{"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\/lv\/exhibit\/poster-17\/","title":{"rendered":"plak\u0101ts 17"},"content":{"rendered":"
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Bru\u0146inieka t\u016bre<\/b><\/h2>

V\u0113sturiskais dzi\u013cums:<\/b> Bru\u0146inieka ce\u013cojums ir matem\u0101tiska sec\u012bba, kur\u0101 bru\u0146inieks katru \u0161aha laukumu apmekl\u0113 tie\u0161i vienu reizi. Tas ir gan strat\u0113\u0123isks izaicin\u0101jums, gan klasiska atp\u016btas matem\u0101tikas probl\u0113ma.<\/span><\/p>

\u00a0<\/p>

Izcelsme:<\/b><\/p>

\u0160\u012b probl\u0113ma neb\u016bt nav m\u016bsdienu atkl\u0101jums. Agr\u0101kie zin\u0101mie risin\u0101jumi dat\u0113jami ar 9. gadsimtu, un tos sniedza t\u0101di Bagd\u0101des meistari k\u0101 Al-Adli un As-Suli. Turkl\u0101t 9. gadsimta indie\u0161u literat\u016br\u0101 Ka\u0161miras dzejnieks Rudrata demonstr\u0113ja \u0161o matem\u0101tisko est\u0113tiku sav\u0101 darb\u0101 Kavyalankara, kur vi\u0146\u0161 sacer\u0113ja dzejoli, kas sekoja bru\u0146inieka ce\u013cojuma sec\u012bbai.<\/p>

\u00a0<\/p>

Rietumu literat\u016bra:<\/b><\/p>

13. gadsimt\u0101 Kast\u012blijas karalis Alfonso X sav\u0101 slavenaj\u0101 Libro de los Juegos (Sp\u0113\u013cu gr\u0101mat\u0101) aprakst\u012bja sare\u017e\u0123\u012btus manevrus, kuru pamat\u0101 bija bru\u0146inieka kust\u012bbas. Tom\u0113r m\u016bsdienu matem\u0101tiskos pamatus \u0161ai probl\u0113mai 1759. gad\u0101 lika Leonhards Eulers, kura veikt\u0101 anal\u012bze tagad ir atz\u012bta par vienu no Grafu teorijas st\u016brakme\u0146iem.<\/p>

\u00a0<\/p>

Raksturojums:<\/b><\/p>

Sl\u0113gta (atk\u0101rtota) ekskursija:<\/b> Ja bru\u0146inieks fini\u0161\u0113 laukum\u0101, kas ir tie\u0161i vienu bru\u0146inieka g\u0101jienu att\u0101lum\u0101 no s\u0101kuma laukuma, tas var nekav\u0113joties s\u0101kt ce\u013cu no jauna.<\/p>

\u00a0<\/p>

Atkl\u0101t\u0101 t\u016bre:<\/b><\/p>

Ja bru\u0146inieks apmekl\u0113 visus laukumus, bet beidzas laukum\u0101, no kura ar vienu g\u0101jienu nevar sasniegt s\u0101kuma punktu.<\/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 Queens probl\u0113ma: Dijkstra un struktur\u0113t\u0101s programm\u0113\u0161anas dzim\u0161ana<\/b><\/h2>

\u0160o probl\u0113mu 1848. gad\u0101 izvirz\u012bja Makss Bezzels, piev\u0113r\u0161ot t\u0101du \u0123\u0113niju k\u0101 Karls Fr\u012bdrihs Gauss uzman\u012bbu, bet 20. gadsimta 70. gados viens no m\u016bsdienu datorzin\u0101tnes pamatlic\u0113jiem Edsgers Dikstra (Edsger W. Dijkstra) to p\u0101rveidoja par \u201cprogramm\u0113\u0161anas manifestu\u201d.<\/p>

Dijkstras un DFS saist\u012bba<\/b><\/h3>

Sav\u0101 fundament\u0101laj\u0101 darb\u0101, <\/span>Piez\u012bmes par struktur\u0113to programm\u0113\u0161anu<\/span><\/i> (1972) Dijkstra izmantoja 8 Queens probl\u0113mu, lai par\u0101d\u012btu, k\u0101 algoritmu var sistem\u0101tiski konstru\u0113t, izmantojot procesu, ko vi\u0146\u0161 sauca par \u201cpak\u0101penisku uzlabo\u0161anu\u201d.\u201d<\/span><\/p>

  • DFS un atpaka\u013cejo\u0161as darb\u012bbas: Dijkstra defin\u0113ja metodi, kas paredz, ka d\u0101ma tiek novietota rind\u0101 un nolai\u017eas uz n\u0101kamo (DFS - Depth-First Search) un atgrie\u017eas uz iepriek\u0161\u0113jo soli, lai m\u0113\u0123in\u0101tu izmantot citu iesp\u0113ju, non\u0101kot strupce\u013c\u0101 (Backtracking), k\u0101 struktur\u0113t\u0101s programm\u0113\u0161anas t\u012br\u0101ko piem\u0113ru.<\/li><\/ul>

    Atpaka\u013cce\u013cu izseko\u0161anas sp\u0113ks:<\/b><\/p>

    P\u0113c Dijkstras dom\u0101m, \u0161\u012b pieeja ir pirmais noz\u012bm\u012bgais pagrieziena punkts \u201cizm\u0113\u0123in\u0101jumu un k\u013c\u016bdu\u201d procesa pilnveido\u0161an\u0101 par nevainojamu lo\u0123isku sec\u012bbu, ko var izmantot, lai<\/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\u0161u un \u0161aha d\u0113\u013ca probl\u0113ma: eksponenci\u0101la izaugsme<\/b><\/h3>

    Le\u0123enda un izcelsme:<\/b><\/p>

    Saska\u0146\u0101 ar st\u0101stu, kad \u0161aha izgudrot\u0101js Sisa bin Dahirs prezent\u0113ja sp\u0113li Indijas karalim, karalis vi\u0146am jaut\u0101ja, k\u0101du atl\u012bdz\u012bbu vi\u0146\u0161 v\u0113l\u0113tos. Sisa izteica \u0161\u0137ietami pietic\u012bgu l\u016bgumu: \u201cEs gribu vienu kvie\u0161u graudu par pirmo \u0161aha laukumu, divus par otro, \u010detrus par tre\u0161o un par katru n\u0101kamo laukumu divreiz vair\u0101k nek\u0101 par iepriek\u0161\u0113jo.\u201d Sissa Sissa teica: \u201cEs gribu vienu kvie\u0161u graudu par pirmo \u0161aha laukumu, divus par otro, \u010detrus par tre\u0161o un par katru n\u0101kamo divreiz vair\u0101k nek\u0101 par iepriek\u0161\u0113jo.\u201d Karalis s\u0101kotn\u0113ji noraid\u012bja \u0161o l\u016bgumu, dom\u0101dams, ka t\u0101 ir tikai \"sauji\u0146a kvie\u0161u\", tom\u0113r, kad s\u0101ka apr\u0113\u0137inus, k\u013cuva skaidrs, ka ne valsts kase, ne visas pasaules kvie\u0161u kr\u0101jumi neb\u016bs pietiekami, lai izpild\u012btu \u0161o pras\u012bbu.<\/p>

    V\u0113sturiskais ieraksts: Ibn Khallikan (1256)<\/b><\/p>

    Pirmo zin\u0101mo rakstisko liec\u012bbu par \u0161o slaveno st\u0101stu 1256. gad\u0101 dokument\u0113ja slavenais biogr\u0101fs un v\u0113sturnieks Ibn Khallikans. Ibn Khallikan iek\u013c\u0101va \u0161o notikumu sav\u0101 darb\u0101 ne tikai k\u0101 st\u0101stu, bet ar\u012b k\u0101 pier\u0101d\u012bjumu tam, k\u0101 matem\u0101tika papla\u0161ina izt\u0113les robe\u017eas.<\/p>

    Matem\u0101tisk\u0101 realit\u0101te:<\/b><\/p>

    \u0160is piepras\u012bjums par 64 laukumiem uz \u0161aha d\u0113\u013ca ir t\u012br\u0101kais \u0123eometrisk\u0101s progresijas (eksponenci\u0101l\u0101 pieauguma) piem\u0113rs. Summu katr\u0101 laukum\u0101 apr\u0113\u0137ina, izmantojot formulu 2n-1<\/sup><\/strong> . Vien\u0101dojums, kas nosaka kop\u0113jo kvie\u0161u daudzumu, ir \u0161\u0101ds:<\/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>

    Masveida skaitlis, kas izriet no \u0161\u012b apr\u0113\u0137ina, ir:<\/p>

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

    K\u0101p\u0113c tas ir tik svar\u012bgi?<\/b><\/p>

    • Izaugsmes m\u0113rogs:<\/b> \u0160is skaitlis ir aptuveni 2000 rei\u017eu liel\u0101ks par pa\u0161reiz\u0113jo kop\u0113jo kvie\u0161u gada produkciju pasaul\u0113.\u00a0<\/span><\/li><\/ul>

      Strat\u0113\u0123isk\u0101 m\u0101c\u012bba:<\/b> \u0160\u012b probl\u0113ma ir sena gudr\u012bbas m\u0101c\u012bba, kas l\u012bderiem un strat\u0113\u0123iem m\u0101ca, k\u0101 nelielas izmai\u0146as (\u201cdubulto\u0161an\u0101s\u201d) laika gait\u0101 var p\u0101rv\u0113rsties par nekontrol\u0113jamiem sp\u0113kiem.<\/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\/lv\/wp-json\/wp\/v2\/pages\/963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shatranj.art\/lv\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/shatranj.art\/lv\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/shatranj.art\/lv\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shatranj.art\/lv\/wp-json\/wp\/v2\/comments?post=963"}],"version-history":[{"count":22,"href":"https:\/\/shatranj.art\/lv\/wp-json\/wp\/v2\/pages\/963\/revisions"}],"predecessor-version":[{"id":1443,"href":"https:\/\/shatranj.art\/lv\/wp-json\/wp\/v2\/pages\/963\/revisions\/1443"}],"up":[{"embeddable":true,"href":"https:\/\/shatranj.art\/lv\/wp-json\/wp\/v2\/pages\/743"}],"wp:attachment":[{"href":"https:\/\/shatranj.art\/lv\/wp-json\/wp\/v2\/media?parent=963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}