{"id":702,"date":"2021-05-16T02:45:45","date_gmt":"2021-05-15T18:45:45","guid":{"rendered":"https:\/\/blog.cruciferslab.net\/?p=702"},"modified":"2021-05-16T02:45:45","modified_gmt":"2021-05-15T18:45:45","slug":"gcj-2021-round-2","status":"publish","type":"post","link":"https:\/\/blog.cruciferslab.net\/?p=702","title":{"rendered":"GCJ 2021 Round 2"},"content":{"rendered":"\n<p>\u5148\u63d0\u7d50\u679c\uff1a\u56e0\u70ba\u4e00\u500b\u505a\u5b8c\u984c\u76ee\u5f8c\u7684\u6c7a\u7b56\u5931\u8aa4\uff0c\u4eca\u5e74\u53c8\u5728 R2 \u843d\u99ac\u4e86\u3002<\/p>\n\n\n\n<p>\u610f\u5916\u7684\u9019\u5834\u7684\u96e3\u5ea6\u4e26\u6c92\u6709\u5f88\u9ad8\uff1b\u5982\u679c\u662f\u5e73\u5e38\u5c31\u6709\u5728\u6e96\u5099\u7a0b\u5f0f\u8a2d\u8a08\u7af6\u8cfd\u7684\u4eba\u61c9\u8a72\u53ef\u4ee5\u8f15\u9b06\u6eff\u5206\u5427\u3002\u524d\u4e09\u984c\u6211\u7684\u6642\u9593\u662f\u7d04\u4e00\u5c0f\u6642\u51fa\u982d\uff0c\u7b2c\u56db\u984c\u6709\u60f3\u51fa\u6b63\u78ba\u6f14\u7b97\u6cd5\u7684\u8a71\u4e00\u500b\u534a\u5c0f\u6642\u53ef\u4ee5\u662f\u7dbd\u7dbd\u6709\u9918\u7684\uff0d\uff0d\u4f46 (ry<\/p>\n\n\n\n<p>\u5206\u6578\u622a\u5716\u4ee5\u4e0b\u6709\u96f7\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-1-1024x151.png\" alt=\"\" class=\"wp-image-704\" width=\"826\" height=\"121\" srcset=\"https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-1-1024x151.png 1024w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-1-300x44.png 300w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-1-150x22.png 150w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-1-768x113.png 768w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-1-1536x227.png 1536w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-1.png 1808w\" sizes=\"auto, (max-width: 826px) 100vw, 826px\" \/><\/figure>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">Q1. Minimum Sort<\/h2>\n\n\n\n<p>\u56db\u984c\u5168\u90e8\u7c21\u55ae\u770b\u904e\u4e00\u904d\u4e4b\u5f8c\u56de\u982d\u5c31\u767c\u73fe\u6709\u4eba\u7b2c\u4e00\u984c AC \u4e86\uff0c\u60f3\u8aaa\u7b2c\u4e00\u984c\u5c31\u4e92\u52d5\u984c\u662f\u4e0d\u662f\u6709\u4ec0\u9ebc\u9b3c\u53ef\u4ee5\u641e\u6240\u4ee5\u518d\u4ed4\u7d30\u770b\u4e86\u4e00\u4e0b\uff1b\u4e4b\u5f8c\u5728 Mathematica \u6c42\u4e86\u9019\u4e00\u500b\u503c\u4e4b\u5f8c\u5c31\u77e5\u9053\u597d\u7684\uff0c\u679c\u7136\u88ab\u800d\u4e86\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"228\" height=\"50\" src=\"https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-2.png\" alt=\"\" class=\"wp-image-705\" srcset=\"https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-2.png 228w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-2-150x33.png 150w\" sizes=\"auto, (max-width: 228px) 100vw, 228px\" \/><\/figure>\n\n\n\n<p>\u9019\u500b\u503c\u986f\u8457\u5730\u5c0f\u65bc 6 \u6240\u4ee5\u6700\u76f4\u63a5\u7684\u554f\u6cd5\u5c31\u884c\u4e86\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. Matrygons<\/h2>\n\n\n\n<p>\u5f88\u5bb9\u6613\u767c\u73fe\u6b63\u591a\u908a\u5f62\u908a\u6578\u4e4b\u9593\u7684\u56e0\u6578\u95dc\u4fc2\uff0c\u628a\u9019\u500b\u56e0\u6578\u95dc\u4fc2\u5beb\u4e0b\u4f86\u5c31\u6703\u662f\uff1a\u8f38\u5165\u503c N \u8981\u627e\u6b63\u6574\u6578 \\((a_1,a_2,\\dots,a_k)\\)\uff0c\u6eff\u8db3 \\(a_1\\geq3,a_2,a_3,\\cdots,a_k\\geq2\\)\uff0c\u4f7f\u5f97\u6709 $$N=a_1+a_1 a_2+a_1 a_2 a_3+\\cdots+a_1 a_2\\cdots a_k=a_1(1+a_2(1+a_3(\\cdots a_{k-1}(1+a_k)\\cdots)))$$ \u8f38\u51fa\u5c31\u662f\u6700\u5927\u7684 k \u503c\u3002<\/p>\n\n\n\n<p>\u4e0a\u9762\u5f0f\u5b50\u7684\u5957\u5a03\u5f0f\u7d50\u69cb (\u7e7c\u7e8c\u5957\u7528\u984c\u76ee\u7684\u6bd4\u65b9 XD) \u5f88\u81ea\u7136\u7684\u5c31\u80fd\u5f97\u5230 DP \u7d50\u69cb\uff1b\u4e0d\u904e\u554f\u984c\u5728 \\(a_1\\geq3\\) \u7684\u9650\u5236\u3002\u5982\u679c\u5b83\u80fd\u662f 2 \u7684\u8a71\u90a3 DP \u5f0f\u5c31\u5f88\u55ae\u7d14\uff0c\u62c6\u51fa\u6240\u6709\u56e0\u6578\u5f8c\u53bb\u770b\u770b \\(a_1\\) \u53d6\u8ab0\u80fd\u5920\u5f97\u5230\u6700\u5927\u5c64\u6578\uff0c\u52a0 1 \u6307\u5b9a\u9032\u4f86\u5c31\u597d\u3002\u597d\u5728\u9019\u554f\u984c\u5bb9\u6613\u89e3\u6c7a\uff1a\u5728 DP \u6642\u5148\u505a \\(a_1\\geq3\\) \u7684\u7b54\u6848\uff0c\u6284\u53bb\u53e6\u4e00\u500b\u9663\u5217\u8a18\u8d77\u4f86\u4e4b\u5f8c\u518d\u628a \\(a_1=2\\) \u7684\u72c0\u6cc1\u7b97\u5b8c\u5c31\u597d\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. Hidden Pancakes<\/h2>\n\n\n\n<p>\u628a\u7d66\u5b9a\u6578\u5b57\u80fd\u63a8\u5f97\u7684\u5927\u5c0f\u95dc\u4fc2\u756b\u51fa\u4f86\u4e4b\u5f8c\u5bb9\u6613\u770b\u5f97\u51fa\u4f86\u5b83\u5011\u5f62\u6210\u4e86 n \u500b\u6578\u7684\u6709\u5411\u7121\u5708\u6a39\uff0c\u800c\u6240\u6c42\u5373\u662f\u9019\u500b\u6a39\u7684\u62d3\u64b2\u6392\u5e8f\u7a2e\u985e\u6578\u3002\u4e00\u822c\u7684<a href=\"https:\/\/en.wikipedia.org\/wiki\/Linear_extension\" data-type=\"URL\" data-id=\"https:\/\/en.wikipedia.org\/wiki\/Linear_extension\">\u6709\u5411\u7121\u5708\u5716 (DAG) \u7684\u62d3\u64b2\u6392\u5e8f\u6578\u554f\u984c<\/a>\u5176\u5be6\u662f #P-complete\uff0c\u4e0d\u662f\u5bb9\u6613\u80fd\u505a\u7684\u984c\u76ee\uff1b\u4e0d\u904e\u9019\u4e00\u984c\u7684\u7d50\u69cb\u984d\u5916\u9084\u6703\u5f62\u6210\u4e00\u68f5\u6a39\uff0c\u800c\u7d44\u5408\u6578\u554f\u984c\u4e2d\u6c92\u6709\u9650\u5236\u901a\u5e38\u4ee3\u8868\u66f4\u597d\u7b97\uff1b\u4e00\u500b\u9ede\u6307\u5411\u7684\u5404\u300c\u5b50\u6a39\u300d\u4e4b\u9593\u6c92\u6709\u9023\u7d50\u95dc\u4fc2\uff0c\u6240\u4ee5\u53ef\u4ee5\u5404\u81ea\u6c42\u51fa\u7d44\u5408\u6578\u4e4b\u5f8c\u5408\u4f75\u8d77\u4f86\u3002\u516c\u5f0f\u5f88\u5bb9\u6613\u5beb\uff1a\u905e\u8ff4\u5730\u6c42\u51fa\u5404\u5225\u5b50\u6a39\u7d44\u5408\u6578\u4e58\u8d77\u4f86\u5f8c\uff0c\u518d\u4e58\u4e0a\u5c07\u6240\u6709\u9ede\u5206\u7d66\u6240\u6709\u5b50\u6a39\u7684\u7d44\u5408\u6578\uff0c\u5373\u662f\u9019\u500b\u6a39\u7684\u7d44\u5408\u6578\u4e86\u3002<\/p>\n\n\n\n<p>\u9019\u88e1\u5c31\u662f\u6211\u6587\u9996\u63d0\u5230\u7684\u6c7a\u7b56\u932f\u8aa4\u4e86\uff1a\u7531\u65bc\u539f\u984c\u8981\u6c42\u6a21 10<sup>9<\/sup>+7 \u7684\u95dc\u4fc2\uff0c\u6c42\u5206\u5806\u7684\u7d44\u5408\u6578\u7528\u5230\u7684\u9664\u6cd5\u6703\u9700\u8981\u4f7f\u7528\u5ef6\u4f38\u6b50\u57fa\u91cc\u5fb7\u6f14\u7b97\u6cd5\u6c42\u7b97\u6a21 10<sup>9<\/sup>+7 \u7684\u4e58\u6cd5\u53cd\u5143\u7d20\u3002\u539f\u672c\u6211\u6c92\u591a\u60f3\u76f4\u63a5\u5728\u6bcf\u6b21\u8981\u6c42\u6642\u5c31\u7b97\u4e00\u6b21\uff0c\u60f3\u8aaa\u61c9\u8a72\u9084\u597d\u7684\u6240\u4ee5\u5728\u770b\u5230\u5c0f\u6e2c\u8cc7\u904e\u4e4b\u5f8c\u5c31\u53bb\u505a Q4 \u4e86\uff0c\u8cfd\u5f8c\u624d\u767c\u73fe\u96b1\u85cf\u7684\u5927\u6e2c\u8cc7\u662f TLE\uff0d\uff0d\u800c\u5728\u591a\u82b1\u4e86\u7d04\u5341\u5206\u9418\u628a\u968e\u4e58\u548c\u968e\u4e58\u5012\u6578\u6a21 10<sup>9<\/sup>+7 \u5efa\u8868\u4e4b\u5f8c\u5c31\u9806\u5229\u901a\u904e\u4e86\u3002\u4e0a\u9762\u622a\u5716\u53ef\u4ee5\u770b\u5230\u9019\u984c\u9001\u51fa\u7684\u6642\u9593\u624d\u53ea\u662f\u958b\u8cfd\u4e00\u5c0f\u6642\u800c\u5df2\uff0c\u4e5f\u5c31\u662f\u5982\u679c\u6211\u7576\u6642\u6c7a\u5b9a\u53bb\u628a\u9019\u908a\u6539\u8d77\u4f86\u7684\u8a71\uff0c\u62ff\u5230\u9019 21 \u5206\u5c31\u80fd\u9032\u5230\u6649\u7d1a\u5708\u4e86\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q4. Retiling<\/h2>\n\n\n\n<p>\u9019\u984c\u6703\u60f3\u63d0\u7684\u539f\u56e0\u5176\u5be6\u55ae\u7d14\u53ea\u662f\u7d00\u9304\u4e00\u4e0b\u6709\u60f3\u5230\u6b63\u89e3\uff0c\u53ea\u4e0d\u904e\u56e0\u70ba\u592a\u4e45\u6c92\u5beb\u9019\u7a2e\u6f14\u7b97\u6cd5\u7684\u95dc\u4fc2\u4e00\u5c0f\u6642\u534a\u9084\u662f\u4f86\u4e0d\u53ca\u628a\u6f14\u7b97\u6cd5\u7d66\u5be6\u4f5c\u51fa\u4f86\u3002\u6b63\u89e3\u53ef\u4ee5\u53bb\u770b\u5b98\u65b9\u7684\u984c\u89e3\uff0c\u6211\u7684\u601d\u8003\u904e\u7a0b\u5e7e\u4e4e\u5c31\u8ddf\u984c\u89e3\u7684\u6558\u8ff0\u65b9\u5f0f\u4e00\u6a23\u4e86\u5c31\u4e0d\u591a\u5728\u9019\u88e1\u63d0\uff1b\u53ea\u662f\u539f\u672c\u6709\u6253\u7b97\u904e\u653e\u6389\u5927\u6e2c\u8cc7\u5148\u505a\u5c0f\u7684\uff0c\u4f46\u9019\u4e00\u984c\u7684\u5c0f\u6e2c\u8cc7\u5176\u5be6\u4e26\u6c92\u6709\u6bd4\u8f03\u597d\u505a\uff0c\u5728\u5168\u90e8\u60f3\u904e\u4e4b\u5f8c\u6703\u767c\u73fe\u5c0f\u6e2c\u8cc7\u7684\u4f5c\u7528\u53ea\u662f\u7576\u505a\u627e\u5230\u5927\u6e2c\u8cc7\u505a\u6cd5\u7684\u6a4b\u800c\u5df2\uff0c\u6240\u4ee5\u5f8c\u4f86\u9084\u662f\u5617\u8a66\u4e00\u53e3\u6c23\u5beb\u51fa\u4f86\uff0c\u53ea\u662f\u521d\u7248\u5beb\u5b8c\u6642\u9593\u5c31\u5feb\u5230\u4e86\u6240\u4ee5 (\u5012)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u7e3d\u7d50<\/h2>\n\n\n\n<p>\u561b\uff0c\u4e5f\u5c31\u4e0d\u7528\u70ba\u6c7a\u7b56\u932f\u8aa4\u627e\u7406\u7531\u4e86\uff0c\u5931\u8aa4\u5c31\u662f\u5931\u8aa4\u3002\u4eca\u5e74 GCJ \u679c\u7136\u9084\u662f\u53ea\u80fd\u5230\u9019\u88e1\u70ba\u6b62\u4e86\u3002<\/p>\n\n\n\n<p>\u5c31\u5728\u9019\u88e1\u63d0\u4e00\u4e0b\u597d\u4e86\uff1a\u4eca\u5e74\u63a5\u4e0b\u4f86\u7684\u4e00\u5169\u500b\u6708\u6211\u6709\u4e00\u4e9b\u8a08\u756b\u8981\u958b\u8dd1\uff0c\u9019\u500b\u539f\u672c\u662f\u8981\u7b49\u5169\u9031\u5f8c\u53e6\u4e00\u4ef6\u4e8b\u5b8c\u6210\u5f8c\u624d\u6703\u6b63\u5f0f\u958b\u59cb\u7684\uff0c\u4e0d\u904e\u6700\u8fd1\u7684\u5927\u4e8b\u8b93\u9019\u53e6\u4e00\u4ef6\u4e8b\u61c9\u8a72\u53ef\u4ee5\u4e0d\u7528\u8655\u7406\u4e86\uff0c\u6240\u4ee5\u6703\u63d0\u524d\u958b\u8dd1\u3002\u61c9\u8a72\u6703\u6709\u4e00\u4e9b\u80fd\u5728\u9019\u88e1\u767c\u8868\u7684\u6771\u897f\u51fa\u4f86\uff0c\u5c31\u8acb\u671f\u5f85\u5427\u3002<\/p>\n\n\n\n<p>\u4e0b\u4e00\u5834\u4e0b\u9031\u65e5\u665a\u4e0a\u7684 GKS Round C \u518d\u898b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5148\u63d0\u7d50\u679c\uff1a\u56e0\u70ba\u4e00\u500b\u505a\u5b8c\u984c\u76ee\u5f8c\u7684\u6c7a\u7b56\u5931\u8aa4\uff0c\u4eca\u5e74\u53c8\u5728 R2 \u843d\u99ac\u4e86\u3002 \u610f\u5916\u7684\u9019\u5834\u7684\u96e3\u5ea6\u4e26\u6c92\u6709\u5f88\u9ad8\uff1b\u5982\u679c\u662f\u5e73\u5e38\u5c31\u6709\u5728 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7,4],"tags":[],"class_list":["post-702","post","type-post","status-publish","format-standard","hentry","category-gcj","category-programming"],"_links":{"self":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/702","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=702"}],"version-history":[{"count":5,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/702\/revisions"}],"predecessor-version":[{"id":710,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/702\/revisions\/710"}],"wp:attachment":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=702"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=702"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=702"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}