{"id":410,"date":"1453-08-18T01:46:13","date_gmt":"1969-12-31T16:00:00","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=410"},"modified":"2023-05-22T16:59:39","modified_gmt":"2023-05-22T08:59:39","slug":"%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/","title":{"rendered":"\u3010\u4e13\u9898\u3011Polya \u8ba1\u6570\u5b9a\u7406"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_65 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-69e4799b919eb\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-69e4799b919eb\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#References\" title=\"References:\">References:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#Burnside_%E5%AE%9A%E7%90%86\" title=\"Burnside \u5b9a\u7406\">Burnside \u5b9a\u7406<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#Polya_%E5%AE%9A%E7%90%86\" title=\"Polya \u5b9a\u7406\">Polya \u5b9a\u7406<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#%E8%AF%81%E6%98%8E\" title=\"\u8bc1\u660e\">\u8bc1\u660e<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#%E5%BC%95%E7%90%86_1%EF%BC%9A\" title=\"\u5f15\u7406 1\uff1a\">\u5f15\u7406 1\uff1a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#%E6%8E%A8%E8%AE%BA_2\" title=\"\u63a8\u8bba 2\">\u63a8\u8bba 2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#Burnside_%E5%AE%9A%E7%90%86-2\" title=\"Burnside \u5b9a\u7406\">Burnside \u5b9a\u7406<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#%E4%BE%8B%E9%A2%98\" title=\"\u4f8b\u9898\">\u4f8b\u9898<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#HOJ_2084_The_Colored_Cubes\" title=\"HOJ 2084. The Colored Cubes\">HOJ 2084. The Colored Cubes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#HOJ_2647_Megaminx\" title=\"HOJ 2647. Megaminx\">HOJ 2647. Megaminx<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#SGU_294_Hes_Circles\" title=\"SGU 294. He&#8217;s Circles\">SGU 294. He&#8217;s Circles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#POJ_2154_Color\" title=\"POJ 2154. Color\">POJ 2154. Color<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#UVA_10601_Cubes\" title=\"UVA 10601. Cubes\">UVA 10601. Cubes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#SPOJ_TRANSP_Transposing_is_Fun\" title=\"SPOJ TRANSP. Transposing is Fun\">SPOJ TRANSP. Transposing is Fun<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#AHOI2002_%E9%BB%91%E7%99%BD%E7%93%B7%E7%A0%96\" title=\"[AHOI2002] \u9ed1\u767d\u74f7\u7816\">[AHOI2002] \u9ed1\u767d\u74f7\u7816<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#SGU_282_Isomorphism\" title=\"SGU 282. Isomorphism\">SGU 282. Isomorphism<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#Luogu_P5818_JSOI2011%E5%90%8C%E5%88%86%E5%BC%82%E6%9E%84%E4%BD%93%E8%AE%A1%E6%95%B0\" title=\"Luogu P5818. [JSOI2011]\u540c\u5206\u5f02\u6784\u4f53\u8ba1\u6570\">Luogu P5818. [JSOI2011]\u540c\u5206\u5f02\u6784\u4f53\u8ba1\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#Luogu_P6597_%E7%83%AF%E7%83%83%E8%AE%A1%E6%95%B0\" title=\"Luogu P6597. \u70ef\u70c3\u8ba1\u6570\">Luogu P6597. \u70ef\u70c3\u8ba1\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#Luogu_P6598_%E7%83%B7%E7%83%83%E8%AE%A1%E6%95%B0\" title=\"Luogu P6598 \u70f7\u70c3\u8ba1\u6570\">Luogu P6598 \u70f7\u70c3\u8ba1\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#Luogu_P4708_%E7%94%BB%E7%94%BB\" title=\"Luogu P4708. \u753b\u753b\">Luogu P4708. \u753b\u753b<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#SGU_208_Toral_Tickets\" title=\"SGU 208. Toral Tickets\">SGU 208. Toral Tickets<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/%e3%80%90%e4%b8%93%e9%a2%98%e3%80%91polay-%e8%ae%a1%e6%95%b0%e5%ae%9a%e7%90%86\/#External_link\" title=\"External link: \">External link: <\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n\n<h2><span class=\"ez-toc-section\" id=\"References\"><\/span>References:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"http:\/\/www.cppblog.com\/sdfond\/archive\/2010\/02\/06\/107403.aspx\">Polya \u5b9a\u7406\u518d\u5c0f\u7ed3<\/a><br \/>\n<a href=\"http:\/\/www.douban.com\/note\/281137077\/\">\u7ec4\u5408\u6570\u5b66 \u539f\u4e66\u7b2c 5 \u7248<\/a><br \/>\n<a href=\"http:\/\/vfleaking.blog.163.com\/blog\/static\/174807634201341913040467\/\">\u9664\u6570\u51fd\u6570\u7684\u6e10\u8fd1\u4e0a\u754c\uff1f by vfleaking<\/a><\/p>\n<p>\u3002\u3002\u7edf\u8ba1\u5728\u67d0\u4e2a\u7f6e\u6362\u7fa4\u4f5c\u7528\u4e0b\u3002\u3002\u8ba1\u7b97\u4e0d\u7b49\u4ef7\u7684\u7740\u8272\u65b9\u6848\u6570\u7684\u95ee\u9898\u3002\u3002\u3002<br \/>\n\u3002\u3002\u53ef\u4ee5\u901a\u8fc7 Burnside \u5b9a\u7406\u3002\u3002\u8f6c\u5316\u4e3a\u679a\u4e3e\u6bcf\u4e00\u4e2a\u7f6e\u6362\u3002\u3002\u3002\u7edf\u8ba1\u5728\u8be5\u7f6e\u6362\u4f5c\u7528\u4e0b\u7b49\u4ef7\u7684\u7740\u8272\u65b9\u6848\u6570\u7684\u95ee\u9898\u3002\u3002<br \/>\n\u3002\u3002\u800c Polya \u5b9a\u7406\u5219\u662f\u5de7\u5999\u7684\u5229\u7528\u540c\u4e00\u5faa\u73af\u5185\u7740\u8272\u5fc5\u987b\u76f8\u540c\u8fd9\u4e2a\u4e8b\u5b9e\uff0c\u8fdb\u4e00\u6b65\u7b80\u5316\u540e\u8005\u7684\u8ba1\u7b97\u3002\u3002\u3002<\/p>\n<p>\u2014\u2014\u2014\u2014\u2014\u2014<\/p>\n<p>\u4e60\u9898\uff1a<br \/>\n<a href=\"http:\/\/acm.hust.edu.cn\/vjudge\/contest\/view.action?cid=2823#overview\">http:\/\/acm.hust.edu.cn\/vjudge\/contest\/view.action?cid=2823#overview<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Burnside_%E5%AE%9A%E7%90%86\"><\/span>Burnside \u5b9a\u7406<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8bbe G \u662f X \u7684\u7f6e\u6362\u7fa4\uff0c\u800c C \u662f X \u4e2d\u5bf9 G \u5c01\u95ed\u7684\u7740\u8272\u96c6\u5408\u3002<br \/>\n\u5219 C \u4e2d\u975e\u7b49\u4ef7\u7740\u8272\u6570 N(G, C) \u7531\u4e0b\u5f0f\u7ed9\u51fa\uff1a<\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 41px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-4f24b46fdd41bd34c68e56ab13610e45_l3.png\" height=\"41\" width=\"186\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#091;&#124;&#71;&#124;&#32;&#78;&#40;&#71;&#44;&#32;&#67;&#41;&#32;&#61;&#32;&#92;&#115;&#117;&#109;&#95;&#123;&#102;&#92;&#105;&#110;&#32;&#103;&#125;&#124;&#67;&#40;&#102;&#41;&#124;&#92;&#093;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Polya_%E5%AE%9A%E7%90%86\"><\/span>Polya \u5b9a\u7406<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8bbe <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/> \u662f\u96c6\u5408 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> \u7684\u7f6e\u6362\u3002\u5047\u5982\u6211\u4eec\u7528 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/> \u79cd\u989c\u8272\u5bf9 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> \u7740\u8272\uff0c\u5219\u5bf9 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/> \u4e0d\u53d8\u7684\u7740\u8272\u6570\u4e0e <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/> \u7684\u5faa\u73af\u6570 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> \u6709\u5173\uff1a<\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 19px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-a02658dd28ad7d7fe7fa5ce854cd66b1_l3.png\" height=\"19\" width=\"86\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#091;&#124;&#67;&#40;&#102;&#41;&#124;&#32;&#61;&#32;&#107;&#94;&#114;&#92;&#093;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<p>\u3002\u3002\u3002<\/p>\n<p>\u2014\u2014\u2014\u2014\u2014\u2014<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E8%AF%81%E6%98%8E\"><\/span>\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"%E5%BC%95%E7%90%86_1%EF%BC%9A\"><\/span>\u5f15\u7406 1\uff1a<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u5bf9\u4e8e\u6bcf\u4e00\u79cd\u7740\u8272 c\uff0cc \u7684\u7a33\u5b9a\u6838 G(c) \u662f\u7f6e\u6362\u7fa4\uff0c\u800c\u4e14\u5bf9 G \u4e2d\u7684\u4efb\u610f\u7f6e\u6362 f \u4e0e g\u3002<br \/>\ng<em>c = f<\/em>c \u5f53\u4e14\u4ec5\u5f53 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-e782d3803ce4cebd8efab3932318c86b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#94;&#123;&#45;&#49;&#125;&#32;&#42;&#32;&#103;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"55\" style=\"vertical-align: -4px;\"\/> \u5c5e\u4e8e G(c)\u3002<\/p>\n<h4><span class=\"ez-toc-section\" id=\"%E6%8E%A8%E8%AE%BA_2\"><\/span>\u63a8\u8bba 2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u8bbe c \u4e3a C \u4e2d\u7684\u4e00\u79cd\u7740\u8272\uff0c\u90a3\u4e48\u4e0e c \u7b49\u4ef7\u7684\u7740\u8272\u6570\u7b49\u4e8e G \u4e2d\u7f6e\u6362\u4e2a\u6570\uff0c\u9664\u4ee5 c \u7684\u7a33\u5b9a\u6838\u4e2d\u7f6e\u6362\u7684\u4e2a\u6570\u3002<\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 43px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-8c4c06321193614e52dd304ba987419b_l3.png\" height=\"43\" width=\"239\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#091;&#78;&#40;&#99;&#41;&#32;&#61;&#32;&#124;&#123;&#102;&#42;&#99;&#58;&#32;&#102;&#92;&#105;&#110;&#32;&#71;&#125;&#124;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#124;&#71;&#124;&#125;&#123;&#124;&#71;&#40;&#99;&#41;&#124;&#125;&#92;&#093;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<p>\u3002<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Burnside_%E5%AE%9A%E7%90%86-2\"><\/span>Burnside \u5b9a\u7406<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u3002\u3002\u8003\u5bdf\u3002\u3002\u6240\u6709\u6ee1\u8db3 f*c = c \u7684\u4e8c\u5143\u7ec4 (f, c)\u3002\u3002\u53cc\u8ba1\u6570\u3002\u3002<br \/>\n\u679a\u4e3e f \u3002\u3002\u5f97\u5230 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-a059e56779ed7c5cf622d184dace8c67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#117;&#109;&#95;&#123;&#102;&#92;&#105;&#110;&#32;&#103;&#125;&#124;&#67;&#40;&#102;&#41;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"93\" style=\"vertical-align: -8px;\"\/>\u3002\u3002\uff08\u901a\u8fc7\u7f6e\u6362 f \u4e0d\u53d8\u7684\u7740\u8272\u51e0\u4f55\uff09<br \/>\n\u679a\u4e3e c \u3002\u3002\u5f97\u5230 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-58630f539a971cfb73964f6465962eea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#117;&#109;&#95;&#123;&#99;&#92;&#105;&#110;&#32;&#67;&#125;&#124;&#71;&#40;&#99;&#41;&#124;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"92\" style=\"vertical-align: -6px;\"\/>\u3002\u3002\uff08c \u5173\u4e8e\u7f6e\u6362\u7fa4 G \u7684\u7a33\u5b9a\u6838\uff09<br \/>\n\u6839\u636e\u63a8\u8bba 2 \u6709\uff1a<\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 19px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-2398829e98c24963f3767cc18c3fd827_l3.png\" height=\"19\" width=\"126\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#091;&#124;&#71;&#40;&#99;&#41;&#124;&#32;&#78;&#40;&#99;&#41;&#32;&#61;&#32;&#124;&#71;&#124;&#92;&#093;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 46px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.shuizilong.com\/house\/wp-content\/ql-cache\/quicklatex.com-c022789157c0d675c8e35fce44a24d94_l3.png\" height=\"46\" width=\"159\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#091;&#92;&#115;&#117;&#109;&#95;&#123;&#99;&#92;&#105;&#110;&#32;&#67;&#125;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#78;&#40;&#99;&#41;&#125;&#32;&#61;&#32;&#78;&#40;&#71;&#44;&#67;&#41;&#92;&#093;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<p> \uff08\u56e0\u4e3a\u6bcf\u4e2a\u975e\u7b49\u4ef7\u7740\u8272\u5bf9\u5de6\u5f0f\u7684\u8d21\u732e\u4e3a 1\u3002\uff09<\/p>\n<p><!--more--><\/p>\n<h1><span class=\"ez-toc-section\" id=\"%E4%BE%8B%E9%A2%98\"><\/span>\u4f8b\u9898<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"HOJ_2084_The_Colored_Cubes\"><\/span>HOJ 2084. The Colored Cubes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"http:\/\/acm.hit.edu.cn\/problemset\/2084\">HOJ 2084. The Colored Cubes<\/a><\/li>\n<\/ul>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\ninline LL f(DB x){\r\n    return (pow(x, 6) + 3 * pow(x, 4) + 12 * pow(x, 3) + 8 * pow(x, 2)) \/ 24;\r\n}\r\n\r\nint main() {\r\n    int n; while (cin &gt;&gt; n &amp;&amp; n){\r\n        cout &lt;&lt; f(n) &lt;&lt; endl;\r\n    }\r\n}\r\n\r\n<\/pre>\n<h2><span class=\"ez-toc-section\" id=\"HOJ_2647_Megaminx\"><\/span>HOJ 2647. Megaminx<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"http:\/\/acm.hit.edu.cn\/problemset\/2647\">HOJ 2647. Megaminx<\/a><\/li>\n<\/ul>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\ninline LL f(DB x){\r\n    return (pow(x, 12) + 15 * pow(x, 6) + 44 * pow(x, 4)) \/ 60;\r\n}\r\n\r\nint main() {\r\n    int n; while (cin &gt;&gt; n){\r\n        cout &lt;&lt; f(n) &lt;&lt; endl;\r\n    }\r\n}\r\n<\/pre>\n<h2><span class=\"ez-toc-section\" id=\"SGU_294_Hes_Circles\"><\/span>SGU 294. He&#8217;s Circles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/vjudge.net\/problem\/SGU-294\">SGU 294. He&#8217;s Circles<\/a><\/li>\n<\/ul>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\n#include &lt;lastweapon\/bignum&gt;\r\nusing namespace lastweapon;\r\n\r\nconst int PMAX = int(2e5) + 9;\r\nVI P; bitset&lt;PMAX&gt; isP; int phi&#x5B;PMAX];\r\nvoid sieve(){\r\n    phi&#x5B;1] = 1; FOR(i, 2, PMAX){\r\n        if (!isP&#x5B;i]) P.PB(i), phi&#x5B;i] = i-1;\r\n        for (int j=0;j&lt;SZ(P)&amp;&amp;i*P&#x5B;j]&lt;PMAX;++j){\r\n            isP&#x5B;i*P&#x5B;j]]=1; if (!(i%P&#x5B;j])){\r\n                phi&#x5B;i*P&#x5B;j]] = phi&#x5B;i] * P&#x5B;j];\r\n                break;\r\n            } else{\r\n                phi&#x5B;i*P&#x5B;j]] = phi&#x5B;i] * (P&#x5B;j] - 1);\r\n            }\r\n        }\r\n    }\r\n}\r\n\r\nint main() {\r\n#ifndef ONLINE_JUDGE\r\n    \/\/freopen(&quot;in.txt&quot;, &quot;r&quot;, stdin);\r\n#endif\r\n\r\n    sieve();\r\n\r\n    int n; RD(n);\r\n    bignum z;\r\n    \/\/REP_1(i, n) z += pow(bignum(2), __gcd(i, n));\r\n    REP_1(d, n) if (n % d == 0) {\r\n        z += pow(bignum(2), d) * phi&#x5B;n\/d];\r\n    }\r\n    z \/= n;\r\n    cout &lt;&lt; z &lt;&lt; endl;\r\n}\r\n\r\n<\/pre>\n<h2><span class=\"ez-toc-section\" id=\"POJ_2154_Color\"><\/span>POJ 2154. Color<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/vjudge.net\/problem\/POJ-2154\">https:\/\/vjudge.net\/problem\/POJ-2154<\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"UVA_10601_Cubes\"><\/span>UVA 10601. Cubes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/vjudge.net\/problem\/UVA-10601\">https:\/\/vjudge.net\/problem\/UVA-10601<\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"SPOJ_TRANSP_Transposing_is_Fun\"><\/span>SPOJ TRANSP. Transposing is Fun<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/vjudge.net\/problem\/SPOJ-TRANSP\">https:\/\/vjudge.net\/problem\/SPOJ-TRANSP<\/a><\/li>\n<li><a href=\"https:\/\/vjudge.net\/problem\/SPOJ-TRANSP2\">https:\/\/vjudge.net\/problem\/SPOJ-TRANSP2<\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"AHOI2002_%E9%BB%91%E7%99%BD%E7%93%B7%E7%A0%96\"><\/span>[AHOI2002] \u9ed1\u767d\u74f7\u7816<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P2561\">Luogu P2561. [AHOI2002]\u9ed1\u767d\u74f7\u7816<\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"SGU_282_Isomorphism\"><\/span>SGU 282. Isomorphism<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/vjudge.net\/problem\/SGU-282\">SGU 282. Isomorphism<\/a><\/li>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P4128\">Luogu P4128. [SHOI2006] \u6709\u8272\u56fe<\/a><\/li>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P4727\">Luogu P4727. [HNOI2009]\u56fe\u7684\u540c\u6784\u8ba1\u6570<\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Luogu_P5818_JSOI2011%E5%90%8C%E5%88%86%E5%BC%82%E6%9E%84%E4%BD%93%E8%AE%A1%E6%95%B0\"><\/span>Luogu P5818. [JSOI2011]\u540c\u5206\u5f02\u6784\u4f53\u8ba1\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P5818\">https:\/\/www.luogu.com.cn\/problem\/P5818<\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Luogu_P6597_%E7%83%AF%E7%83%83%E8%AE%A1%E6%95%B0\"><\/span>Luogu P6597. \u70ef\u70c3\u8ba1\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P6597\">https:\/\/www.luogu.com.cn\/problem\/P6597<\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Luogu_P6598_%E7%83%B7%E7%83%83%E8%AE%A1%E6%95%B0\"><\/span>Luogu P6598 \u70f7\u70c3\u8ba1\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P6598\">https:\/\/www.luogu.com.cn\/problem\/P6598<\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Luogu_P4708_%E7%94%BB%E7%94%BB\"><\/span>Luogu P4708. \u753b\u753b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P4708\">https:\/\/www.luogu.com.cn\/problem\/P4708<\/a><\/li>\n<\/ul>\n<p>\u65e0\u6807\u53f7\u6b27\u62c9\u56fe\u8ba1\u6570\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"SGU_208_Toral_Tickets\"><\/span>SGU 208. Toral Tickets<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewProblem.action?id=14886\">http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewProblem.action?id=14886<\/a><\/li>\n<li><a href=\"http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewSource.action?id=631448\">http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewSource.action?id=631448<\/a><\/li>\n<\/ul>\n<p><a href=\"http:\/\/acm.tju.edu.cn\/toj\/showp2795.html\">TJU 2795 The Queen&#8217;s New Necklaces<\/a> <a href=\"http:\/\/acm.uestc.edu.cn\/problem.php?pid=1153\">&#8230;<\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"External_link\"><\/span>External link: <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><a href=\"http:\/\/www.cnblogs.com\/UESTC_Opera\/archive\/2010\/10\/05\/1844361.html\">http:\/\/www.cnblogs.com\/UESTC_Opera\/archive\/2010\/10\/05\/1844361.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>References: Polya \u5b9a\u7406\u518d\u5c0f\u7ed3 \u7ec4\u5408\u6570\u5b66 \u539f\u4e66\u7b2c 5 \u7248 \u9664\u6570\u51fd\u6570\u7684\u6e10\u8fd1\u4e0a\u754c\uff1f by vfleaking \u3002\u3002\u7edf\u8ba1\u5728\u67d0\u4e2a\u7f6e\u6362\u7fa4\u4f5c\u7528\u4e0b\u3002\u3002\u8ba1\u7b97\u4e0d\u7b49\u4ef7\u7684\u7740\u8272\u65b9\u6848\u6570\u7684\u95ee\u9898\u3002\u3002\u3002 \u3002\u3002\u53ef\u4ee5\u901a\u8fc7 Burnside \u5b9a\u7406\u3002\u3002\u8f6c\u5316\u4e3a\u679a\u4e3e\u6bcf\u4e00\u4e2a\u7f6e\u6362\u3002\u3002\u3002\u7edf\u8ba1\u5728\u8be5\u7f6e\u6362\u4f5c\u7528\u4e0b\u7b49\u4ef7\u7684\u7740\u8272\u65b9\u6848\u6570\u7684\u95ee\u9898\u3002\u3002 \u3002\u3002\u800c Polya \u5b9a\u7406\u5219\u662f\u5de7\u5999\u7684\u5229\u7528\u540c\u4e00\u5faa\u73af\u5185\u7740\u8272\u5fc5\u987b\u76f8\u540c\u8fd9\u4e2a\u4e8b\u5b9e\uff0c\u8fdb\u4e00\u6b65\u7b80\u5316\u540e\u8005\u7684\u8ba1\u7b97\u3002\u3002\u3002 \u2014\u2014\u2014\u2014\u2014\u2014 \u4e60\u9898\uff1a http:\/\/acm.hust.edu.cn\/vjudge\/contest\/view.action?cid=2823#overview Burnside \u5b9a\u7406 \u8bbe G \u662f X \u7684\u7f6e\u6362\u7fa4\uff0c\u800c C \u662f X \u4e2d\u5bf9 G \u5c01\u95ed\u7684\u7740\u8272\u96c6\u5408\u3002 \u5219 C \u4e2d\u975e\u7b49\u4ef7\u7740\u8272\u6570 N(G, C) \u7531\u4e0b\u5f0f\u7ed9\u51fa\uff1a &nbsp; &nbsp; Polya \u5b9a\u7406 \u8bbe \u662f\u96c6\u5408 \u7684\u7f6e\u6362\u3002\u5047\u5982\u6211\u4eec\u7528 \u79cd\u989c\u8272\u5bf9 \u7740\u8272\uff0c\u5219\u5bf9 \u4e0d\u53d8\u7684\u7740\u8272\u6570\u4e0e \u7684\u5faa\u73af\u6570 \u6709\u5173\uff1a &nbsp; &nbsp; \u3002\u3002\u3002 \u2014\u2014\u2014\u2014\u2014\u2014 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[97],"tags":[],"class_list":["post-410","post","type-post","status-publish","format-standard","hentry","category-topic"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-6C","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/410","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=410"}],"version-history":[{"count":14,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/410\/revisions"}],"predecessor-version":[{"id":2873,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/410\/revisions\/2873"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=410"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=410"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=410"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}