{"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\/zh_hk\/exhibit\/poster-17\/","title":{"rendered":"\u6d77\u5831 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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\u9a0e\u58eb\u4e4b\u65c5<\/b><\/h2>

\u6b77\u53f2\u6df1\u5ea6\uff1a<\/b> Knight's Tour \u662f\u4e00\u500b\u6578\u5b78\u9806\u5e8f\uff0c\u5728\u9019\u500b\u9806\u5e8f\u4e2d\uff0c\u99ac\u6703\u6e96\u78ba\u5730\u5230\u9054\u68cb\u76e4\u4e0a\u7684\u6bcf\u500b\u65b9\u683c\u4e00\u6b21\u3002\u5b83\u65e2\u662f\u7b56\u7565\u6311\u6230\uff0c\u4e5f\u662f\u5a1b\u6a02\u6578\u5b78\u7684\u7d93\u5178\u554f\u984c\u3002.<\/span><\/p>

\u00a0<\/p>

\u8d77\u6e90\uff1a<\/b><\/p>

\u9019\u500b\u554f\u984c\u9060\u4e0d\u662f\u73fe\u4ee3\u7684\u767c\u73fe\u3002\u5df2\u77e5\u6700\u65e9\u7684\u89e3\u6cd5\u53ef\u8ffd\u6eaf\u5230 9 \u4e16\u7d00\uff0c\u7531 Al-Adli \u548c As-Suli \u7b49\u5df4\u683c\u9054\u5927\u5e2b\u63d0\u4f9b\u3002\u6b64\u5916\uff0c\u5728 9 \u4e16\u7d00\u7684\u5370\u5ea6\u6587\u5b78\u4e2d\uff0c\u514b\u4ec0\u7c73\u723e\u8a69\u4eba Rudrata \u5728\u4ed6\u7684\u4f5c\u54c1 Kavyalankara \u4e2d\u5c55\u73fe\u4e86\u9019\u7a2e\u6578\u5b78\u7f8e\u5b78\uff0c\u4ed6\u5275\u4f5c\u4e86\u4e00\u9996\u8a69\uff0c\u6309\u7167\u9a0e\u58eb\u51fa\u5de1\u7684\u9806\u5e8f\u4f86\u5beb\u3002.<\/p>

\u00a0<\/p>

\u897f\u65b9\u6587\u5b78\uff1a<\/b><\/p>

\u5728 13 \u4e16\u7d00\uff0c\u5361\u65af\u63d0\u570b\u738b\u963f\u65b9\u7d22\u5341\u4e16 (King Alfonso X of Castile) \u5728\u4ed6\u8457\u540d\u7684\u300a\u904a\u6232\u66f8\u300b(Libro de los Juegos) \u4e2d\uff0c\u4ee5\u9a0e\u58eb\u884c\u52d5\u70ba\u57fa\u790e\uff0c\u63cf\u7e6a\u4e86\u8907\u96dc\u7684\u6f14\u7fd2\u3002\u7136\u800c\uff0c\u9019\u500b\u554f\u984c\u7684\u73fe\u4ee3\u6578\u5b78\u57fa\u790e\u662f\u7531 Leonhard Euler \u5728 1759 \u5e74\u5960\u5b9a\u7684\uff0c\u4ed6\u7684\u5206\u6790\u73fe\u5728\u5df2\u88ab\u516c\u8a8d\u70ba\u5716\u5f62\u7406\u8ad6\u7684\u57fa\u77f3\u4e4b\u4e00\u3002.<\/p>

\u00a0<\/p>

\u7279\u6027\uff1a<\/b><\/p>

\u5c01\u9589 (Re-entrant) \u5c0e\u89bd\uff1a<\/b> \u5982\u679c\u9a0e\u58eb\u5728\u8ddd\u96e2\u8d77\u59cb\u4f4d\u7f6e\u6b63\u597d\u4e00\u6b65\u7684\u4f4d\u7f6e\u7d50\u675f\uff0c\u5141\u8a31\u5b83\u7acb\u5373\u518d\u6b21\u958b\u59cb\u5de1\u904a\u3002.<\/p>

\u00a0<\/p>

\u958b\u653e\u4e4b\u65c5\uff1a<\/b><\/p>

\u5982\u679c\u99ac\u8a2a\u554f\u4e86\u6bcf\u500b\u65b9\u683c\uff0c\u4f46\u662f\u7d50\u675f\u5728\u4e00\u500b\u65b9\u683c\u4e0a\uff0c\u5f9e\u9019\u500b\u65b9\u683c\u5b83\u7121\u6cd5\u5728\u4e00\u6b21\u79fb\u52d5\u4e2d\u5230\u9054\u8d77\u9ede\u3002.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

\n\t\t\t\t
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8 \u7687\u540e\u554f\u984c\uff1aDijkstra \u8207\u7d50\u69cb\u5316\u7a0b\u5f0f\u8a2d\u8a08\u7684\u8a95\u751f<\/b><\/h2>

\u9019\u500b\u554f\u984c\u65bc 1848 \u5e74\u7531 Max Bezzel \u63d0\u51fa\uff0c\u4e26\u5f15\u8d77 Carl Friedrich Gauss \u7b49\u5929\u624d\u7684\u6ce8\u610f\uff0c\u5728 1970 \u5e74\u4ee3\u7531\u73fe\u4ee3\u96fb\u8166\u79d1\u5b78\u4e4b\u7236\u4e4b\u4e00 Edsger W. Dijkstra \u8f49\u5316\u70ba\u300c\u7a0b\u5f0f\u8a2d\u8a08\u5ba3\u8a00\u300d\u3002.<\/p>

Dijkstra \u8207 DFS \u7684\u95dc\u4fc2<\/b><\/h3>

\u5728\u4ed6\u7684\u958b\u5275\u6027\u8457\u4f5c\u4e2d\u3001, <\/span>\u7d50\u69cb\u5316\u7a0b\u5f0f\u8a2d\u8a08\u6ce8\u610f\u4e8b\u9805<\/span><\/i> 1972 \u5e74\uff09\uff0cDijkstra \u5229\u7528 8 \u7687\u540e\u554f\u984c (8 Queens Problem) \u4f86\u8aaa\u660e\u5982\u4f55\u900f\u904e\u4ed6\u7a31\u70ba\u300c\u9010\u6b65\u7cbe\u9032\u300d\u7684\u904e\u7a0b\uff0c\u6709\u7cfb\u7d71\u5730\u5efa\u69cb\u6f14\u7b97\u6cd5\u3002\u201c<\/span><\/p>

  • DFS \u548c Backtracking\uff1aDijkstra \u5b9a\u7fa9\u4e86\u4e00\u7a2e\u65b9\u6cd5\uff0c\u5c07\u4e00\u500b\u7687\u540e\u653e\u5728\u4e00\u6392\uff0c\u7136\u5f8c\u4e0b\u4e00\u500b\u7687\u540e\uff08\u6df1\u5ea6\u512a\u5148\u641c\u7d22 - DFS\uff09\uff0c\u7576\u9047\u5230\u6b7b\u80e1\u540c\u6642\uff0c\u8fd4\u56de\u4e0a\u4e00\u6b65\u5617\u8a66\u4e0d\u540c\u7684\u53ef\u80fd\u6027\uff08Backtracking\uff09\uff0c\u9019\u662f\u7d50\u69cb\u5316\u7de8\u7a0b\u6700\u7d14\u7cb9\u7684\u4f8b\u5b50\u3002.<\/li><\/ul>

    \u56de\u6eaf\u7684\u529b\u91cf\uff1a<\/b><\/p>

    Dijkstra \u8a8d\u70ba\uff0c\u9019\u7a2e\u65b9\u6cd5\u662f\u5c07\u300c\u8a66\u9a57\u8207\u932f\u8aa4\u300d\u904e\u7a0b\u7cbe\u7149\u6210\u7121\u7455\u75b5\u7684\u908f\u8f2f\u9806\u5e8f\u7684\u7b2c\u4e00\u500b\u91cd\u8981\u91cc\u7a0b\u7891\uff0c\u800c\u9019\u500b\u9806\u5e8f\u53ef\u4ee5\u8b93\u5408\u4f5c\u5925\u4f34\u3001\u5b78\u8853\u754c\u548c\u793e\u6703\u4e0a\u7684\u4eba\u5011\uff0c\u90fd\u80fd\u5f9e\u4e2d\u53d7\u76ca\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

    \n\t\t\t\t
    \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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    \u5c0f\u9ea5\u8207\u68cb\u76e4\u554f\u984c\uff1a\u6307\u6578\u5f0f\u6210\u9577<\/b><\/h3>

    \u50b3\u8aaa\u8207\u8d77\u6e90\uff1a<\/b><\/p>

    \u6839\u64da\u9019\u500b\u6545\u4e8b\uff0c\u7576\u8c61\u68cb\u7684\u767c\u660e\u8005 Sissa bin Dahir \u5c07\u8c61\u68cb\u5448\u737b\u7d66\u5370\u5ea6\u570b\u738b\u6642\uff0c\u570b\u738b\u554f\u4ed6\u60f3\u8981\u4ec0\u9ebc\u734e\u8cde\u3002Sissa \u63d0\u51fa\u4e86\u4e00\u500b\u770b\u4f3c\u6eab\u548c\u7684\u8981\u6c42\uff1a\u300c\u6211\u8981\u4e00\u7c92\u9ea5\u5b50\u4f5c\u70ba\u68cb\u76e4\u4e0a\u7b2c\u4e00\u500b\u65b9\u683c\u7684\u734e\u52f5\uff0c\u7b2c\u4e8c\u500b\u65b9\u683c\u5169\u7c92\uff0c\u7b2c\u4e09\u500b\u65b9\u683c\u56db\u7c92\uff0c\u4e4b\u5f8c\u6bcf\u500b\u65b9\u683c\u7684\u734e\u52f5\u90fd\u662f\u524d\u4e00\u500b\u65b9\u683c\u7684\u5169\u500d\u300d\u3002\u570b\u738b\u8d77\u521d\u99c1\u56de\u4e86\u9019\u500b\u8981\u6c42\uff0c\u8a8d\u70ba\u9019\u53ea\u662f\u300c\u4e00\u5c0f\u64ae\u9ea5\u5b50\u300d\uff1b\u7136\u800c\uff0c\u7576\u8a08\u7b97\u958b\u59cb\u6642\uff0c\u570b\u5eab\u6216\u5168\u4e16\u754c\u7684\u5c0f\u9ea5\u5b58\u91cf\u986f\u7136\u90fd\u4e0d\u8db3\u4ee5\u6eff\u8db3\u9019\u500b\u8981\u6c42\u3002.<\/p>

    \u6b77\u53f2\u8a18\u9304\uff1aIbn Khallikan (1256)<\/b><\/p>

    1256 \u5e74\uff0c\u8457\u540d\u7684\u50b3\u8a18\u4f5c\u5bb6\u548c\u6b77\u53f2\u5b78\u5bb6 Ibn Khallikan \u9996\u6b21\u4ee5\u6587\u5b57\u8a18\u9304\u4e86\u9019\u500b\u8457\u540d\u7684\u6545\u4e8b\u3002Ibn Khallikan \u5c07\u9019\u500b\u4e8b\u4ef6\u7d0d\u5165\u4ed6\u7684\u8457\u4f5c\u4e2d\uff0c\u4e0d\u53ea\u662f\u4f5c\u70ba\u4e00\u500b\u6545\u4e8b\uff0c\u800c\u662f\u4f5c\u70ba\u6578\u5b78\u5982\u4f55\u7a81\u7834\u60f3\u50cf\u529b\u754c\u9650\u7684\u8b49\u64da\u3002.<\/p>

    \u6578\u5b78\u73fe\u5be6\uff1a<\/b><\/p>

    \u5c0d\u65bc\u68cb\u76e4\u4e0a\u7684 64 \u500b\u65b9\u683c\u6240\u63d0\u51fa\u7684\u9019\u9805\u8981\u6c42\uff0c\u662f\u5e7e\u4f55\u905e\u589e (\u6307\u6578\u6210\u9577) \u6700\u7d14\u7cb9\u7684\u7bc4\u4f8b\u3002\u6bcf\u500b\u65b9\u683c\u4e0a\u7684\u91d1\u984d\u4f7f\u7528\u516c\u5f0f\u8a08\u7b97 2n-1<\/sup><\/strong> . .\u63d0\u4f9b\u5c0f\u9ea5\u7e3d\u91cf\u7684\u516c\u5f0f\u5982\u4e0b\uff1a<\/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>

    \u8a08\u7b97\u5f97\u51fa\u7684\u9f90\u5927\u6578\u5b57\u70ba<\/p>

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

    \u70ba\u4f55\u5982\u6b64\u91cd\u8981\uff1f<\/b><\/p>

    • \u6210\u9577\u898f\u6a21\uff1a<\/b> \u9019\u500b\u6578\u5b57\u7d04\u76f8\u7576\u65bc\u76ee\u524d\u5168\u7403\u5c0f\u9ea5\u5e74\u7e3d\u7522\u91cf\u7684 2,000 \u500d\u3002.\u00a0<\/span><\/li><\/ul>

      \u7b56\u7565\u8ab2\u7a0b\uff1a<\/b> \u9019\u500b\u554f\u984c\u662f\u53e4\u8001\u7684\u667a\u6167\u6559\u8a13\uff0c\u6559\u5c0e\u9818\u5c0e\u8005\u548c\u6230\u7565\u5bb6\u5982\u4f55\u8b93\u5fae\u5c0f\u7684\u8b8a\u5316\uff08\u300c\u500d\u589e\u300d\uff09\u96a8\u8457\u6642\u9593\u7684\u63a8\u79fb\u800c\u8f49\u5316\u70ba\u7121\u6cd5\u63a7\u5236\u7684\u529b\u91cf\u3002.<\/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\/zh_hk\/wp-json\/wp\/v2\/pages\/963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shatranj.art\/zh_hk\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/shatranj.art\/zh_hk\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/shatranj.art\/zh_hk\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shatranj.art\/zh_hk\/wp-json\/wp\/v2\/comments?post=963"}],"version-history":[{"count":22,"href":"https:\/\/shatranj.art\/zh_hk\/wp-json\/wp\/v2\/pages\/963\/revisions"}],"predecessor-version":[{"id":1443,"href":"https:\/\/shatranj.art\/zh_hk\/wp-json\/wp\/v2\/pages\/963\/revisions\/1443"}],"up":[{"embeddable":true,"href":"https:\/\/shatranj.art\/zh_hk\/wp-json\/wp\/v2\/pages\/743"}],"wp:attachment":[{"href":"https:\/\/shatranj.art\/zh_hk\/wp-json\/wp\/v2\/media?parent=963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}