
packing samasya

packing samasya haah ganitatil optimization samasyancha eka varg aahe jyamadhye vastoo containermadhye ekatra pack karnyacha prayatna karane samavisht aahe. ektar ekach container shakya titkya datpane pack karane kinwa shakya titkya qamee container vaparoon serve vastoo pack karane heey uddisht aahe. yapaiki anek samasya vastavik jivanatil packaging, sathavan aanee vahatukichya samasyanshi sambandhit asoo shakatat. pratyek packing samasyemadhye duheri aavaran samasya asate, jee containerchya pratyek bhagala purnapane jhakanyasathi samaan vastunpaiki kitee aavashyak aahet, jithe vastoonna overlap karanyachi parvanagi aahe heey vicharte.
dabyachya packing samasyemadhye, tumhala dile jaateh
sahasa packing vastoo aanee itar vastoo kinwa containerchya bhintinmadhye paraspar naan julata asane aavashyak aahe. kahee prakaranmadhye, packing kamal ghanata asalelya ekach containerchi rachana shodhane haah uddesh aahe. adhik samanyatah, serve vastoo shakya titkya qamee containermadhye gundalane haah uddesh aahe. kahee prakaranmadhye (ekmekanshi aanee/kinwa containerchya seames) vastunche ativyapti karane shakya aahe parantu teey qamee kele pahije.
amaryad jaaget packing.
yapaiki anek samasya, jevha containercha aakar serve dishanni vadhavala jaato, tevha anant euclidean jaaget shakya titkya daat vastoonchya packing samasyeshi samatulya hotat. hii samasya anek vaidnyanik shakhanshi sambandhit aahe aanee tyavar lakshaniy laksh denyat aale aahe. thomas callister helsney yogya siddha karnyapurvi shekado varshanni keplarchya andajane golanchya packingsathi eka ishtatam upay gruheet dharala. lambvartulakar, chatushkon, trikoni (teen sakaratmak aksh-samantar kiranansah ghananche sanyojan) aanee asman-golakar diamers platonic aanee archemedian ghanpadarthansah itar anek aakaranni laksh vedhale aahe.
vartulanchi shatkon packing.
yaa samasya vartul packing prameyatil kalpananpeksha ganitiyadrushtya vegalya aahet. sambandhit vartul packing samasya prushthbhagavaril packing vartulanshi sambandhit aahe, kadachit vegvegalya aakaranchi, udaharanarth samtal kinwa goal.
itar parimananmadhil vartulachya samkakshanna kadhihi ekapeksha mothya parimananmadhye sampoorn karyakshamatene bharata yet nahee (eka-aayami vishvat, vartul analogue fakt done bindu asatat). mhanjech, jarr tumhi fakt vartule pack karat asal tarr nehmich naan vaparleli jaaga asel. shatakoni packing haah vartulanna pack karnyacha sarvat karyaksham marg, andaje 91 takke karyakshamta nirman karato.
uchch parimananmadhye goal packing.
teen aayamanmadhye, jawalun bharalelya sanrachana golanchi sarvottam "jaali" packing detat aanee serve packingspacky sarvottam asalyache manale jaate. teen aayamanmadhye 'sadhya' goal packings ('sadhya' chee kaljipurvak vyakhya kelee jaat aahe) nauu sambhavya paribhashit packing aahet. 8-aayami eae8 jaali aanee 24-aayami jantu jaali dekhil tyanchya sambandhit vastavik aayami jaaget ishtatam asalyache siddha jhaale aahe.
teen aayamanmadhye platonic ghan padarthanche packing.
trimiteey jaaga purnapane bharnyasathi ghananchi vyavastha sahajpane kelee jaau shakate, ghan madhmash heey sarvat naisargik packing aahe. itar konatehi platonic ghan swatahun jaaga tayar karoo shakat nahee, parantu kahee prathamik parinam dnyat aahet. tetrahedra kiman 85 takke packing sadhya karoo shakate. niyamit dodekahedramadhil sarvottam packingpacky eka varr namood kelelya chehara-kendrit ghan (eff. see. see.) jaalivar aadharit aahe.
tetrahedra aanee aktahedra ekatra tetrahedral-aktahedral madhmashya mhanoon olakhalya jaanarya vyavasthet serve jaaga bharoo shakatat.
yadruchchik packings sthanik sudharana paddhatinche sanyojan karnare anukaran asey soochit karate qee icosahedra, dodekahedra aanee aktahedra sathee jaali packing serve packing vyapak vargat ishtatam aahet.
trimiteey containermadhye packing.
vegvegalya cuboidmadhye cuboidmadhye.
dilelya vastoochya ghanpadarthanchya sanchala pack karnyasathi aavashyak asalelya ghanpatra containerchi (dabe) kiman sankhya nishchit qaraa. pack karnyasathi aayatakruti cuboids pratyek akshavar 90 anshanni firavale jaau shakatat.
euclidean chendumadhye goal qaraa.
sarvat lahan chendu shodhanyatil samasya mhanje, khulya ekak chendula tyachya aat pack kele jaau shakate, yache uttar sootra 1 asalyas-aayami euclidean jaaget aanee konatehi nirbandh naan thevata anant-aayami hilbert jaaget sope aanee sampoorn aahe. samanya samasyecha swad denyasathi yethe tapshilvar varnan karane yogya aahe. yaa prakaranat, jodichya dishene sparshika ekak chendunche eka sanrachana upalabdh aahe. kendranna niyamit sootra _ 3 aayami simplexchya sheersh sootra _ 2 varr dhaar 2 saha thewa; heey orthonormal aadharapasun sahajpane lakshat yete. eka chhotya gananevarun asey disun yete qee barricenterpasoon pratyek shirobinduche antar sootra 4 aahe. shivay, jagechya itar konatyahi binduche "kiman" eka shirobindupasoonche antar jaast asane aavashyak aahe. chenduchya samaveshachya babatit, sootra _ 2 varr kendrit ughade ekak chendu trijya sootra _ 6 chya chendumadhye samavisht kele jaatat, jeey yaa sanrachanesathi kiman aahe.
heey sanrachana ishtatam aahe heey darshavinyasathi, sootra 7 heey bindu sutravar kendrit trijyechya chendumadhye asalelya vighatit khulya ekak chenduche kendra asoo dya. pratyek sutrasathi sambandhit sootra 12 madhye sootra 11 ghet asalelya maryadit sanch sootra 9 madheel sootra 10 madheel nakashacha vichar qaraa. kaaran serve sootra 14, sootra 15 sathee haah nakasha 1-lipsitz aahe aanee kirzbron prameyadvare too 1-lipsitz nakashaparyant vistarato joou jaagtik staravar paribhashit keela aahe; visheshtah, eka bindu sootra 16 astitvat aahe, jyamadhye serve sutrasathi sootra 18 aahe, tyamule teey sootra dekhil 19 aahe. heey darshavite qee jarr aanee fakt sootra 20 asel tarr chenduchya trijyet vighatit ekak khule chendu aahet. laksh dya qee anant-aayami hilbert spacemadhye asey soochit karate qee chenduchya trijyechya asankhya vighatit ekak aahet, udaharanarth, jarr chenduchya trijyechya aat eka unitche sootra, jethe chenduchya trijyechya aat eka sootra 23 aahe, aanee jarr chenduchya trijyechya aat eka sootra 23 aahe, tarr heey dekhil sootra 19 aahe. heey darshavate qee jarr aanee fakt sootra 20 asel tarach chenduchya trijyet vighatit ekak khule chendu aahet. laksh dya qee shivay, sootra _ 25 sathee, trijyechya chenduchya aat vighatit khulya ekak chendunchi kamal sankhya sootra _ 26 aahe.
eka ghankshetratil goal.
dilelya vyasachya golakar vastunchi sankhya nishchit qaraa jee _ 27 yaa aakarachya sootrachya ghanamadhye pack kelee jaau shakate.
eka nalkamadhye eksarkhe goal.
dilelya trijyasah nalakachi kiman unchi nishchit qaraa jee trijyechya samaan golanchi bharr ghalel. chhotya trijyesathi goal kramane sanrachanechi vyavastha karatat, jyanna stambhakar sanrachana mhanatat.
golanmadhye bahubhuj.
dilelya aakaracha eksaman, ekak aakarman polyhedrala vyapanari kiman trijya nishchit qaraa.
dvimiteey containermadhye packing.
dvimiteey packing samasyanchya anek prakarancha abhyas keela gela aahe. adhik mahitisathi link keleli prushthe pahaa.
vartulanchi packing.
tumhala ekak vartule dilee jaatat aanee tyanna shakya titkya lahan containermadhye pack karave lagate. anek prakarchya containercha abhyas keela gela aaheh
chaukoni packing.
tumhala ekak chauras dile jaatat aanee tyanna shakya titkya lahan containermadhye pack karave lagate, jithe containercha prakar badalatoh
sambandhit kshetre.
tiling kinwa tessellation samasyanmadhye, antar nasave kinwa ativyapti nasavi. yaa prakarchya anek kodimadhye aayatakruti kinwa bahubhakshi bhaganna mothya aayatakruti kinwa itar chauras aakarat gundalane samavisht asate.
konatyahi antar kinwa ativyaptishivay aayatakanmadhye (ghankshetra) farasbandi aayatakanvar (aanee ghankshetra) mahattvapoorn pramey aaheth
bahupadi jhukanyacha abhyas mukhyatve done prakarchya samasyanshi sambandhit aaheh sarvasamaveshak farshansah aayatakruti tyle karane aanee pratyek 'aine'-ominopaiki eka aayatakrutimadhye pack karane.
dusya prakarche eka abhijat kode mhanje serve baaraa panchkoniyanna 3 × 20,4 × 15,5 × 12 kinwa 6 × 10 aakarachya aayatakanmadhye mandane.
aniyamit vastunchi packing.
aniyamit vastunche packing hii eka samasya aahe jee bund swarupachya upayayojananna yogya prakare udhar dett nahee; tathapi, vyavharik paryavaran vidnyanala lagoo karane khoop mahatvache aahe. udaharanarth, aniyamit aakarache matiche kann aakar aanee aakar badalat asalyane vegvegale pack karatat, jyamule vanaspatinchya prajatinna mulanchya rachnanshi julavun ghenyasathi aanee matimadhye panyachi halchal karnyas anumati denyasathi mahattvapoorn parinam hotat.
dilelya chauras containermadhye bahubhujancha dilela sanch basoo shakato qee nahee heey tharvanyachi samasya vastavik astitvavadi siddhantasathi purn asalyache darshavile gele aahe.
bahya duve.
anek kode pustake tasech ganiteey niyatkalikanmadhye packing samasyanvaril lekh asatat.