{"id":859,"date":"2021-10-17T00:46:54","date_gmt":"2021-10-16T16:46:54","guid":{"rendered":"https:\/\/blog.cruciferslab.net\/?p=859"},"modified":"2021-10-17T00:53:49","modified_gmt":"2021-10-16T16:53:49","slug":"gks-2021-round-g","status":"publish","type":"post","link":"https:\/\/blog.cruciferslab.net\/?p=859","title":{"rendered":"GKS 2021 Round G"},"content":{"rendered":"\n

\u7c21\u55ae\u63d0\u4e00\u4e0b Round F \u6c92\u53c3\u6230\u7684\u539f\u56e0\uff1a\u56e0\u70ba\u5b83\u5728\u534a\u591c\u3002\u4e0a\u500b\u6708\u521d\u56e0\u70ba\u4e00\u4e9b\u4e8b\u60c5\u56de\u8001\u5bb6\u4f86\uff0c\u986f\u7136\u4e0d\u53ef\u80fd\u5728\u6709\u5bb6\u4eba\u5728\u7684\u6642\u5019\u534a\u591c\u8d77\u4f86\u5beb code\u2026\u2026<\/p>\n\n\n\n

\u9019\u6b21\u6210\u7e3e\u662f 108 \u540d\uff0c\u53ea\u6709 Q3 \u7684\u5927\u6e2c\u8cc7\u6c92\u904e\u3002\u5206\u6578\u622a\u5716\u4ee5\u4e0b\u6709\u96f7\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n\n\n\n\n

Q1. Dogs and Cats<\/h2>\n\n\n\n

\u7e3d\u5171\u6700\u591a\u53ea\u6709\u4e00\u842c\u96bb\u52d5\u7269\uff0c\u6240\u4ee5\u5c31\u7167\u984c\u610f\u9935\u904e\u53bb\u5c31\u884c\u4e86\u3002\u4e0d\u7528\u592a\u591a\u8655\u7406\u3002<\/p>\n\n\n\n

Q4. Simple Polygon<\/h2>\n\n\n\n

\u7136\u5f8c\u5c31\u505c\u4f4f\u4e86\u3002Q2 \u521d\u770b\u597d\u50cf\u6709\u9ede\u53ef\u6015\u6240\u4ee5\u8df3\u904e\uff0cQ3 \u597d\u50cf\u8981\u597d\u4e00\u9ede\u7684\u505a\u6cd5\uff0cQ4\u2026\u2026\u6709\u9ede\u4e0d\u597d\u6e4a\u7684\u6a23\u5b50\u3002\u4e0d\u904e\u8981\u6c42\u683c\u5b50\u9ede\u9019\u4ef6\u4e8b\u5176\u5be6\u8b93\u6211\u60f3\u5230\u76ae\u514b\u5b9a\u7406<\/a>\uff1a\u7c21\u55ae\u591a\u908a\u5f62\u662f\u76ae\u514b\u5b9a\u7406\u7684\u524d\u63d0\uff0c\u800c\u984c\u76ee\u7d66\u7684\u76ee\u6a19\u662f\u9762\u7a4d\u6578\u503c\u7684\u5169\u500d\uff0c\u8ddf\u5b9a\u7406\u7684\u5f62\u5f0f\u4e5f\u5f88\u5408\u3002<\/p>\n\n\n\n

\u518d\u4ed4\u7d30\u60f3\u60f3\uff0c\u76ae\u514b\u5b9a\u7406\u5176\u5be6\u9084\u544a\u8a34\u4e86\u6211\u5011\u5230\u5e95\u8981\u600e\u9ebc\u69cb\u9020\u51fa\u8981\u7684\u5f62\u72c0\u3002\u600e\u9ebc\u8aaa\uff1f\u5982\u679c\uff0c\u6211\u5011\u6709\u8fa6\u6cd5\u4f7f\u69cb\u9020\u51fa\u4f86\u7684\u591a\u908a\u5f62\u5167\u90e8\u4e0d\u542b\u4efb\u4f55\u683c\u9ede\uff0c\u90a3\u53ea\u8981\u63a7\u5236\u908a\u4e0a\u7684\u683c\u9ede\u6578\u5c31\u80fd\u505a\u51fa\u4efb\u610f 1\/2 \u500d\u6578\u7684\u5f62\u72c0\u4e86\uff1b\u7a0d\u5fae\u53d6\u4e00\u9ede\u5de7\uff0c\u5176\u81f3\u53ef\u4ee5\u628a\u908a\u4e0a\u683c\u9ede\u6578\u5168\u90e8\u653e\u5728\u540c\u4e00\u908a\uff0c\u8b93\u9019\u4e00\u908a\u7684\u53e6\u4e00\u9802\u9ede\u4e00\u8def\u5ef6\u4f38\u51fa\u53bb\u3002<\/p>\n\n\n\n

\u7a0d\u5fae\u5beb\u756b\u4e86\u4e00\u6703\u4e4b\u5f8c\uff0c\u6211\u627e\u5230\u4e86\u9019\u500b\u69cb\u9020\u6cd5\uff1a<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

\u9078\u53d6 0 \u5230 N-1 \u865f\u9ede\uff0c\u4f9d\u7167\u5716\u4e2d\u7684\u9023\u6cd5\u9023\u6210 N \u908a\u5f62 (\u6700\u5f8c\u4e00\u908a\u662f\u6700\u53f3\u908a\u53ea\u6709\u4e00\u500b\u908a\u5728\u5716\u4e0a\u7684\u5169\u9ede\u76f8\u9023)\uff1b\u5982\u679c\u9762\u7a4d\u8981\u66f4\u5927\u7684\u8a71\uff0c\u5247\u628a N-1 \u865f\u9ede\u6cbf\u8457\u5716\u4e2d\u7684\u908a\u7684\u65b9\u5411\u5f80\u5916\u62c9\u51fa\u53bb\uff0c\u6bcf\u8981\u591a 1\/2 \u9762\u7a4d\u5c31\u591a\u62c9\u5230\u4e0b\u4e00\u500b\u683c\u9ede\u3002\u5bb9\u6613\u770b\u5230\u9019\u500b\u591a\u908a\u5f62 (\u5305\u542b\u5ef6\u4f38\u51fa\u53bb\u7684\u5f62\u72c0) \u5167\u90e8\u4e0d\u542b\u683c\u9ede\uff0c\u800c\u5ef6\u4f38\u51fa\u53bb\u6703\u628a\u908a\u4e0a\u7684\u683c\u9ede\u90fd\u653e\u5728\u540c\u4e00\u908a (\u62c9\u51fa\u53bb\u7684\u90a3\u500b\u908a) \u4e0a\uff0c\u56e0\u6b64\u53ef\u4ee5\u5bb9\u6613\u7684\u78ba\u8a8d\u9019\u6a23\u78ba\u5be6\u80fd\u69cb\u9020\u51fa\u6240\u8981\u9762\u7a4d\u4f86\u3002<\/p>\n\n\n\n

\u7121\u89e3\u7684\u72c0\u6cc1\u5462\uff1f\u5247\u9084\u662f\u56de\u5230\u76ae\u514b\u5b9a\u7406\u3002N \u908a\u5f62\u6709 N \u500b\u9802\u9ede\uff0c\u6240\u4ee5\u908a\u754c\u4e0a\u7684\u683c\u9ede\u6578\u81f3\u5c11\u662f N\uff0c\u56e0\u6b64\u9762\u7a4d\u81f3\u5c11\u662f N\/2-1 (\u5c0d\u61c9\u8f38\u5165\u503c N-2)\uff0c\u56e0\u6b64\u6bd4\u9019\u500b\u66f4\u5c0f\u7684\u8f38\u5165\u503c\u5c31\u80fd\u5224\u5b9a\u70ba\u7121\u89e3\u3002<\/p>\n\n\n\n

\u4e0d\u904e\u6211\u7684\u69cb\u9020\u6cd5\u7a0d\u5fae\u9700\u8981\u591a\u4e00\u9ede\u9ede\u9ede\u7684\u8a08\u7b97 (k \u865f\u9ede x \u5ea7\u6a19\u662f \\(\\lfloor k\/2\\rfloor\\)\uff0c\u4f46 y \u5ea7\u6a19\u8981\u5f9e \\(\\lfloor k\/4\\rfloor\\) \u4e0a\u5224\u5b9a\u662f\u9918 0 \u6216 3 \u518d\u52a0 1\uff0c\u7136\u5f8c\u5ef6\u4f38\u7684\u65b9\u5411\u5c0d\u9918 0 \u9918 1 \u662f\u53f3\u4e0a\uff0c\u9918 2 \u9918 3 \u662f\u53f3\uff0c\u4e5f\u8981\u505a\u5224\u65b7)\uff1b\u984c\u89e3\u7684\u69cb\u9020\u6cd5\u662f\u4e00\u6a23\u7684\u9053\u7406\uff0c\u4f46\u53d6\u4e86\u66f4\u5de7\u7684\u64fa\u6cd5\u8b93\u8f38\u51fa\u5ea7\u6a19\u5e7e\u4e4e\u6c92\u6709\u5224\u65b7\u5f0f\u3002<\/p>\n\n\n\n

Q2. Staying Hydrated<\/h2>\n\n\n\n

\u9019\u984c\u6211\u5b8c\u5168\u88ab\u5b83\u552c\u4f4f\u4e86\uff0c\u56e0\u70ba\u770b\u8d77\u4f86\u597d\u50cf\u662f\u4e00\u500b\u5f88\u53ef\u6015\u7684\u6700\u4f73\u5316\u554f\u984c\uff1b\u4e0d\u904e\u4ed4\u7d30\u770b\u4e0b\u53bb\u624d\u767c\u73fe\u984c\u76ee\u88e1\u5176\u5be6\u6709\u597d\u4e9b\u500b\u5f31\u9ede\u5b58\u5728\u3002<\/p>\n\n\n\n

\u7b2c\u4e00\u500b\u9ede\u5c31\u662f\uff1a\u984c\u76ee\u8981\u6700\u5c0f\u5316\u7684\u662f\u66fc\u54c8\u9813\u8ddd\u96e2\uff0c\u4e0d\u662f\u6b50\u6c0f\u8ddd\u96e2\u3002\u4ee5\u4e00\u500b\u7528\u9019\u7a2e\u6545\u4e8b\u51fa\u7684\u984c\u76ee\u4f86\u8aaa\uff0c\u6c42\u66fc\u54c8\u9813\u8ddd\u96e2\u5176\u5be6\u9084\u6eff\u602a\u7684\uff1b\u4ed4\u7d30\u60f3\u5c31\u6703\u767c\u73fe\uff0c\u6c42\u66fc\u54c8\u9813\u8ddd\u96e2\u7684\u548c\u4ee3\u8868\u5176\u5be6\u6211\u5011\u53ef\u4ee5\u628a\u5169\u500b\u5ea7\u6a19\u8ef8\u62c6\u958b\u7b97\u3002\u4e8c\u7dad\u7684\u984c\u76ee\u8b8a\u6210\u4e86\u5169\u500b\u4e00\u7dad\u984c\u76ee\uff0c\u5b83\u8981\u6211\u5011\u5728\u6578\u7dda\u4e0a\u627e\u4e00\u500b\u9ede\uff0c\u4f7f\u5176\u5c0d\u7d66\u5b9a\u7684\u8a31\u591a\u5340\u9593\u7684\u8ddd\u96e2\u548c\u6700\u5c0f\u3002<\/p>\n\n\n\n

\u597d\u50cf\u9084\u662f\u5f88\u9ebb\u7169\uff1f\u6211\u5728\u601d\u8003\u5230\u5e95\u8981\u8a66\u7b97\u54ea\u4e9b\u9ede\u6642\u624d\u6ce8\u610f\u5230\uff1a\u5982\u679c\u8a66\u7b97\u7684\u9ede\u5728\u5169\u500b\u6771\u897f\u4e4b\u9593\u79fb\u52d5\u7684\u8a71\uff0c\u5c0d\u9019\u5169\u500b\u6771\u897f\u4e4b\u9593\u7684\u8ddd\u96e2\u548c\u662f\u56fa\u5b9a\u7684\u3002\u9019\u500b\u6027\u8cea\u5176\u5be6\u99ac\u4e0a\u8b93\u6211\u806f\u60f3\u5230\u4e00\u500b\u984c\u578b\u7684\u901f\u89e3\uff1a\u5f62\u5982 \\(\\sum_i\\left|x-a_i\\right|\\) \u5f0f\u5b50\u7684\u6975\u5c0f\u503c\u767c\u751f\u5728 x \u503c\u70ba\u6240\u6709 \\(a_i\\) \u7684\u4e2d\u4f4d\u6578\u6642\u3002\u9019\u500b\u901f\u89e3\u6709\u500b\u5f88\u5e7e\u4f55\u76f4\u89ba\u7684\u8b49\u660e<\/a>\uff0c\u800c\u5c31\u662f\u9019\u500b\u8b49\u660e\u88e1\u300cx \u503c\u5728\u5ea7\u6a19\u8ef8\u4e0a\u6383\u904e\u53bb\u6642\u7684\u8ddd\u96e2\u548c\u7684\u8b8a\u5316\u300d\u8b93\u6211\u767c\u73fe\u540c\u6a23\u7684\u8ad6\u8b49\u4e5f\u80fd\u7528\u5728\u9019\u500b\u984c\u76ee\u88e1\uff1b\u5dee\u5225\u53ea\u6709\u5728\u5c0d\u55ae\u9ede\u6642\u7d93\u904e\u659c\u7387\u6703\u52a0 2\uff0c\u4f46\u5c0d\u5340\u9593\u6642\u9019\u500b\u52a0 2 \u6703\u62c6\u6210\u5169\u500b\u52a0 1 \u5206\u5225\u5728\u5169\u7aef\u589e\u52a0\u3002\u56e0\u6b64\uff0c\u540c\u6a23\u7684\u7d50\u8ad6\uff0d\uff0d\u6975\u5c0f\u503c\u767c\u751f\u5728\u4e2d\u4f4d\u6578\uff0d\uff0d\u5c0d\u9019\u500b\u72c0\u6cc1\u4e5f\u6703\u6210\u7acb\u3002<\/p>\n\n\n\n

\u6240\u4ee5\u7b54\u6848\u5c31\u5f88\u7c21\u55ae\u4e86\uff1ax y \u5ea7\u6a19\u5404\u81ea\u6536\u96c6\u8d77\u4f86\uff0c\u6392\u5e8f\u6c42\u4e2d\u4f4d\u6578\u5373\u53ef\u3002\u7531\u65bc\u5ea7\u6a19\u6578\u91cf\u4e00\u5b9a\u662f\u5076\u6578\uff0c\u4e2d\u4f4d\u6578\u4e00\u5b9a\u662f\u5728\u5169\u500b\u6578\u4e4b\u9593\uff1b\u984c\u76ee\u8981\u6c42\u8981\u7d66\u51fa\u5ea7\u6a19\u6700\u5c0f\u7684\u90a3\u500b\uff0c\u6240\u4ee5\u7b54\u6848\u5c31\u662f\u9019 2K \u500b\u6578\u4e2d\u7b2c K \u5c0f\u7684\u90a3\u500b\u3002<\/p>\n\n\n\n

Q3. Banana Bunches<\/h2>\n\n\n\n

\u6700\u5f8c\u9019\u984c\u2026\u2026\u6211\u5361\u5728 \\(O(N^4)\\) \u505a\u6cd5\u597d\u4e00\u9663\u5b50\uff0c\u7136\u5f8c\u5728\u5beb code \u7684\u904e\u7a0b\u4e4b\u4e2d\u624d\u767c\u73fe\u5230\u53ef\u4ee5\u5beb \\(O(N^3)\\)\uff0c\u96d6\u7136\u89ba\u5f97 5000 \u7684\u4e09\u6b21\u65b9\u611f\u89ba\u6709\u9ede\u5fae\u5999\u4f46\u5c31\u9084\u662f\u5beb\u4e0a\u53bb\u4e86\u3002\u679c\u7136\u5927\u6e2c\u8cc7\u5403\u4e86 TLE\u3002<\/p>\n\n\n\n

\u4e4b\u6240\u4ee5\u6c92\u8003\u616e\u5230\u66f4\u5feb\u7684\u505a\u6cd5\u5176\u5be6\u662f\u88ab\u7a7a\u9593\u5361\u4f4f\u4e86\uff1a\u7c21\u55ae\u7684\u8a18\u9304\u6cd5\u597d\u50cf\u6703\u9700\u8981 \\(O(NK)\\) \u7684\u7a7a\u9593\u7528\u4f86\u66ab\u5b58\u6771\u897f\u53ca\u540c\u6a23\u7684\u6642\u9593\u4f86\u8a08\u7b97\uff0c\u4f46 K \u53ef\u4ee5\u5230\u4e00\u767e\u842c\uff0c\\(O(NK)\\) \u57fa\u672c\u4e0a\u6c92\u6551\u3002\u9019\u500b\u7684\u89e3\u6c7a\u6cd5\u5c31\u8acb\u53c3\u8003\u984c\u89e3\u4e86\u3002<\/p>\n\n\n\n

\u5c0f\u7d50<\/h2>\n\n\n\n

\u5f9e\u4e0a\u9762\u622a\u5716\u53ef\u4ee5\u770b\u5230\uff0c\u6211\u628a 1 4 2 \u4e09\u984c\u505a\u5b8c\u7684\u6642\u9593\u9084\u4e0d\u5230\u4e00\u5c0f\u6642\uff0c\u800c\u56e0\u70ba\u5148\u505a\u4e86\u7b2c 4 \u984c\u9019\u500b\u5927\u5206\u984c\uff0c\u5728\u90a3\u500b\u7576\u4e0b\u6211\u7684\u5206\u6578 (67 \u5206) \u4e00\u5ea6\u5230\u4e86\u66ab\u5b9a\u7b2c\u4e94\u540d (\u7576\u6642\u7684\u524d\u4e09\u540d\u5df2\u7834\u53f0\uff0c\u7b2c\u56db\u540d\u5247\u4e5f\u662f\u53ea\u5269 3 \u5927\u6e2c\u8cc7\u7684 86 \u5206)\u3002\u53ef\u60dc\u4e00\u76f4\u6c92\u80fd\u885d\u7834 Q3 \u9019\u500b \\(O(NK)\\) \u7684\u7246\u6240\u4ee5\u6700\u7d42\u505c\u5728\u4e86\u9019\u500b\u4f4d\u7f6e\u3002<\/p>\n\n\n\n

Round H \u662f\u5728\u4e2d\u5348\uff0c\u770b\u770b\u5230\u6642\u5019\u6211\u80fd\u4e0d\u80fd\u53c3\u6230\u5427\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u7c21\u55ae\u63d0\u4e00\u4e0b Round F \u6c92\u53c3\u6230\u7684\u539f\u56e0\uff1a\u56e0\u70ba\u5b83\u5728\u534a\u591c\u3002\u4e0a\u500b\u6708\u521d\u56e0\u70ba\u4e00\u4e9b\u4e8b\u60c5\u56de\u8001\u5bb6\u4f86\uff0c\u986f\u7136\u4e0d\u53ef\u80fd\u5728\u6709\u5bb6\u4eba\u5728\u7684\u6642 […]<\/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-859","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\/859","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=859"}],"version-history":[{"count":5,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/859\/revisions"}],"predecessor-version":[{"id":866,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/859\/revisions\/866"}],"wp:attachment":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=859"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=859"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=859"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}