{"id":1016,"date":"2022-05-22T23:02:11","date_gmt":"2022-05-22T15:02:11","guid":{"rendered":"https:\/\/blog.cruciferslab.net\/?p=1016"},"modified":"2022-05-22T23:02:11","modified_gmt":"2022-05-22T15:02:11","slug":"gks-2022-round-c","status":"publish","type":"post","link":"https:\/\/blog.cruciferslab.net\/?p=1016","title":{"rendered":"GKS 2022 Round C"},"content":{"rendered":"\n

\u7d50\u679c\u665a\u4e03\u5176\u5be6\u4e5f\u4e0d\u662f\u4ec0\u9ebc\u597d\u6642\u9593\u3002\u9084\u597d GKS \u7684\u96e3\u5ea6\u4e00\u822c\u4f86\u8aaa\u504f\u4f4e\uff0c\u6240\u4ee5\u4e2d\u9593\u8dd1\u53bb\u908a\u505a\u4e8b\u908a\u60f3\u984c\u76ee\u9084\u662f\u53ef\u4ee5\u7684\u3002<\/p>\n\n\n\n

\u7834\u53f0\u6642\u9593\u662f\u6bd4\u8cfd\u7d42\u4e86\u524d 15 \u5206\u9418\uff0c\u6392\u540d 188 \u540d\uff1b\u4e0d\u904e\u5982\u679c\u4e0d\u8a08\u6eff\u5206\u9b54\u738b Q4 \u5927\u6e2c\u8cc7\u7684\u8a71\uff0c\u5230 Q4 \u5c0f\u901a\u904e\u7684\u6642\u9593\u662f 1 \u5c0f\u6642 23 \u5206\u9418\uff0c\u5927\u7d04\u624d\u7528\u53bb\u4e00\u534a\u6642\u9593\u800c\u5df2\u3002<\/p>\n\n\n\n

\u7167\u4f8b\u5206\u6578\u622a\u5716\u4ee5\u4e0b\u6709\u96f7\u3002<\/p>\n\n\n\n

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

Q1. New Password<\/h2>\n\n\n\n

\u7c21\u55ae\u984c\u3002<\/p>\n\n\n\n

Q2. Range Partition<\/h2>\n\n\n\n

\u9019\u984c\u662f GCJ 1A Q2<\/a> \u7684\u7c21\u55ae\u7248\u3002\u90a3\u6642\u7684\u984c\u76ee\u662f\u6211\u5011\u8981\u69cb\u9020\u51fa\u4e00\u7d44\u6578\u8b93\u67d0\u500b\u7bc4\u570d\u5167\u90fd\u6709\u89e3\uff0c\u800c\u9019\u984c\u5247\u662f\u7d66\u5b9a\u4e86\u4f60\u8981\u7528 1~N \u9019\u4e9b\u6578\u4f86\u69cb\u9020\u67d0\u500b\u7bc4\u570d\u5167\u7684\u89e3\u3002\u69cb\u9020\u7684\u65b9\u5f0f\u5176\u5be6\u5f88\u985e\u4f3c\uff0c\u751a\u81f3\u9084\u66f4\u63a5\u8fd1 UVa 10025 \u7684\u69cb\u9020\u6cd5\uff0c\u6240\u4ee5\u5c31\u4e0d\u5728\u9019\u88e1\u591a\u6558\u8ff0\u4e86\u3002<\/p>\n\n\n\n

Q3. Ants on a Stick<\/h2>\n\n\n\n

\u9019\u984c\u7684\u95dc\u9375\u662f\u4e00\u500b\u89c0\u5bdf\uff1a\u628a\u879e\u87fb\u7684\u8def\u7dda\u7d66\u756b\u51fa\u4f86\u53ef\u4ee5\u770b\u5230\u5176\u5be6\u53ef\u4ee5\u4e0d\u8b93\u5b83\u5011\u78b0\u649e\uff0c\u5c31\u7576\u505a\u4e92\u76f8\u7a7f\u904e\u5c31\u597d\u4e86\u3002\u9019\u6a23\u4e00\u4f86\uff0c\u6389\u843d\u6642\u9593\u5c31\u76f4\u63a5\u628a\u6240\u6709\u879e\u87fb\u76f4\u8d70\u6389\u843d\u7684\u6642\u9593\u7d66\u641c\u96c6\u8d77\u4f86\u5c31\u597d\u4e86\u3002\u81f3\u65bc\u662f\u8ab0\u6389\u843d\uff1f\u53ef\u4ee5\u8b49\u660e\uff0c\u671d\u5411\u5169\u500b\u65b9\u5411\u7684\u879e\u87fb\u6578\u662f\u56fa\u5b9a\u7684\uff0c\u4e0d\u7ba1\u5982\u4f55\u78b0\u649e\uff0c\u56e0\u6b64\u6700\u7d42\u6240\u6709\u5de6\u908a\u7684\u879e\u87fb\u6703\u5f80\u5de6\u6389\uff0c\u6240\u6709\u5f80\u53f3\u7684\u879e\u87fb\u6703\u5f80\u53f3\u6389\uff0c\u9019\u6a23\u5c31\u80fd\u5c0d\u51fa\u8ab0\u5728\u4ec0\u9ebc\u6642\u5019\u6389\u843d\u4e86\u3002\u5be6\u969b\u5beb\u8d77\u4f86\u6700\u5f8c\u9019\u4e00\u6b65\u5c31\u548c\u5408\u4f75\u6392\u5e8f\u6cd5\u985e\u4f3c\uff0c\u5169\u500b\u6307\u6a19\u81ea\u5169\u908a\u5f80\u5167\u6383\uff0c\u8ab0\u5148\u6389\u843d\u5c31\u8f38\u51fa\u8ab0\uff0c\u4e00\u8d77\u6389\u843d\u5c31\u5148\u8f38\u51fa\u5c0f\u7684\u865f\u78bc\u5373\u53ef\u3002<\/p>\n\n\n\n

Q4. Palindromic Deletions<\/h2>\n\n\n\n

\u9996\u5148\u5148\u63d0\u4e00\u4e0b\u9019\u984c\u7684\u8f38\u51fa\u683c\u5f0f\uff1a\u9019\u5176\u5be6\u662f\u548c\u53bb\u5e74\u7684 GKS Round H Q4<\/a> \u662f\u4e00\u6a23\u7684\uff0c\u6240\u4ee5\u5c31\u8acb\u53c3\u8003\u90a3\u908a\u4e86\u3002<\/p>\n\n\n\n

\u9019\u984c\u7684\u7c21\u55ae\u505a\u6cd5\u662f\u5c0d\u6240\u6709\u5b50\u5e8f\u5217\u9032\u884c DP\u3002DP \u5f0f\u5f88\u597d\u63a8\uff1a\u6bcf\u500b\u4f4d\u7f6e\u90fd\u522a\u522a\u770b\uff0c\u6c42\u6240\u6709\u9019\u4e9b\u7d50\u679c\u7684\u5e73\u5747\u503c\uff0c\u7136\u5f8c\u5982\u679c\u9019\u500b\u5b50\u5e8f\u5217\u672c\u8eab\u662f\u8ff4\u6587\u5c31\u518d +1 \u5c31\u884c\u4e86\u3002\u9019\u6a23\u505a\u7684\u72c0\u614b\u6578\u662f \\(2^N\\)\uff0c\u6bcf\u500b\u72c0\u614b\u8981\u8dd1\u4e00\u6b21\u6240\u6709\u4f4d\u7f6e\uff0c\u6240\u4ee5\u7e3d\u6642\u9593\u662f \\(O(N\\times 2^N)\\)\uff0c\u662f\u500b\u8b93\u5c0f\u6e2c\u8cc7\u80fd\u904e\u7684\u505a\u6cd5\u3002\u7531\u65bc\u6211\u524d\u4e09\u984c\u505a\u5b8c\u53ea\u7528\u4e86 40 \u5206\u9418\uff0c\u6642\u9593\u96d6\u7136\u6eff\u5145\u88d5\u4e0d\u904e\u6709\u9ede\u8f49\u4e0d\u958b\u5230\u5e95\u8981\u600e\u9ebc\u7b97\u5927\u4e00\u9ede\u7684 N\uff0c\u6240\u4ee5\u6c7a\u5b9a\u5148\u5beb\u4e86\u4e00\u4efd DP \u89e3\u9001\u4e0a\u53bb\uff0c\u9001\u4e0a\u53bb\u7684\u6642\u9593\u5c31\u662f\u525b\u624d\u63d0\u7684\u7d04\u83ab\u4e2d\u5834\u3002<\/p>\n\n\n\n

\u5f8c\u4f86\u60f3\u5230\u5927\u6e2c\u8cc7\u89e3\u6cd5\u7684\u95dc\u9375\u662f\uff1a\u65e2\u7136\u6211\u5011\u53ea\u8981\u6c42\u671f\u671b\u503c\uff0c\u90a3\u628a\u6bcf\u500b\u5c0d\u671f\u671b\u503c\u6709\u8ca2\u737b\u7684\u6771\u897f\u5206\u958b\u770b\u5982\u4f55\uff1f<\/p>\n\n\n\n

\u5230\u5e95\u4ec0\u9ebc\u6771\u897f\u5c0d\u671f\u671b\u503c\u6709\u8ca2\u737b\uff1f\u5c31\u662f\u904a\u6232\u904e\u7a0b\u4e2d\u51fa\u73fe\u7684\u8ff4\u6587\u3002\u628a\u6240\u6709 \\(N!\\) \u7a2e\u904e\u7a0b\u5217\u51fa\u4f86\u5427\uff1a\u8003\u616e\u4e00\u500b\u5b50\u5e8f\u5217\u9577\u5ea6 \\(K\\leq N\\)\u3002\u5168\u90e8\u7684 \\(N!\\) \u7a2e\u522a\u9664\u904e\u7a0b\u4e2d\u6bcf\u500b\u9577\u5ea6\u70ba \\(K\\) \u7684\u5b50\u5e8f\u5217\u90fd\u6709\u51fa\u73fe\uff0c\u800c\u4e14\u90fd\u51fa\u73fe\u4e00\u6a23\u591a\u6b21\uff0c\u56e0\u6b64\u7279\u5b9a\u4e00\u500b\u9577\u5ea6\u70ba \\(K\\) \u7684\u5b50\u5e8f\u5217\u6709 \\(1\/C(N,K)\\) \u7684\u6a5f\u6703\u51fa\u73fe\u5728\u904a\u6232\u4e2d\u3002\u5982\u679c\u9019\u500b\u5b50\u5e8f\u5217\u662f\u8ff4\u6587\uff0c\u90a3\u5b83\u5c31\u5c0d\u6700\u7d42\u7684\u671f\u671b\u503c\u8ca2\u737b\u4e86 \\(1\/C(N,K)\\)\uff1b\u90a3\u6211\u5011\u53ea\u8981\u628a\u6240\u6709\u9019\u4e9b\u8ca2\u737b\u5168\u90e8\u52a0\u8d77\u4f86\u5c31\u662f\u6240\u8981\u6c42\u7684\u671f\u671b\u503c\u4e86\u3002<\/p>\n\n\n\n

\u56e0\u6b64\u6211\u5011\u8981\u6c42\u7684\u5176\u5be6\u662f\uff1a\u6bcf\u500b\u5340\u9593 [x,y)<\/code> \u7576\u4e2d\uff0c\u9577\u5ea6\u70ba k<\/code> \u7684\u8ff4\u6587\u500b\u6578\u3002\u9019\u662f\u4e00\u500b\u4e09\u7dad\u7684 DP \u5f0f\uff1a\u5340\u9593 [x,y)<\/code> \u7684\u9577\u5ea6 k<\/code> \u8ff4\u6587\u500b\u6578\u53ef\u4ee5\u7528\u6392\u5bb9\u6c42\u51fa\u4f86\uff0c\u5b83\u7b49\u65bc\u5340\u9593 [x+1,y)<\/code> \u7684\u9577\u5ea6 k<\/code> \u8ff4\u6587\u6578\uff0c\u52a0\u4e0a\u5340\u9593 [x,y-1)<\/code> \u7684\u9577\u5ea6 k<\/code> \u8ff4\u6587\u6578\uff0c\u6e1b\u53bb\u5340\u9593 [x+1,y-1)<\/code> \u7684\u9577\u5ea6 k<\/code> \u8ff4\u6587\u6578\uff1b\u5982\u679c\u5169\u500b\u7aef\u9ede [x]<\/code> \u548c [y-1]<\/code> \u76f8\u540c\u7684\u8a71\uff0c\u9084\u8981\u518d\u7b97\u4e0a\u5340\u9593 [x+1,y-1)<\/code> \u7684\u9577\u5ea6 k-2<\/code> \u8ff4\u6587\u6578 (\u52a0\u4e0a\u9019\u5169\u500b\u7aef\u9ede\u4e5f\u662f\u8ff4\u6587)\u3002\u5340\u9593\u500b\u6578\u662f \\(O(N^2)\\)\uff0c\u8ff4\u6587\u9577\u5ea6\u6700\u9577\u662f N\uff0c\u6240\u4ee5 DP \u7a7a\u9593\u662f \\(O(N^3)\\)\uff0c\u5c0d \\(N\\leq400\\) \u662f\u8f15\u9b06\u904e\u95dc\u3002<\/p>\n\n\n\n

\u81f3\u65bc\u6211\u5728\u90a3\u4e4b\u5f8c\u9001\u5230\u7b2c\u56db\u6b21\u624d\u904e\u7684\u539f\u56e0\u662f\u2026\u2026\u7b97\u6392\u5bb9\u6642\u6ea2\u4f4d\u4e86\u3002\u6bcf\u6b21\u90fd\u88ab\u6ea2\u4f4d\u5a4a\u2026\u2026<\/p>\n\n\n\n

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

GCJ \u6557\u9663\u4e4b\u5f8c\u53ea\u597d\u5728 GKS \u88e1\u627e\u56de\u4e00\u9ede\u9ede\u81ea\u4fe1\u4e86\u3002\u96d6\u7136\u4e2d\u9593\u8dd1\u53bb\u5beb\u4e86\u53ea\u80fd\u904e Q4 \u5c0f\u6e2c\u8cc7\u7684\u505a\u6cd5\u5c31\u662f\u3002(\u6c57)<\/p>\n\n\n\n

\u9019\u6b21\u6eff\u5206\u4e00\u5171\u6709 223 \u500b\uff0c\u800c\u5c11 Q4 \u5927\u7684 73 \u5206\u7d04\u6709 300 \u500b\uff0c\u7b97\u4e0a\u4e2d\u9593\u5176\u4ed6\u7684\u5206\u6578\u5f8c 73 \u5206\u7684\u6700\u4f4e\u540d\u6b21\u662f 553 \u540d\u3002\u679c\u7136 Q4 \u5927\u9019\u500b\u9b54\u738b\u4e0d\u597d\u6253\u2026\u2026<\/p>\n\n\n\n

GKS \u63a5\u4e0b\u4f86\u5728 6 \u6708\u5e95\u6709\u500b\u7df4\u7fd2\u56de\uff0c\u7136\u5f8c Round D \u662f 7\/10\u3002\u662f\u8aaa\u611f\u89ba\u9019\u88e1\u8b8a\u6210 GCJ \u7d00\u9304\u7528\u4e86\u2026\u2026\u4e4b\u5f8c\u770b\u770b\u80fd\u4e0d\u80fd\u627e\u4e9b\u5225\u7684\u984c\u6750\u4f86\u5beb\u5beb\u5427\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u7d50\u679c\u665a\u4e03\u5176\u5be6\u4e5f\u4e0d\u662f\u4ec0\u9ebc\u597d\u6642\u9593\u3002\u9084\u597d GKS \u7684\u96e3\u5ea6\u4e00\u822c\u4f86\u8aaa\u504f\u4f4e\uff0c\u6240\u4ee5\u4e2d\u9593\u8dd1\u53bb\u908a\u505a\u4e8b\u908a\u60f3\u984c\u76ee\u9084\u662f\u53ef\u4ee5\u7684\u3002 \u7834\u53f0\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-1016","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\/1016","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=1016"}],"version-history":[{"count":2,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/1016\/revisions"}],"predecessor-version":[{"id":1019,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/1016\/revisions\/1019"}],"wp:attachment":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1016"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1016"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1016"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}