{"id":434,"date":"2010-11-25T19:15:00","date_gmt":"2010-11-25T11:15:00","guid":{"rendered":"http:\/\/localhost\/?p=434"},"modified":"2010-11-25T19:15:00","modified_gmt":"2010-11-25T11:15:00","slug":"poi_2010_stage_i_problem_solutions","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/wjmzbmr\/?p=434","title":{"rendered":"POI 2010 Stage I \u9898\u89e3"},"content":{"rendered":"<p> <a href=\"http:\/\/main.edu.pl\/user.phtml?op=showtask&amp;task=gil&amp;con=OI17\">Guilds<br \/><\/a>\u50bb\u53c9\u9898\uff0c\u9996\u5148\u5982\u679c\u6709\u4e00\u4e2a\u5b64\u7acb\u70b9\u663e\u7136\u4e0d\u884c\u3002\u5176\u6b21\u628a\u56fe\u770b\u6210\u6811\uff08\u5ffd\u7565\u591a\u4f59\u8fb9\uff09\uff0c\u5947\u6570\u5c42\u67d3K\uff0c\u5076\u6570\u5c42\u67d3S\u5c31\u53ef\u4ee5\u4e86\u3002\u3002<br \/><a href=\"http:\/\/main.edu.pl\/user.phtml?op=showtask&amp;task=kol&amp;con=OI17\">Railway<br \/><\/a>\u89c1\u6d32\u59b9\u7684\u535a\u5ba2&gt;_&lt;<br \/><a href=\"http:\/\/main.edu.pl\/user.phtml?op=showtask&amp;task=kor&amp;con=OI17\">Beads<\/a><br \/>\u9996\u5148\u6ce8\u610f\u5230\u5982\u679c\u679a\u4e3e\u6bcf\u4e2aK\u3002\u3002\u90a3\u4e48\u5b9e\u9645\u4e0a\u8981\u8003\u8651\u7684\u9879\u94fe\u603b\u4e2a\u6570\u4e3aN\/1+N\/2+&#8230;=O(NLogN)<br \/>\u90a3\u4e48\u679a\u4e3eK\u7684\u8bdd\u3002\u5982\u679c\u80fd\u5feb\u901f\u8ba1\u7b97\u51fa\u6240\u6709\u9879\u94fe\u7684Hash\u503c\u6765\u5224\u91cd\uff0c\u8fd8\u662fdoable\u7684\u3002\u3002<br \/>\u90a3\u4e48Hash\u7528\u500d\u589e\u7b97\uff0c\u5224\u91cd\u7684\u8bdd\u8981\u8003\u8651\u7ffb\u8f6c\uff0c\u7528\u4e24\u4e2a\u96c6\u5408\u641e\uff0c\u4e00\u4e2a\u96c6\u5408\u4fdd\u5b58\u5bf9\u79f0\u7684\u4e32\uff0c\u4e00\u4e2a\u4fdd\u5b58\u975e\u5bf9\u79f0\u7684\u3002\u3002<br \/>\u9047\u5230\u5bf9\u79f0\u4e32\uff0c\u653e\u5165\u96c6\u5408\uff0c\u9047\u5230\u975e\u5bf9\u79f0\u7684\u5c31\u628a\u5b83\u548c\u5b83\u7684\u53cd\u8f6c\u4e00\u8d77\u653e\u5165\u96c6\u5408\u3002\u3002<br \/>\u7136\u540e\u7ed3\u679c\u5c31\u662f|\u5bf9\u79f0\u96c6\u5408|+|\u975e\u5bf9\u79f0\u96c6\u5408|\/2<br \/><a href=\"http:\/\/main.edu.pl\/user.phtml?op=showtask&amp;task=naj&amp;con=OI17\">Divine divisor<\/a><br \/>\u5f88\u5bb9\u6613\u60f3\u5230\u56e0\u5f0f\u5206\u89e3\u4e4b\u540e\u778e\u641e\u3002\u3002\u4f46\u662f\u6211\u7528rho+miller-rabin\u641e\u4e86\u5f88\u4e45\u8fd8\u662f\u53ea\u670989\u5206&gt;_&lt;\u3002\u3002<br \/>\u770b\u4e86\u6807\u7a0b\u4e4b\u540e\u624d\u660e\u767d\uff0c\u56e0\u4e3a\u6240\u6709\u6570\u5c0f\u4e8e10^18\uff0c\u90a3\u4e48\u9996\u5148\u7528\u6240\u6709\u5c0f\u4e8e10^6\u7684\u7d20\u6570\u53bb\u9664\u3002\u3002<br \/>\u90a3\u4e48\u63a5\u4e0b\u6765\u7684\u6570\u5982\u679c\u67093\u4e2a\u8d28\u56e0\u6570pqr\uff0c\u5c31\u77db\u76fe\u4e86\u3002\u6240\u4ee5\u53ea\u53ef\u80fd\u662fp\uff0cpq,p^2\u8fd9\u6837\u7684\u5f62\u5f0f\u3002\u3002<br \/>\u7136\u540e\u8003\u8651\u5b83\u4eec\u4e4b\u95f4\u4e24\u4e24\u7684\u6700\u5927\u516c\u7ea6\u6570\u3002\u7531\u4e8e\u6240\u6709\u6570\u6700\u591a\u53ea\u67092\u4e2a\u7d20\u56e0\u5b50\uff0c\u90a3\u4e48\u5982\u679c\u8be5\u6700\u5927\u516c\u7ea6\u6570\u662f\u67d0\u6570\u7684\u771f\u56e0\u5b50\u3002\u5c31\u80af\u5b9a\u662f\u7d20\u6570\u3002\u3002<br \/>\u7136\u540e\u8003\u8651\u67d0\u6570\u53ef\u80fd\u662fp^2\u7684\u60c5\u51b5\u3002\u3002\u6839\u53f7\u4e00\u4e0b\u5c31\u53ef\u4ee5\u4e86\u3002\u3002<br \/>\u7136\u540e\u5269\u4e0b\u6765\u7684\u6570\u8981\u4e48\u662fpq,\u8981\u4e48\u662fp\u3002\u3002\u800c\u4e14\u4e24\u4e24\u4e4b\u95f4\u8981\u4e48\u76f8\u7b49\u8981\u4e48\u4e92\u8d28\u3002\u3002\u6240\u4ee5\u53ef\u4ee5\u76f4\u63a5\u62ffpq\u53bb\u9664\u6240\u6709\u6570\u3002\u3002\u7ed3\u679c\u7b97\u4e24\u4efd\u5c31\u53ef\u4ee5\u4e86\u3002\u3002<br \/>\u7136\u540e\u7528miller-rabin\u5224\u65ad\u662f\u5426\u662f\u7d20\u6570\u3002\u3002OK\u4e86\u3002<a href=\"http:\/\/main.edu.pl\/user.phtml?op=showtask&amp;task=tes&amp;con=OI17\"><\/a><br \/>\u50bb\u53c9\u9898\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u6570\u50a8\u5b58\u4e00\u4e2a\u6570\u7ec4\u8868\u793a\u5728\u539f\u5e8f\u5217\u4e2d\u7684\u4f4d\u7f6e\u96c6\u5408\u3002\u3002<br \/>\u7136\u540e\u4e00\u4e2a\u4e2a\u5f80\u4e0b\u627e\uff0c\u6bcf\u6b21\u627e\u5f53\u524d\u4f4d\u7f6e\u540e\u7684\u7b2c\u4e00\u4e2a\u8be2\u95ee\u5e8f\u5217\u7684\u5f53\u524d\u6570\u3002\u3002<br \/>\u627e\u4e0d\u5230\u5c31\u6302\u4e86\u3002\u3002 <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Guilds\u50bb\u53c9\u9898\uff0c\u9996\u5148\u5982\u679c\u6709\u4e00\u4e2a\u5b64\u7acb\u70b9\u663e\u7136\u4e0d\u884c\u3002\u5176\u6b21\u628a\u56fe\u770b\u6210\u6811\uff08\u5ffd\u7565\u591a\u4f59\u8fb9\uff09\uff0c\u5947\u6570\u5c42\u67d3K\uff0c\u5076\u6570\u5c42\u67d3S\u5c31\u53ef\u4ee5\u4e86\u3002\u3002Railway\u89c1\u6d32\u59b9\u7684\u535a\u5ba2&gt;_&lt;Beads\u9996\u5148\u6ce8\u610f\u5230\u5982\u679c\u679a\u4e3e\u6bcf\u4e2aK\u3002\u3002\u90a3\u4e48\u5b9e\u9645\u4e0a\u8981\u8003\u8651\u7684\u9879\u94fe\u603b\u4e2a\u6570\u4e3aN\/1+N\/2+&#8230;=O(NLogN)\u90a3\u4e48\u679a\u4e3eK\u7684\u8bdd\u3002\u5982\u679c\u80fd\u5feb\u901f\u8ba1\u7b97\u51fa\u6240\u6709\u9879\u94fe\u7684Hash\u503c\u6765\u5224\u91cd\uff0c\u8fd8\u662fdoable\u7684\u3002\u3002\u90a3\u4e48Hash\u7528\u500d\u589e\u7b97\uff0c\u5224\u91cd\u7684\u8bdd\u8981\u8003\u8651\u7ffb\u8f6c\uff0c\u7528\u4e24\u4e2a\u96c6\u5408\u641e\uff0c\u4e00\u4e2a\u96c6\u5408\u4fdd\u5b58\u5bf9\u79f0\u7684\u4e32\uff0c\u4e00\u4e2a\u4fdd\u5b58\u975e\u5bf9\u79f0\u7684\u3002\u3002\u9047\u5230\u5bf9\u79f0\u4e32\uff0c\u653e\u5165\u96c6\u5408\uff0c\u9047\u5230\u975e\u5bf9\u79f0\u7684\u5c31\u628a\u5b83\u548c\u5b83\u7684\u53cd\u8f6c\u4e00\u8d77\u653e\u5165\u96c6\u5408\u3002\u3002\u7136\u540e\u7ed3\u679c\u5c31\u662f|\u5bf9\u79f0\u96c6\u5408|+|\u975e\u5bf9\u79f0\u96c6\u5408|\/2Divine 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