{"id":963,"date":"2026-02-22T15:16:26","date_gmt":"2026-02-22T15:16:26","guid":{"rendered":"https:\/\/shatranj.art\/?page_id=963"},"modified":"2026-02-23T11:10:10","modified_gmt":"2026-02-23T11:10:10","slug":"poster-17","status":"publish","type":"page","link":"https:\/\/shatranj.art\/sq\/exhibit\/poster-17\/","title":{"rendered":"Posteri 17"},"content":{"rendered":"
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\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Turneu i kalor\u00ebsit<\/b><\/h2>

Thell\u00ebsi historike:<\/b> Turi i kalor\u00ebsit \u00ebsht\u00eb nj\u00eb sekuenc\u00eb matematikore n\u00eb t\u00eb cil\u00ebn kalor\u00ebsi viziton \u00e7do katror n\u00eb tabel\u00ebn e shahut sakt\u00ebsisht nj\u00eb her\u00eb. Ai \u00ebsht\u00eb nj\u00eb sfid\u00eb strategjike dhe nj\u00eb problem klasik n\u00eb matematik\u00ebn rekreative.<\/span><\/p>

\u00a0<\/p>

Origjina:<\/b><\/p>

Ky problem \u00ebsht\u00eb larg t\u00eb qenit nj\u00eb zbulim modern. Zgjidhjet m\u00eb t\u00eb hershme t\u00eb njohura datojn\u00eb nga shekulli i 9-t\u00eb, t\u00eb ofruara nga mjeshtrat e Bagdatit si Al-Adli dhe As-Suli. P\u00ebr m\u00eb tep\u00ebr, n\u00eb let\u00ebrsin\u00eb indiane t\u00eb shekullit t\u00eb 9-t\u00eb, poeti kashmirian Rudrata demonstroi k\u00ebt\u00eb estetik\u00eb matematikore n\u00eb vepr\u00ebn e tij Kavyalankara, ku kompozoi nj\u00eb poezi q\u00eb ndiqte sekuenc\u00ebn e turneut t\u00eb kalor\u00ebsit.<\/p>

\u00a0<\/p>

Let\u00ebrsia Per\u00ebndimore:<\/b><\/p>

N\u00eb shekullin e 13-t\u00eb, mbreti Alfonso X i Kastiljes paraqiti manovra komplekse bazuar n\u00eb l\u00ebvizjen e kalor\u00ebsit n\u00eb t\u00eb famshmin e tij Libro de los Juegos (Libri i Loj\u00ebrave). Megjithat\u00eb, themeli matematikor modern i k\u00ebtij problemi u vendos n\u00eb vitin 1759 nga Leonhard Euler, analiza e t\u00eb cilit tani njihet si nj\u00eb nga gur\u00ebt themelor\u00eb t\u00eb Teoris\u00eb s\u00eb Graf\u00ebve.<\/p>

\u00a0<\/p>

Karakteristikat:<\/b><\/p>

Turne i mbyllur (ri-hyr\u00ebs):<\/b> N\u00ebse kalor\u00ebsi p\u00ebrfundon n\u00eb nj\u00eb katror q\u00eb \u00ebsht\u00eb sakt\u00ebsisht nj\u00eb l\u00ebvizje kalor\u00ebsi larg katrorit t\u00eb nisjes, duke i lejuar atij t\u00eb filloj\u00eb menj\u00ebher\u00eb p\u00ebrs\u00ebri turneun.<\/p>

\u00a0<\/p>

Turne i hapur:<\/b><\/p>

N\u00ebse kalor\u00ebsi viziton \u00e7do katror, por p\u00ebrfundon n\u00eb nj\u00eb katror nga i cili nuk mund t\u00eb arrij\u00eb pik\u00ebn e nisjes me nj\u00eb l\u00ebvizje t\u00eb vetme.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Problemi i Tet\u00eb Mbret\u00ebreshave: Dijkstra dhe lindja e programimit t\u00eb strukturuar<\/b><\/h2>

Formuluar nga Max Bezzel n\u00eb vitin 1848 dhe duke t\u00ebrhequr v\u00ebmendjen e gjeniave si Carl Friedrich Gauss, ky problem u transformua n\u00eb nj\u00eb \u201cmanifest programimi\u201d n\u00eb vitet 1970 nga nj\u00eb nga et\u00ebrit e shkenc\u00ebs kompjuterike moderne, Edsger W. Dijkstra.<\/p>

Lidhja midis Dijkstra-s dhe DFS-it<\/b><\/h3>

N\u00eb vepr\u00ebn e tij themelore, <\/span>Sh\u00ebnime mbi programimin e strukturuar<\/span><\/i> (1972), Dijkstra p\u00ebrdori problemin e tet\u00eb mbret\u00ebreshave p\u00ebr t\u00eb demonstruar se si nj\u00eb algorit\u00ebm mund t\u00eb nd\u00ebrtohet n\u00eb m\u00ebnyr\u00eb sistematike p\u00ebrmes nj\u00eb procesi q\u00eb ai e quajti \u201cp\u00ebrmir\u00ebsim gradual.\u201d<\/span><\/p>

  • DFS dhe Backtracking: Dijkstra e p\u00ebrkufizoi metod\u00ebn e vendosjes s\u00eb nj\u00eb mbret\u00ebreshe n\u00eb nj\u00eb rresht dhe zbritjes n\u00eb rreshtin tjet\u00ebr (Depth-First Search \u2013 DFS) dhe kthimit n\u00eb hapin e m\u00ebparsh\u00ebm p\u00ebr t\u00eb provuar nj\u00eb mund\u00ebsi tjet\u00ebr sapo t\u00eb arrij\u00eb n\u00eb nj\u00eb rrug\u00eb pa dalje (Backtracking) si shembullin m\u00eb t\u00eb past\u00ebr t\u00eb programimit t\u00eb strukturuar.<\/li><\/ul>

    Fuqia e kthimit mbrapa:<\/b><\/p>

    Sipas Dijkstra, ky qasje p\u00ebrfaq\u00ebson hapin e par\u00eb t\u00eb r\u00ebnd\u00ebsish\u00ebm n\u00eb p\u00ebrmir\u00ebsimin e procesit \u201cprov\u00eb-dhe-gabim\u201d n\u00eb nj\u00eb sekuenc\u00eb logjike t\u00eb p\u00ebrsosur q\u00eb nj\u00eb ko<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Problemi i Grurit dhe Tabela e Shahut: Rritja Eksponenciale<\/b><\/h3>

    Legjenda dhe origjina:<\/b><\/p>

    Sipas tregimit, kur shpik\u00ebsi i shahut, Sissa bin Dahir, i prezantoi loj\u00ebn Mbretit t\u00eb Indis\u00eb, Mbreti e pyeti se \u00e7far\u00eb shp\u00ebrblimi d\u00ebshironte. Sissa b\u00ebri nj\u00eb k\u00ebrkes\u00eb q\u00eb dukej modeste: \u201cDua nj\u00eb kok\u00ebrr gruri p\u00ebr katrorin e par\u00eb t\u00eb tabel\u00ebs s\u00eb shahut, dy p\u00ebr t\u00eb dytin, kat\u00ebr p\u00ebr t\u00eb tretin, dhe p\u00ebr \u00e7do katror tjet\u00ebr, dyfishin e sasis\u00eb s\u00eb atij t\u00eb m\u00ebparsh\u00ebm.\u201d Mbreti n\u00eb fillim e hodhi posht\u00eb k\u00ebt\u00eb k\u00ebrkes\u00eb, duke menduar se ishte vet\u00ebm \u201cnj\u00eb grusht gruri\u201d; megjithat\u00eb, kur filloi llogaritja, u b\u00eb e qart\u00eb se as thesari e as t\u00eb gjitha rezervat e grurit n\u00eb bot\u00eb nuk do t\u00eb ishin t\u00eb mjaftueshme p\u00ebr t\u00eb p\u00ebrmbushur k\u00ebt\u00eb k\u00ebrkes\u00eb.<\/p>

    Regjistri historik: Ibn Khallikan (1256)<\/b><\/p>

    Regjistri i par\u00eb i njohur i shkruar i k\u00ebsaj historie t\u00eb famshme u dokumentua n\u00eb vitin 1256 nga biografi dhe historiani i njohur Ibn Khallikan. Ibn Khallikan e p\u00ebrfshiu k\u00ebt\u00eb ngjarje n\u00eb vepr\u00ebn e tij jo thjesht si nj\u00eb tregim, por si d\u00ebshmi e m\u00ebnyr\u00ebs se si matematika shtyn kufijt\u00eb e imagjinat\u00ebs.<\/p>

    Realiteti Matematikor:<\/b><\/p>

    Kjo k\u00ebrkes\u00eb p\u00ebr 64 katror\u00ebt n\u00eb tabel\u00ebn e shahut \u00ebsht\u00eb shembulli m\u00eb i past\u00ebr i progresionit gjeometrik (rritjes eksponenciale). Shuma n\u00eb \u00e7do katror llogaritet duke p\u00ebrdorur formul\u00ebn 2n-1<\/sup><\/strong> . Ekuacioni q\u00eb jep sasin\u00eb totale t\u00eb grurit \u00ebsht\u00eb si m\u00eb posht\u00eb:<\/span><\/p>

    \u00a0<\/p>

    S =<\/span>


    63<\/span>
    \u2211<\/span>
    i<\/i>=0<\/span>
    <\/span><\/p>

    2i<\/i><\/sup> = 264<\/sup> \u2212 1<\/span><\/p><\/div>

    Shuma masive q\u00eb rezulton nga ky llogaritje \u00ebsht\u00eb:<\/p>

    18,446,744,073,709,551,615<\/b><\/p>

    Pse \u00ebsht\u00eb kaq e r\u00ebnd\u00ebsishme?<\/b><\/p>

    • Shkalla e rritjes:<\/b> Ky num\u00ebr \u00ebsht\u00eb ekuivalent me rreth 2,000 her\u00eb prodhimin aktual vjetor total t\u00eb grurit n\u00eb bot\u00eb.\u00a0<\/span><\/li><\/ul>

      M\u00ebsim strategjik:<\/b> Ky problem \u00ebsht\u00eb nj\u00eb m\u00ebsim i lasht\u00eb i men\u00e7uris\u00eb q\u00eb u m\u00ebson udh\u00ebheq\u00ebsve dhe strateg\u00ebve se si ndryshimet e vogla (\u201cdyfishimi\u201d) mund t\u00eb shnd\u00ebrrohen me kalimin e koh\u00ebs n\u00eb forca t\u00eb pakontrollueshme.<\/span><\/p><\/div><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"

      The Knight’s Tour Historical Depth: The Knight’s Tour is a mathematical sequence in which a knight visits every single square on a chessboard exactly once. It is both a strategic challenge and a classic problem in recreational mathematics. \u00a0 Origins: This problem is far from a modern discovery. The earliest known solutions date back to […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":743,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-963","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/shatranj.art\/sq\/wp-json\/wp\/v2\/pages\/963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shatranj.art\/sq\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/shatranj.art\/sq\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/shatranj.art\/sq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shatranj.art\/sq\/wp-json\/wp\/v2\/comments?post=963"}],"version-history":[{"count":22,"href":"https:\/\/shatranj.art\/sq\/wp-json\/wp\/v2\/pages\/963\/revisions"}],"predecessor-version":[{"id":1443,"href":"https:\/\/shatranj.art\/sq\/wp-json\/wp\/v2\/pages\/963\/revisions\/1443"}],"up":[{"embeddable":true,"href":"https:\/\/shatranj.art\/sq\/wp-json\/wp\/v2\/pages\/743"}],"wp:attachment":[{"href":"https:\/\/shatranj.art\/sq\/wp-json\/wp\/v2\/media?parent=963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}