{"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\/lt\/exhibit\/poster-17\/","title":{"rendered":"17 plakatas"},"content":{"rendered":"
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Riterio kelion\u0117<\/b><\/h2>

Istorinis gylis:<\/b> Riterio kelion\u0117 - tai matematin\u0117 seka, kai riteris lygiai vien\u0105 kart\u0105 aplanko kiekvien\u0105 \u0161achmat\u0173 lentos kvadrat\u0105. Tai ir strateginis i\u0161\u0161\u016bkis, ir klasikinis pramogin\u0117s matematikos u\u017edavinys.<\/span><\/p>

\u00a0<\/p>

Kilm\u0117:<\/b><\/p>

\u0160i problema toli gra\u017eu n\u0117ra \u0161iuolaikinis atradimas. Pirmieji \u017einomi sprendimai datuojami IX a., kuriuos pateik\u0117 Bagdado meistrai, tokie kaip Al-Adli ir As-Suli. Be to, IX a. Indijos literat\u016broje Ka\u0161myro poetas Rudrata \u0161i\u0105 matematin\u0119 estetik\u0105 pademonstravo savo k\u016brinyje \"Kavyalankara\", kur suk\u016br\u0117 eil\u0117ra\u0161t\u012f, kuriame sek\u0117 riterio kelion\u0117s sek\u0105.<\/p>

\u00a0<\/p>

Vakar\u0173 literat\u016bra:<\/b><\/p>

XIII a. Kastilijos karalius Alfonsas X savo garsiojoje \"\u017daidim\u0173 knygoje\" (Libro de los Juegos) apra\u0161\u0117 sud\u0117tingus manevrus, pagr\u012fstus riterio judesiais. Ta\u010diau \u0161iuolaikin\u012f matematin\u012f pagrind\u0105 \u0161iai problemai 1759 m. pad\u0117jo Leonhardas Euleris, kurio analiz\u0117 dabar pripa\u017e\u012fstama kaip vienas i\u0161 graf\u0173 teorijos kertini\u0173 akmen\u0173.<\/p>

\u00a0<\/p>

Savyb\u0117s:<\/b><\/p>

U\u017edaras (pakartotinis) turas:<\/b> Jei riteris atsiduria aik\u0161tel\u0117je, kuri yra lygiai vienu riterio \u0117jimu toliau nuo pradin\u0117s aik\u0161tel\u0117s, jis gali i\u0161 karto prad\u0117ti kelion\u0119 i\u0161 naujo.<\/p>

\u00a0<\/p>

Atviras turas:<\/b><\/p>

Jei raitelis aplanko kiekvien\u0105 kvadrat\u0105, bet atsiduria tokioje aik\u0161t\u0117je, i\u0161 kurios vienu \u0117jimu negali pasiekti pradinio ta\u0161ko.<\/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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8 karalieni\u0173 problema: Dijkstra ir strukt\u016brizuoto programavimo gimimas<\/b><\/h2>

1848 m. Maxo Bezzelio i\u0161kelta ir toki\u0173 genij\u0173 kaip Carlas Friedrichas Gaussas d\u0117mesio sulaukusi problema XX a. a\u0161tuntajame de\u0161imtmetyje vieno i\u0161 \u0161iuolaikin\u0117s informatikos pradinink\u0173 Edsgerio W. Dijkstros buvo paversta \u201cprogramavimo manifestu\u201d.<\/p>

Dijkstros ir DFS ry\u0161ys<\/b><\/h3>

Savo pagrindiniame veikale, <\/span>Pastabos apie strukt\u016brin\u012f programavim\u0105<\/span><\/i> (1972 m.) Dijkstra pasinaudojo 8 Queens problema, kad parodyt\u0173, kaip galima sistemingai kurti algoritm\u0105, taikant proces\u0105, kur\u012f jis pavadino \u201claipsni\u0161ku tobulinimu\u201d.\u201d<\/span><\/p>

  • DFS ir atsilikimas: Dijkstra apibr\u0117\u017e\u0117 metod\u0105, pagal kur\u012f dama dama \u012f eil\u0119 ir einama \u012f kit\u0105 (angl. Depth-First Search - DFS), o patekus \u012f aklaviet\u0119 gr\u012f\u017etama \u012f ankstesn\u012f \u017eingsn\u012f ir bandoma rasti kit\u0105 galimyb\u0119 (angl. Backtracking), kaip gryniausi\u0105 strukt\u016brizuoto programavimo pavyzd\u012f.<\/li><\/ul>

    Gr\u012f\u017eimo atgal galia:<\/b><\/p>

    Pasak Dijkstros, \u0161is metodas yra pirmasis svarbus etapas tobulinant \u201cbandym\u0173 ir klaid\u0173\u201d proces\u0105 iki nepriekai\u0161tingos login\u0117s sekos, kuri\u0105 galima<\/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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    Kvie\u010di\u0173 ir \u0161achmat\u0173 lentos problema: eksponentinis augimas<\/b><\/h3>

    Legenda ir kilm\u0117:<\/b><\/p>

    Pasak pasakojimo, kai \u0161achmat\u0173 i\u0161rad\u0117jas Sisa bin Dahiras pristat\u0117 \u017eaidim\u0105 Indijos karaliui, karalius paklaus\u0117, kokio atlygio jis nor\u0117t\u0173. Sisa i\u0161sak\u0117 i\u0161 pa\u017ei\u016bros kukl\u0173 pra\u0161ym\u0105: \u201cU\u017e pirm\u0105j\u012f \u0161achmat\u0173 lentos kvadrat\u0105 noriu vieno kvie\u010dio gr\u016bdo, u\u017e antr\u0105j\u012f - dviej\u0173, u\u017e tre\u010di\u0105j\u012f - keturi\u0173, o u\u017e kiekvien\u0105 paskesn\u012f kvadrat\u0105 - dvigubai daugiau nei u\u017e ankstesn\u012fj\u012f\u201d. Karalius i\u0161 prad\u017ei\u0173 atmet\u0117 \u0161\u012f pra\u0161ym\u0105, manydamas, kad tai tik \u201csauja kvie\u010di\u0173\u201d, ta\u010diau prad\u0117jus skai\u010diuoti tapo ai\u0161ku, kad nei i\u017edo, nei viso pasaulio kvie\u010di\u0173 atsarg\u0173 neu\u017eteks \u0161iam reikalavimui patenkinti.<\/p>

    Istorinis \u012fra\u0161as: Ibn Khallikan (1256 m.)<\/b><\/p>

    Pirmasis \u017einomas ra\u0161ytinis \u0161ios garsios istorijos \u0161altinis - 1256 m. \u017eymaus biografo ir istoriko Ibn Challikano. Ibn Challikanas \u012ftrauk\u0117 \u0161\u012f \u012fvyk\u012f \u012f savo darb\u0105 ne tik kaip pasakojim\u0105, bet ir kaip \u012frodym\u0105, kaip matematika i\u0161ple\u010dia vaizduot\u0117s ribas.<\/p>

    Matematin\u0117 tikrov\u0117:<\/b><\/p>

    \u0160is pra\u0161ymas, pateiktas 64 \u0161achmat\u0173 lentos kvadratams, yra gryniausias geometrin\u0117s progresijos (eksponentinio augimo) pavyzdys. Suma kiekviename kvadrat\u0117lyje apskai\u010diuojama pagal formul\u0119 2n-1<\/sup><\/strong> . Lygtis, pagal kuri\u0105 apskai\u010diuojamas bendras kvie\u010di\u0173 kiekis, yra tokia:<\/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>

    Atlikus \u0161\u012f skai\u010diavim\u0105 gautas did\u017eiulis skai\u010dius:<\/p>

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

    Kod\u0117l tai taip svarbu?<\/b><\/p>

    • Augimo mastas:<\/b> \u0160is skai\u010dius prilygsta ma\u017edaug 2 000 kart\u0173 didesnei dabartinei bendrai metinei kvie\u010di\u0173 gamybai pasaulyje.\u00a0<\/span><\/li><\/ul>

      Strategin\u0117 pamoka:<\/b> \u0160i problema - tai senov\u0117s i\u0161minties pamoka, kuri moko vadovus ir strategus, kaip ma\u017ei poky\u010diai (\u201cpadvigub\u0117jimas\u201d) laikui b\u0117gant gali virsti nekontroliuojamomis j\u0117gomis.<\/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\/lt\/wp-json\/wp\/v2\/pages\/963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shatranj.art\/lt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/shatranj.art\/lt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/shatranj.art\/lt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shatranj.art\/lt\/wp-json\/wp\/v2\/comments?post=963"}],"version-history":[{"count":22,"href":"https:\/\/shatranj.art\/lt\/wp-json\/wp\/v2\/pages\/963\/revisions"}],"predecessor-version":[{"id":1443,"href":"https:\/\/shatranj.art\/lt\/wp-json\/wp\/v2\/pages\/963\/revisions\/1443"}],"up":[{"embeddable":true,"href":"https:\/\/shatranj.art\/lt\/wp-json\/wp\/v2\/pages\/743"}],"wp:attachment":[{"href":"https:\/\/shatranj.art\/lt\/wp-json\/wp\/v2\/media?parent=963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}