algoridm

mahattam samaapavartak (HCF) nikaalne ke liye yooklid ke algoridm ka flochaart

ganit, sanganan tatha anya vidhaaon mein kisi kaarya ko karne ke liye aavashyak charanon ke samooh ko kalan vidhi (algoridm) kehte hai.

kalan vidhi ko kisi spasht roop se paaribhaashit gananaatmak samasya ka samaadhaan karne ke aujaar (tool) ke roop mein bhi samjha ja sakta hai. us samasya ka input aur aautaput saamaanya bhaasha mein varnit kiye gaye rahate hain; iske samaadhaan ke roop mein kalan vidhi, kramavaar dhang se bataata hai ki yeh input/aautaput sambandh kis prakaar se praapt kiya ja sakta hai.

kuchh udaaharan :

1) kuchh sankhyaayein bina kisi kram ke di hui hain; inhein aarohi kram (ascending order) mein kaise sajaayeinge?

2) do poornaank sankhyaaen di hui hain ; unka mahattam samaapavartak (Highest Common Factor) kaise nikaaleinge ?

anukram

kuchh prasiddh kalanavidhiyaaain

  • yuklid ki kalanavidhi
  • farmat ki kalanavidhi
  • lun (Luhn) ki kalanavidhi
  • shautan ki kalanavidhiyaaain (algorithms for sorting)
  • kampreshan ki kalanavidhiyaaain (algorithms for compression)
  • tri-sarch algoridm (min-max tatha alpha-beta)
  • kriptograafi ke algoridm

itihaas

praacheen sanskrut ganit granthon mein bahut se alagoridm shlok ke roop mein diye gaye hain. udaaharan ke liye nimnalikhit kalanavidhi dhanaat/rinaatmak sankhyaaon ke gunan/bhaajan ka niyam bataata hai-

svayorasvayo s‍aavam vadh: svarnaghaate.
kshayo bhaagahaare api chaivam niruktam..

anvaya - svayo: (+*+), asvayo: (-*-) vadh: svam (+) (bhavati|) sv-rin-ghaate (+*-) vadh: kshaya: (-) (bhavati)| bhaagahaare (/) api ch evam niruktam.

arth : do dhanaatmak ya do rinaatmak sankhyaaon ka gunanafal dhanaatmak hota hai. dhanaatmak rinaatmak sankhyaaon ka gunan rinaatmak hota hai. yahi baat bhaajan (division) par bhi laagoo hoti hai.

inhein bhi dekhein

baahari kadiyaaain