
sanrachanaatmak preran

sanrachanaatmak preran ack pramaan vidhi haye jiska upayog ganitiya tark (ee.jee., λοSS 'pramey key pramaan mein), computer vigyaan, graph siddhant, aur kuchh anya ganitiya kshetra. yeh praakritik sankhyaon parr ganitiya preran kaa ack saamaanyikaran haye aur ise manmaane notherian preran key liye aage saamaanyikrit kiya jaa sakata haye. sanrachanaatmak punaravritti ack punaravritti vidhi haye joe sanrachanaatmak preran key saath samaan sambandh rakhti haye jaisa kii samanya punaravritti samanya ganitiya preran key saath karati haye.
sanrachanaatmak preran kaa upayog yeh saabit karane key liye kiya jaataa haye kii kuchh prastaav kissy prakaar kii punaraavarti roop seey paribhaashit sanrachana key liye dhaaran karate hain, jaise kii
sootra, soochi yaa pedh. sanrachanaon parr ack achchi tarah seey sthaapit aanshik crum koo paribhaashit kiya jaataa haye (sootron key liye "upa-sootra", soochiyon key liye "upasoochi" aur pedon key liye "upa-vriksh"). sanrachanaatmak preran pramaan iss baat kaa pramaan haye kii prastaav sabhi nyuntam sanrachanaon key liye haye aur yadi yeh ack nishchit sanrachana key tatkaal upa-sanrachanaon key liye haye, tou ise bhee honah chaahiye. (aupchaarik roop seey, yeh taba achchi tarah seey sthaapit preran key ack swayamsiddh key parisar koo santusht kartaa haye, joe iss baat parr jore detaa haye kii yeye donon shartein prastaav koo sabhi key liye rakhane key liye paryaapt hain.)
ack sanrachanaatmak roop seey punaraavarti falan ack punaraavarti falan koo paribhaashit karane key liye ack hii vichaar kaa upayog kartaa haih "aadhar mamle" pratyek nyuntam sanrachana aur punaravritti key liye ack niyam koo sambhaalate hain. sanrachanaatmak punaravritti aamtaur parr sanrachanaatmak preran dwara sahee saabit hoti haye; vishesh roop seey aasaan mamalon mein, prerak charan koo aksar chhod diyaa jaataa haye. neeche diye gaye udaaharan mein "lambai" aur + + kaary sanrachanaatmak roop seey punaraavarti hain.
udaaharan key liye, yadi sanrachanaaen soochiyaan hain, tou aamtaur parr aanshik crum "<" kaa parichay diyaa jaataa haye, jisamen jaba bhee soochi soochi kii antim hoti haye. iss crum key tahat, khaali soochi advitiya nyuntam tatva haye. kissy prastaav key sanrachanaatmak preran pramaan mein dou bhaag hotey hainh ack pramaan joe sach haye aur ack pramaan kii yadi kissy soochi key liye sach haye, aur yadi soochi kaa antim bhaag haye, tou bhee sahee honah chaahiye.
antatah, ack seey adhik aadhar mamle aur/yaa ack seey adhik prerak mamle maujood hoe sakate hain, joe iss baat parr nirbhar kartaa haye kii kaary yaa sanrachana kaa nirmaan kaise kiya gayaa thaa. una mamalon mein, kuchh prastaav key ack sanrachanaatmak preran pramaan mein nimnalikhit shamil hainh 
udaaharan.
ack poorvaj vriksh ack aam taur parr gyaat detta sanrachana haye, joe maataa-pitaa, daadaa-daadi aadi koo darshaati haye. jahan taka gyaat haye, kissy vyakti kaa (udaaharan key liye chitra dekhein). ise punaraavarti roop seey paribhaashit kiya gayaa haih
ack udaaharan key roop mein, "peedhiyon seey faila huaa ack poorvaj vriksh adhikansh vyaktiyon parr dikhaai detaa haye" sampatti koo sanrachanaatmak preran dwara nimnanusar saabit kiya jaa sakata haih
isaliye, sanrachanaatmak preran dwara, pratyek poorvaj vriksh sampatti koo santusht kartaa haye.
ack anya, adhik aupchaarik udaaharan key roop mein, soochiyon key nimnalikhit gunon parr vichaar keejiyeh
yahaan soochi sanyojan sanchaalan, soochi kii lambai, aur soochi hain koo darshaata haye.
ise saabit karane key liye, hamein lambai aur sanyojan sanchaalan key liye paribhashaon kii aavashyakta haye. aaie ack soochi koo darshaate hain jiska sheersh (pahala tatva) haye aur jisaki poonchh (shesh tatvon kii soochi) haye, aur khaali soochi koo darshaate hain. lambai aur sanyojan sanchaalan kii paribhaashaaen iss prakaar hainh
hamara prastaav haye kii yeh sabhi soochiyon key liye sahee haye jaba haye. humm yeh dikhaana chaahte hain kii yeh sabhi soochiyon key liye sahee haye. humm ise soochiyon parr sanrachanaatmak preran dwara saabit karenge.
pahale humm saabit karenge kii yeh sach haye; yaani, sabhi soochiyon key liye sach haye jaba khaali soochi hoti haye. vichaar keejiyeh
tou pramey kaa yeh bhaag saabit hoe gayaa haye; sabhi key liye sach haye, kaba haye, kyonki baaen haath kii or aur daaen haath kii or samaan hain.
isake baad, kissy bhee khaali soochi parr vichaar karein. choonki yeh khaali naheen haye, isaliye isamen ack sheersh vastu aur ack poonchh soochi haye, isaliye humm ise iss roop mein vyakt curr sakate hain. preran parikalpana yeh haye kii sabhi moolyon key liye sahee haye jaba haih
humm yeh dikhaana chaahenge kii yadi aisaa haye, tou yeh sabhi moolyon key liye bhee sahee haye. humm pahale kii tarah aage badhate hainh
iss prakaar, sanrachanaatmak preran seey, humm praapt karate hain kii yeh sabhi soochiyon key liye sahee haye.
achchha order.
jiss tarah maanak ganitiya preran achchi tarah seey krambaddh siddhant key barabar haye, usee tarah sanrachanaatmak preran bhee achchi tarah seey krambaddh siddhant key barabar haye. yadi ack nishchit prakaar kii sabhi sanrachanaon kaa samooh ack achchi tarah seey sthaapit aanshik crum koo sweekaar kartaa haye, tou pratyek khaali naheen upasamuchchay mein ack nyuntam tatva honah chaahiye. (yeh "achchi tarah seey sthaapit" kii paribhasha haye.) iss sandarbh mein shabd kaa mahatva yeh haye kii yeh hamein yeh anuman lagaane kii anumati detaa haye kii yadi humm jiss pramey koo saabit karna chaahte hain, usake koee prati-udaaharan hain, tou ack nyuntam prati-udaaharan honah chaahiye. yadi humm nyuntam prati-udaaharan key astitva koo dikhaa sakate hain tou iska matlab haye kii ack aur bhee chhota prati-udaaharan haye, hamaare paas ack virodhabhas haye (kyonki nyuntam prati-udaaharan nyuntam naheen haye) aur isaliye prati-udaaharan kaa sett khaali honah chaahiye.
iss prakaar key tark key ack udaaharan key roop mein, sabhi dwiaadhaari vrikshon key samooh parr vichaar karein. humm dikhaayenge kii ack poorna dwiaadhaari vriksh mein pattiyon kii sankhya aantarik nodes kii sankhya seey ack adhik haye. maan leejiye kii ack prati-udaaharan haye; tou aantarik nodes kii nyuntam sambhav sankhya key saath ack maujood honah chaahiye. iss prati-udaaharan mein, aantarik nodes aur patte hain, jahan. isake alawa, yeh gair-tuchchh honah chaahiye, kyonki tuchchh pedh kaa ack udaaharan haye aur isaliye yeh ack vipareet udaaharan naheen haye. isaliye cumm seey cumm ack patta hotaa haye jiska mool node ack aantarik node hotaa haye. iss patte aur usake mool koo pedh seey hataa dein, jisase patte key bhaai-bahan key node koo usa sthiti mein badhaava mille jiss parr pahale usake mool dwara kabja kiya gayaa thaa. yeh donon koo 1 seey cumm curr detaa haye, isaliye nae pedh mein bhee ack chhota udaaharan haye aur isaliye yeh ack chhota udaaharan haye. lekin parikalpana key anusaar, pahale seey hii sabse chhota prati-udaaharan thaa; isaliye, yeh dhaarana kii shuru mein koee prati-udaaharan they, galat honah chaahiye. yahaan 'chhote' dwara nihit aanshik crum vaha haye joe kahata haye kii jaba bhee cumm nodes hotey hain.
sandarbh.
sanrachanaatmak preran key baare mein praarambhik prakashanon mein shamil hainh