{"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\/sk\/exhibit\/poster-17\/","title":{"rendered":"plag\u00e1t 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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Rytierske turn\u00e9<\/b><\/h2>

Historick\u00e1 h\u013abka:<\/b> Jazdcova cesta je matematick\u00e1 postupnos\u0165, pri ktorej jazdec nav\u0161t\u00edvi ka\u017ed\u00e9 pol\u00ed\u010dko na \u0161achovnici presne raz. Je to strategick\u00e1 v\u00fdzva a z\u00e1rove\u0148 klasick\u00fd probl\u00e9m rekrea\u010dnej matematiky.<\/span><\/p>

\u00a0<\/p>

P\u00f4vod:<\/b><\/p>

Tento probl\u00e9m nie je ani z\u010faleka novodob\u00fdm objavom. Najstar\u0161ie zn\u00e1me rie\u0161enia poch\u00e1dzaj\u00fa z 9. storo\u010dia a poskytli ich bagdadsk\u00ed majstri ako Al-Adli a As-Suli. Okrem toho v indickej literat\u00fare 9. storo\u010dia ka\u0161m\u00edrsky b\u00e1snik Rudrata demon\u0161troval t\u00fato matematick\u00fa estetiku vo svojom diele Kavyalankara, kde zlo\u017eil b\u00e1se\u0148, ktor\u00e1 sledovala postupnos\u0165 rytierskej cesty.<\/p>

\u00a0<\/p>

Z\u00e1padn\u00e1 literat\u00fara:<\/b><\/p>

V 13. storo\u010d\u00ed kast\u00edlsky kr\u00e1\u013e Alfonz X. vo svojej sl\u00e1vnej knihe Libro de los Juegos (Kniha hier) uviedol zlo\u017eit\u00e9 man\u00e9vre zalo\u017een\u00e9 na pohybe rytiera. Modern\u00fd matematick\u00fd z\u00e1klad probl\u00e9mu v\u0161ak polo\u017eil v roku 1759 Leonhard Euler, ktor\u00e9ho anal\u00fdza je dnes uzn\u00e1van\u00e1 ako jeden zo z\u00e1kladn\u00fdch kame\u0148ov te\u00f3rie grafov.<\/p>

\u00a0<\/p>

Charakteristika:<\/b><\/p>

Uzavret\u00e1 (opakovan\u00e1) prehliadka:<\/b> Ak jazdec skon\u010d\u00ed na pol\u00ed\u010dku, ktor\u00e9 je presne o jeden \u0165ah vzdialen\u00e9 od v\u00fdchodiskov\u00e9ho pol\u00ed\u010dka, m\u00f4\u017ee okam\u017eite za\u010da\u0165 cestu znova.<\/p>

\u00a0<\/p>

Otvoren\u00e1 prehliadka:<\/b><\/p>

Ak jazdec nav\u0161t\u00edvi ka\u017ed\u00e9 pole, ale skon\u010d\u00ed na poli, z ktor\u00e9ho sa nem\u00f4\u017ee dosta\u0165 do v\u00fdchodiskov\u00e9ho bodu jedn\u00fdm \u0165ahom.<\/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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Probl\u00e9m 8 kr\u00e1\u013eovien: Dijkstra a zrod \u0161trukt\u00farovan\u00e9ho programovania<\/b><\/h2>

Tento probl\u00e9m, ktor\u00fd v roku 1848 polo\u017eil Max Bezzel a ktor\u00fd up\u00fatal pozornos\u0165 tak\u00fdch g\u00e9niov, ako bol Carl Friedrich Gauss, transformoval v 70. rokoch 20. storo\u010dia jeden z otcov modernej informatiky Edsger W. Dijkstra do \u201cprogram\u00e1torsk\u00e9ho manifestu\u201d.<\/p>

Spojenie medzi Dijkstrov\u00fdm syst\u00e9mom a syst\u00e9mom DFS<\/b><\/h3>

Vo svojom z\u00e1sadnom diele, <\/span>Pozn\u00e1mky k \u0161trukt\u00farovan\u00e9mu programovaniu<\/span><\/i> (1972) Dijkstra pou\u017eil probl\u00e9m 8 kr\u00e1\u013eovien na demon\u0161tr\u00e1ciu toho, ako mo\u017eno systematicky vytv\u00e1ra\u0165 algoritmus prostredn\u00edctvom procesu, ktor\u00fd nazval \u201cpostupn\u00e9 vylep\u0161ovanie\u201d.\u201d<\/span><\/p>

  • DFS a sp\u00e4tn\u00e9 sledovanie: Dijkstra definoval met\u00f3du kladenia kr\u00e1\u013eovnej do radu a zostupu k \u010fal\u0161iemu (Depth-First Search - DFS) a n\u00e1vratu k predch\u00e1dzaj\u00facemu kroku, aby sa pok\u00fasil o in\u00fa mo\u017enos\u0165, ke\u010f naraz\u00ed na slep\u00fa uli\u010dku (Backtracking), ako naj\u010distej\u0161\u00ed pr\u00edklad \u0161trukt\u00farovan\u00e9ho programovania.<\/li><\/ul>

    Sila sp\u00e4tn\u00e9ho sledovania:<\/b><\/p>

    Pod\u013ea Dijkstru tento pr\u00edstup predstavuje prv\u00fd v\u00fdznamn\u00fd m\u00ed\u013enik v zdokona\u013eovan\u00ed procesu \u201cpokus-omyl\u201d do bezchybnej logickej postupnosti, ktor\u00fa spol<\/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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    Probl\u00e9m p\u0161enice a \u0161achovnice: exponenci\u00e1lny rast<\/b><\/h3>

    Legenda a p\u00f4vod:<\/b><\/p>

    Pod\u013ea pr\u00edbehu, ke\u010f vyn\u00e1lezca \u0161achu Sissa bin Dahir predstavil hru indick\u00e9mu kr\u00e1\u013eovi, kr\u00e1\u013e sa ho op\u00fdtal, ak\u00fa odmenu by chcel. Sissa vyslovil zdanlivo skromn\u00fa po\u017eiadavku: \u201cChcem jedno zrnko p\u0161enice za prv\u00e9 pol\u00ed\u010dko \u0161achovnice, dve za druh\u00e9, \u0161tyri za tretie a za ka\u017ed\u00e9 \u010fal\u0161ie pol\u00ed\u010dko dvojn\u00e1sobok predch\u00e1dzaj\u00faceho.\u201d Kr\u00e1\u013e t\u00fato po\u017eiadavku spo\u010diatku odmietol, preto\u017ee si myslel, \u017ee ide len o \u201chrs\u0165 p\u0161enice\u201d; ke\u010f v\u0161ak za\u010dal po\u010d\u00edta\u0165, uk\u00e1zalo sa, \u017ee na splnenie tejto po\u017eiadavky by nesta\u010dila ani pokladnica, ani v\u0161etky svetov\u00e9 z\u00e1soby p\u0161enice.<\/p>

    Historick\u00fd z\u00e1znam: Ibn Challik\u00e1n (1256)<\/b><\/p>

    Prv\u00fd zn\u00e1my p\u00edsomn\u00fd z\u00e1znam tohto sl\u00e1vneho pr\u00edbehu zaznamenal v roku 1256 zn\u00e1my \u017eivotopisec a historik Ibn Challik\u00e1n. Ibn Challik\u00e1n t\u00fato udalos\u0165 zahrnul do svojho diela nielen ako pr\u00edbeh, ale aj ako d\u00f4kaz toho, ako matematika pos\u00fava hranice predstavivosti.<\/p>

    Matematick\u00e1 realita:<\/b><\/p>

    T\u00e1to po\u017eiadavka na 64 pol\u00ed\u010dok na \u0161achovnici je naj\u010distej\u0161\u00edm pr\u00edkladom geometrickej progresie (exponenci\u00e1lneho rastu). Suma na ka\u017edom pol\u00ed\u010dku sa vypo\u010d\u00edta pod\u013ea vzorca 2n-1<\/sup><\/strong> . Rovnica ur\u010duj\u00faca celkov\u00e9 mno\u017estvo p\u0161enice je nasledovn\u00e1:<\/span><\/p>

    \u00a0<\/p>

    S =<\/span>


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

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

    Obrovsk\u00e9 \u010d\u00edslo, ktor\u00e9 z tohto v\u00fdpo\u010dtu vypl\u00fdva, je:<\/p>

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

    Pre\u010do je to tak\u00e9 d\u00f4le\u017eit\u00e9?<\/b><\/p>

    • Rozsah rastu:<\/b> Toto \u010d\u00edslo zodpoved\u00e1 pribli\u017ene 2000-n\u00e1sobku s\u00fa\u010dasnej celkovej ro\u010dnej produkcie p\u0161enice na svete.\u00a0<\/span><\/li><\/ul>

      Strategick\u00e1 lekcia:<\/b> Tento probl\u00e9m je starod\u00e1vnou lekciou m\u00fadrosti, ktor\u00e1 u\u010d\u00ed vodcov a strat\u00e9gov, ako sa mal\u00e9 zmeny (\u201czdvojenie\u201d) m\u00f4\u017eu \u010dasom zmeni\u0165 na nekontrolovate\u013en\u00e9 sily.<\/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\/sk\/wp-json\/wp\/v2\/pages\/963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shatranj.art\/sk\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/shatranj.art\/sk\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/shatranj.art\/sk\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shatranj.art\/sk\/wp-json\/wp\/v2\/comments?post=963"}],"version-history":[{"count":22,"href":"https:\/\/shatranj.art\/sk\/wp-json\/wp\/v2\/pages\/963\/revisions"}],"predecessor-version":[{"id":1443,"href":"https:\/\/shatranj.art\/sk\/wp-json\/wp\/v2\/pages\/963\/revisions\/1443"}],"up":[{"embeddable":true,"href":"https:\/\/shatranj.art\/sk\/wp-json\/wp\/v2\/pages\/743"}],"wp:attachment":[{"href":"https:\/\/shatranj.art\/sk\/wp-json\/wp\/v2\/media?parent=963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}