{"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\/uz\/exhibit\/poster-17\/","title":{"rendered":"plakat 17"},"content":{"rendered":"
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Ritsarning sayohati<\/b><\/h2>

Tarixiy chuqurlik:<\/b> Shahzoda sayohati \u2014 bu shaxmat taxtasidagi har bir katakchani aynan bir marta ziyorat qiladigan matematik ketma-ketlikdir. Bu nafaqat strategik sinov, balki dam olish matematikasidagi klassik muammo hamdir.<\/span><\/p>

\u00a0<\/p>

Kelib chiqishi:<\/b><\/p>

Bu muammo zamonaviy kashfiyot emas. Eng qadimgi ma'lum yechimlar 9-asrga borib taqaladi; ularni Bag'dod ustalari Al-Adli va As-Suli bergan. Bundan tashqari, 9-asr hind adabiyotida Kashmir shoiri Rudrata Kavyalankara asarida bu matematik estetikani namoyish etgan; u o'z she'rini shaxmatdagi ot yurishi ketma-ketligiga muvofiq tuzgan.<\/p>

\u00a0<\/p>

G\u02bbarb adabiyoti:<\/b><\/p>

13-asrda Kastiliya qirolligi qirol Alfonso X o'zining mashhur Libro de los Juegos (O'yinlar kitobi) asarida ritsar harakatlariga asoslangan murakkab manevrlarni keltirgan. Biroq muammoning zamonaviy matematik poydevori 1759 yilda Leonhard Euler tomonidan qo'yilgan bo'lib, uning tahlili hozirda graf nazariyasining asosiy toshlaridan biri sifatida tan olinadi.<\/p>

\u00a0<\/p>

Xususiyatlari:<\/b><\/p>

Yopiq (qaytadan kirishli) sayohat:<\/b> Agar ot boshlang'ich kvadratdan aynan bir ot yurishi masofada joylashgan kvadratda yakunlasa, u darhol sayohatini yana boshlashi mumkin.<\/p>

\u00a0<\/p>

Ochiq tur:<\/b><\/p>

Agar ritsar har bir katlanmaga tashrif buyursa, lekin yakunda boshlang'ich nuqtaga bitta harakatda yetib bora olmaydigan katlanmada tugatsa.<\/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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Sakkiz malikalar muammosi: Dijkstra va tuzilmali dasturlashning tug'ilishi<\/b><\/h2>

1848 yilda Maks Bezzel tomonidan qo'yilgan va Karl Fridrix Gauss kabi daholar e'tiborini tortgan bu muammo 1970-yillarda zamonaviy kompyuter fanining asoschilaridan biri Edsger V. Dijkstra tomonidan \u201cdasturlash manifesti\u201dga aylantirildi.<\/p>

Dijkstra va DFS o'rtasidagi bog'liqlik<\/b><\/h3>

Uning asosiy asarida, <\/span>Tuzilmaviy dasturlash bo'yicha eslatmalar<\/span><\/i> (1972) yilda Dijkstra sakkiz malika muammosidan foydalangan holda algoritmni \u201cbosqichma-bosqich takomillashtirish\u201d deb atagan jarayon orqali qanday tizimli ravishda yaratish mumkinligini namoyish etdi.\u201d<\/span><\/p>

  • DFS va orqaga qaytish: Dijkstra qatorga shahzodani joylashtirish va keyingisiga o'tish (Depth-First Search \u2013 DFS) hamda o'lik nuqtaga yetganda oldingi bosqichga qaytib, boshqa imkoniyatni sinash (orqaga qaytish) usulini strukturaviy dasturlashning eng sof namunasi deb atagan.<\/li><\/ul>

    Orqaga qaytishning kuchi:<\/b><\/p>

    Dijkstra fikricha, bu yondashuv \u201csinov va xato\u201d jarayonini mukammal mantiqiy ketma-ketlikka aylantirishda birinchi muhim bosqichni tashkil etadi.<\/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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    Bug\u02bbdoy va shaxmat taxtasi muammosi: eksponensial o\u02bbsish<\/b><\/h3>

    Afsonasi va kelib chiqishi:<\/b><\/p>

    Rivoyatga ko'ra, shaxmat ixtirochisi Sissa bin Dahir Hindiston shohiga o'yinni taqdim etganda, shoh undan qanday mukofot xohlayotganini so'radi. Sissa ko'rinishda kamtarona so'rov bilan chiqdi: \u201cMen shaxmat taxtasining birinchi katagiga bir don sholi, ikkinchisiga ikki don, uchinchisiga to'rt don, keyingi har bir katagiga esa oldingisidan ikki baravar ko'p don berilishini xohlayman.\u201d Shoh boshida bu iltimosni \u201cbir hovuch bug'doy\u201d deb hisoblab e'tiborsiz qoldirdi; ammo hisob-kitob boshlangach, na xazina, na dunyoning barcha bug'doy zaxiralari ham bu talabni qondira olmasligi ayon bo'ldi.<\/p>

    Tarixiy manba: Ibn Xallikan (1256)<\/b><\/p>

    Ushbu mashhur hikoyaning birinchi ma'lum yozma manbai 1256 yilda mashhur biograf va tarixchi Ibn Xallikan tomonidan hujjatlashtirilgan. Ibn Xallikan bu voqeani o'z asariga nafaqat hikoya sifatida, balki matematikaning tasavvur chegaralarini qanday kengaytirishini ko'rsatadigan dalil sifatida kiritgan.<\/p>

    Matematik haqiqat:<\/b><\/p>

    Bu shaxmat taxtasidagi 64 kvadrat uchun berilgan so'rov geometrik progressiyaning (eksponent o'sishning) eng sof namunasidir. Har bir kvadratdagi miqdor quyidagi formulaga ko'ra hisoblanadi 2n-1<\/sup><\/strong> . Bug'doyning umumiy miqdorini beruvchi tenglama quyidagicha:<\/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>

    Ushbu hisob-kitob natijasida olingan katta miqdor quyidagicha:<\/p>

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

    Nega bu shunchalik muhim?<\/b><\/p>

    • O'sish shkalasi:<\/b> Bu raqam dunyoning hozirgi yillik bug'doy umumiy hosilidan taxminan 2 000 barobariga teng.\u00a0<\/span><\/li><\/ul>

      Strategik dars:<\/b> Bu muammo rahbarlar va strateglarga kichik o'zgarishlar (\u201cikki baravar oshirish\u201d) vaqt o'tishi bilan nazorat qilib bo'lmaydigan kuchlarga aylanishi mumkinligini o'rgatadigan qadimiy donolik sabog'idir.<\/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\/uz\/wp-json\/wp\/v2\/pages\/963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shatranj.art\/uz\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/shatranj.art\/uz\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/shatranj.art\/uz\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shatranj.art\/uz\/wp-json\/wp\/v2\/comments?post=963"}],"version-history":[{"count":22,"href":"https:\/\/shatranj.art\/uz\/wp-json\/wp\/v2\/pages\/963\/revisions"}],"predecessor-version":[{"id":1443,"href":"https:\/\/shatranj.art\/uz\/wp-json\/wp\/v2\/pages\/963\/revisions\/1443"}],"up":[{"embeddable":true,"href":"https:\/\/shatranj.art\/uz\/wp-json\/wp\/v2\/pages\/743"}],"wp:attachment":[{"href":"https:\/\/shatranj.art\/uz\/wp-json\/wp\/v2\/media?parent=963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}