy v sobě mají zahrnutu
náhodu.
Výstup (resultativnost)
Algoritmus má alespoň jeden výstup, veličinu, která je v požadovaném vztahu k zadaným
vstupům, a tím tvoří odpověď na problém, který algoritmus řeší (algoritmus vede od
zpracování hodnot k výstupu)
Elementárnost
Algoritmus se skládá z konečného počtu jednoduchých (elementárních) kroků.

V praxi jsou proto předmětem zájmu hlavně takové algoritmy, které jsou v nějakém smyslu
kvalitní. Takové algoritmy splňují různá kritéria, měřená např. počtem kroků potřebných pro běh
algoritmu, jednoduchost, efektivitu či eleganci. Problematikou efektivity algoritmů, tzn.
metodami, jak z několika známých algoritmů řešících konkrétní problém vybrat ten nejlepší, se
zabývají odvětví informatiky nazývané algoritmická analýza a teorie složitosti.

Příklad
Určete aritmetický průměr ze tří čísel, která postupně uložíte příkazem čti (proměnná)
do proměnných x,y,z.

začátek
čti (x) ;
čti (y) ;
čti (z) ;
součet := x + y + z;
průměr := součet / 3 ;
konec

Citovaná literatura
1. neznámý. neznámý. informační technologie. [Online] 14. 6 2012. [Citace: 14.. 6. 2012.]
http://student.oapion.cz/ict/uvod/algoritmy.htm.

2. —. wikipedia. wikipedia. [Online] 14.. 6. 2012. [Citace: 14.. 6. 2012.]
http://cs.wikipedia.org/wiki/Algoritmus.

http://cs.wikipedia.org/wiki/Algoritmus

http://student.oapion.cz/ict/uvod/algoritmy.htm

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1. 9.1 Algoritmizace úlohy, vlastnosti algoritmu Žák dovede: vysvětlit pojem algoritmus a jeho základní vlastnosti; algoritmizovat jednoduchou úlohu. Algoritmus je : Algoritmus je přesný návod či postup, kterým lze vyřešit daný typ úlohy. Pojem algoritmu se nejčastěji objevuje při programování, kdy se jím myslí teoretický princip řešení problému (oproti přesnému zápisu v konkrétním programovacím jazyce). Obecně se ale algoritmus může objevit v jakémkoli jiném vědeckém odvětví. Jako jistý druh algoritmu se může chápat i např. kuchařský recept. V užším smyslu se slovem algoritmus rozumí takové postupy, které splňují některé silnější požadavky: Vlastnosti algoritmů Konečnost (finitnost) Každý algoritmus musí skončit v konečném počtu kroků. Tento počet kroků může být libovolně velký (podle rozsahu a hodnot vstupních údajů), ale pro každý jednotlivý vstup musí být konečný. Postupy, které tuto podmínku nesplňují, se mohou nazývat výpočetní metody. Speciálním příkladem nekonečné výpočetní metody je reaktivní proces, který průběžně reaguje s okolním prostředím. Někteří autoři však mezi algoritmy zahrnují i takovéto postupy. Obecnost (hromadnost, masovost, univerzálnost) Algoritmus neřeší jeden konkrétní problém (např. „jak spočítat 3×7“), ale obecnou třídu obdobných problémů (např. „jak spočítat součin dvou celých čísel“), má širokou množinu možných vstupů. Determinovanost Každý krok algoritmu musí být jednoznačně a přesně definován; v každé situaci musí být naprosto zřejmé, co a jak se má provést, jak má provádění algoritmu pokračovat, takže pro stejné vstupy dostaneme pokaždé stejné výsledky. Protože běžný jazyk obvykle neposkytuje naprostou přesnost a jednoznačnost vyjadřování, byly pro zápis algoritmů navrženy programovací jazyky, ve kterých má každý příkaz jasně definovaný význam. Vyjádření výpočetní metody v programovacím jazyce se nazývá program. Některé algoritmy ale determinované nejsou, pravděpodobnostní algoritmy v sobě mají zahrnutu náhodu. Výstup (resultativnost) Algoritmus má alespoň jeden výstup, veličinu, která je v požadovaném vztahu k zadaným vstupům, a tím tvoří odpověď na problém, který algoritmus řeší (algoritmus vede od zpracování hodnot k výstupu) Elementárnost Algoritmus se skládá z konečného počtu jednoduchých (elementárních) kroků. V praxi jsou proto předmětem zájmu hlavně takové algoritmy, které jsou v nějakém smyslu kvalitní. Takové algoritmy splňují různá kritéria, měřená např. počtem kroků potřebných pro běh algoritmu, jednoduchost, efektivitu či eleganci. Problematikou efektivity algoritmů, tzn. metodami, jak z několika známých algoritmů řešících konkrétní problém vybrat ten nejlepší, se zabývají odvětví informatiky nazývané algoritmická analýza a teorie složitosti.

2. Příklad Určete aritmetický průměr ze tří čísel, která postupně uložíte příkazem čti (proměnná) do proměnných x,y,z. začátek čti (x) ; čti (y) ; čti (z) ; součet := x + y + z; průměr := součet / 3 ; konec Citovaná literatura 1. neznámý. neznámý. informační technologie. [Online] 14. 6 2012. [Citace: 14.. 6. 2012.] http://student.oapion.cz/ict/uvod/algoritmy.htm. 2. —. wikipedia. wikipedia. [Online] 14.. 6. 2012. [Citace: 14.. 6. 2012.] http://cs.wikipedia.org/wiki/Algoritmus. http://cs.wikipedia.org/wiki/Algoritmus http://student.oapion.cz/ict/uvod/algoritmy.htm

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