{"id":401,"date":"2010-10-07T22:49:00","date_gmt":"2010-10-07T14:49:00","guid":{"rendered":"http:\/\/localhost\/?p=401"},"modified":"2010-10-07T22:49:00","modified_gmt":"2010-10-07T14:49:00","slug":"problem_solutions_zoj_monthly_october_2010","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/wjmzbmr\/?p=401","title":{"rendered":"ZOJ Monthly, October 2010 \u9898\u89e3"},"content":{"rendered":"<p> \u5c3d\u7ba1\u6bd4\u8d5b\u7684\u65f6\u5019\u8fd8\u662f\u5f88\u591a\u9898\u4e0d\u4f1a\u505a\u3002\u3002\u4e0d\u8fc7\u4e0a\u4e86nimendongde\u8fd9\u4e2a\u53f7\u770b\u4e86lichao\u795e\u7287\u548cgaoxin\u795e\u7287\u7684\u7a0b\u5e8f\u4e4b\u540e\u3002\u3002\u603b\u7b97\u5168\u90e8\u90fd\u4f1a\u4e86\u56e7\u3002\u3002\u3002<br \/>Orz Sro Orz gaoxin&amp;lichao\u795e\u7287<br \/>A\uff0c\u7eaf\u6a21\u62df\u9898\u3002\u3002\u76f4\u63a5\u4e0a\u5c31\u597d\u4e86\u3002\u3002\u4f46\u662f\u6211\u4e00\u5f00\u59cb\u7528cin TLE\uff0c\u7136\u540e\u6539\u6210C\u7684\u540e\u4e0d\u77e5\u9053\u54ea\u91cc\u5199\u4e8c\u4e86WA\u56e7\u3002\u3002<br \/>\u6700\u540e\u662fgaoxin\u795e\u7287\u505a\u7684\u3002\u3002\u6211\u592a\u5f31\u4e86\u56e7\u3002\u3002\u3002<br \/>B,\u7eaf\u6570\u5b66\u9898\uff0c\u6211\u4e00\u5f00\u59cb\u505aWA\uff0c\u6700\u540e\u662flichao\u795e\u7287A\u7684\u56e7\u3002\u3002<br \/>\u8bbe\u4e0a\u9762\u5207\u4e86A\u6b21\uff0c\u4fa7\u9762\u5207\u4e86B\u6b21\uff0c\u514b\u9686\u4e86C\u6b21\uff0c<br \/>\u90a3\u4e48A+B+C=M<br \/>(A==0?1:2A)*(B+1)+C=N<br \/>\u82e5A\u4e3a0\uff0c\u90a3\u4e48\u5f97\u5230N=M+1\u3002\u3002\u663e\u7136\u6b64\u65f6\u7b54\u6848\u4e3a0\u3002\u3002<br \/>\u82e5N&lt;M+1\u3002\u3002\u90a3\u4e48\u7531\u4e8e\u6bcf\u6b21\u64cd\u4f5c\u4e4b\u540e\u5757\u6570\u589e\u52a0\u3002\u3002\u3002\u663e\u7136\u662f\u65e0\u89e3\u7684\u3002\u3002\u3002<br \/>\u90a3\u4e48\u73b0\u5728A&gt;0<br \/>\u89e3\u5f97\uff1a<br \/>2*A*B+A-B=N-M.<br \/>\u8003\u8651\u914d\u5e73\u3002\u3002<br \/>(A-1\/2)(2*B+1)+1\/2=N-M<br \/>(2A-1)(2B+1)=2N-2M-1&#8230;<br \/>\u7136\u540e\u5c31nimendongde\u4e86\u3002\u3002<br \/>\u679a\u4e3e\u53f3\u8fb9\u7684\u56e0\u5b50\u3002\u3002\u3002<br \/>C\uff1a<br \/>\u6309\u6700\u77ed\u8def\u5efa\u56fe\uff0c\u53ef\u4ee5\u53d1\u73b0\u6c42\u662f\u6c42\u4e00\u4e2aACG\u4e2d\u7ecf\u8fc7\u4e00\u4e2a\u70b9\u7684\u8def\u5f84\u6570\u3002\u3002<br \/>\u7136\u540e\u8bbein[t]\u4e3a0-&gt;t\u7684\u8def\u5f84\u6570\uff0cout[t]\u4e3at\u51fa\u53d1\u70b9\u8def\u5f84\u6570.<br \/>\u90a3\u4e48in[t]=Sum{in[i],\u6709\u8fb9i-&gt;t}<br \/>out[t]=Sum{out[i],\u53f3\u8fb9t-&gt;i}+1\u3002\u3002<br \/>\u7136\u540e\u4e58\u8d77\u6765\u5c31OK\u4e86\u3002\u3002<br \/>\u6ce8\u610f10^10*10^10\u4f1a\u8d85long long<br \/>a*b=2*a*(b\/2)+a*(b%2)\u3002\u3002\u3002<br \/>\u4e8e\u662f\u4e8c\u5206\u7684\u4e58\u6cd5\uff08\u8fd9\u3002\u3002\u3002\uff09\u5c31\u53ef\u4ee5\u907f\u514d\u7206long long\u4e86\u56e7\u3002\u3002\u3002<br \/>D\uff1a<br \/>\u975e\u5e38\u6076\u5fc3\u7684\u8ba1\u7b97\u51e0\u4f55\uff0cgaoxin\u795e\u7287\u592a\u5f3a\u4e86\u3002\u3002\u786c\u662fA\u6389\u4e86Orz Sro\u3002\u3002\u3002<br \/>\u5404\u79cd\u9ebb\u70e6\u3002\u3002\u3002<br \/>E\uff1a<br \/>\u9996\u5148\u5c06\u6240\u6709trap\u6309Di\u6392\u5e8f\uff0c\u7136\u540e\u4e00\u4e2a\u4e2a\u5904\u7406\uff0c\u8bb0\u5f55\u5f53\u524d\u6d88\u8017\u65f6\u95f4\u7684\u548cnow\uff0c<br \/>\u6bcf\u6b21\u9047\u5230\u4e00\u4e2atrap\uff0c\u5982\u679c\u5b83\u52a0\u8fdb\u53bb\u4e4b\u540enow\u8d85\u8fc7\u4e86\u5b83\u7684D\u3002\u3002<br \/>\u90a3\u4e48\u5c31\u628a\u5f53\u524d\u8981\u4fee\u590d\u7684\u6240\u6709trap\u4e2d\u82b1\u8d39\u65f6\u95f4\u6700\u5927\u7684\u7ed9\u5220\u6389\u3002\u7528\u5806\u6765\u7ef4\u62a4\u5c31\u53ef\u4ee5\u4e86\u3002\u3002<br \/>F:<br \/>\u5f88\u7b80\u5355\u7684DP\u3002\u3002\u5c31\u662f\u8981\u9ad8\u7cbe\u5ea6\u3002\u3002<br \/>\u7136\u540e\u6ce8\u610f\u5230\u8981\u8f93\u51fa\u7ea6\u5316\u7684\u5206\u6570\uff0c\u7531\u4e8e\u5206\u6bcd\u662fb-a+1\u7684n\u6b21\u65b9\u3002\u3002\u8fd9\u4e2a\u73a9\u610f\u7684\u8d28\u56e0\u6570\u4e0d\u591a\u3002\u3002<br \/>\u4e00\u4e2a\u4e2a\u7684\u4e24\u8fb9\u90fd\u9664\u8fc7\u53bb\u5c31\u53ef\u4ee5\u4e86\u3002\u3002<br \/>\u6211\u7528Java\u5f3aA\u6389\u4e86\u56e7\u3002\u3002\u3002<br \/>G\uff1a<br \/>\u6ce8\u610f\u5bf9\u4e00\u4e2aai\uff0c\u6211\u4eec\u7684di\u80af\u5b9a\u662f\u5b83\u7684\u56e0\u5b50\uff0c\u7136\u540e\u4e00\u4e2a\u6570\u7684\u56e0\u5b50\u6570\u4e00\u822c\u662f\u6bd4\u8f83\u5c0f\u7684\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u679a\u4e3e\u3002\u3002<br \/>\u7136\u540e\u8003\u8651\u4e00\u4e2adi\uff0c\u6211\u4eec\u9700\u8981\u77e5\u9053\u5728x\u5230y\u6709\u591a\u5c11\u6570t<br \/>\u6700\u5927\u516c\u7ea6\u6570\uff08ai,t\uff09=di\u3002\u3002<br \/>\u8fd9\u4e2a\u53ef\u4ee5\u7528\u5bb9\u65a5\u539f\u7406\u89e3\u51b3\u3002\u3002<br \/>\u5177\u4f53\u7684\u8bf4\u5c31\u662f\u8bbeF(n)\u8868\u793ax\u5230y\u4e4b\u95f4\u6709\u591a\u5c11\u6570\u4e0eai\u7684\u6700\u5927\u516c\u7ea6\u6570\u4e3an\u3002\u3002<br \/>\u90a3\u4e48F(n)=x\u5230y\u4e4b\u95f4n\u7684\u500d\u6570-Sum{F(m),m\u662fn\u7684\u500d\u6570}\u3002\u3002\u3002<br \/>\u7b97\u51fa\u8fd9\u4e2a\u5c31\u53ef\u4ee5\u76f4\u63a5DP\u4e86\u3002\u3002<br \/>H\uff1a<br \/>\u8fd9\u4e2a\u592a\u56e7\u4e86\u3002\u3002<br \/>\u8981\u5404\u79cd\u5206\u60c5\u51b5\u8ba8\u8bba\uff1a<br \/>\u8bbea&lt;b<br \/>a=0 b=0:\u6b64\u65f6\u5c31\u662f\u4e00\u4e2a\u70b9\uff0c\u8be5\u70b9\u7684\u60c5\u51b5\u51b3\u5b9a\u4e00\u5207<br \/>a=0 b&gt;0\uff1a\u6b64\u65f6\u662f\u4e00\u7ef4\u7684\u60c5\u51b5\uff0c\u5c31\u662f\u6ee1\u8db3\u6761\u4ef6\u7684\u7ebf\u6bb5\u957f\u5ea6\/\u7ebf\u6bb5\u603b\u957f\u5ea6b<br \/>a&gt;0 b&gt;0\uff1a\u6b64\u65f6\u662f\u4e8c\u7ef4\u7684\u60c5\u51b5\uff0c\u753b\u51fa\u56fe\u6765\u53ef\u4ee5\u53d1\u73b0\u662f\u4e24\u6761\u7ebf\u53bb\u5207\u4e00\u4e2a\u77e9\u5f62\u3002\u3002\u3002<br \/>\u8fd8\u6709\u4e00\u70b9\u3002\u3002\u3002\u5c31\u662f\u5f53\u7b54\u6848=0\u7684\u65f6\u5019\u3002\u6309\u4e0a\u9762\u8fd9\u4e48\u5199\u751a\u81f3\u6709\u53ef\u80fd\u8f93\u51fa-0.000000<br \/>\u8fd9\u3002\u3002\u3002\u3002<br \/>I\uff1a<br \/>\u8ba1\u7b97\u51e0\u4f55\u7684\u6c34\u9898\u3002\u3002\u4e0d\u591a\u8bf4\u4e86\u56e7\u3002\u3002\u3002<br \/>J\uff1a\u795e\u7287\u9898\u554a\u3002\u3002\u3002gaoxin\u548clichao\u795e\u7287\u7684\u505a\u6cd5\u592a\u5f3a\u5927\u4e86\u3002\u3002\u4e25\u91cdOrz\uff01\uff01\uff01\uff01<br \/>\u9996\u5148\u8003\u8651O(n)\u7684\u505a\u6cd5\u3002\u3002<br \/>\u6ce8\u610f\u5230\u53ef\u4ee5\u5217\u671f\u671b\u65b9\u7a0bF[n]=pre*F[n-1]+nxt*F[n+1]+1<br \/>pre\u548cnxt\u5206\u522b\u662f\u5411\u524d\u548c\u5411\u540e\u8d70\u7684\u6982\u7387\u3002\u3002<br \/>\u90a3\u4e48\u89e3\u65b9\u7a0b\u5c31\u662fn^3\u4e86\u3002\u3002<br \/>\u4f46\u8fd9\u9898\u8ddf\u4e0a\u6b21CF\u7684\u67d0\u9898\u5f88\u50cf\u3002\u3002\u8fd9\u4e2a\u77e9\u9635\u662f\u4e00\u4e2a<a href=\"http:\/\/en.wikipedia.org\/wiki\/Tridiagonal_matrix_algorithm\">Tridiagonal_matrix<\/a><br \/><a href=\"http:\/\/en.wikipedia.org\/wiki\/Tridiagonal_matrix_algorithm\">http:\/\/en.wikipedia.org\/wiki\/Tridiagonal_matrix_algorithm<\/a><br \/>\u6240\u4ee5\u53ef\u4ee5O(n)\u6c42\u89e3\u3002\u3002<br \/>\u7136\u540e\u6d4b\u8bd5\u7ec4\u6570\u8fc7\u591a\u3002\u3002\u3002O\uff08n\uff09TLE\u56e7\u3002\u3002\u3002\u3002<br \/>n=2\u7684\u60c5\u51b5\u5f88\u5f88\u56e7\u3002\u3002<br \/>\u53ef\u4ee5\u53d1\u73b0m=2\u7684\u60c5\u51b5\u5173\u4e8en\u6210\u4e8c\u6b21\u5173\u7cfb\u3002\u3002\u662f\u4e00\u4e2an\u7684\u4e8c\u6b21\u51fd\u6570\u3002\u3002<br \/>\u82e5m&gt;2<br \/>\u8bbeF(n,m)\u4e3a\u7b54\u6848<br \/>\u7136\u540e\u795e\u7287\u4eec\u4f3c\u4e4e\u662f\u53d1\u73b0\u5f53n\u53d8\u5927\u4e86\u4e4b\u540eF(n+1,m)-F(n,m)\u5feb\u901f\u8d8b\u5411\u4e8e\u5e38\u6570\u3002\u3002\u3002<br \/>\u6240\u4ee5\u53ea\u9700\u8981\u8ba1\u7b97\u5f88\u5c11\u7684n\u3002\u3002\u5f53\u8fd9\u4e2a\u5e38\u6570\u53d8\u7684\u8db3\u591f\u7a33\u5b9a\u4e4b\u540e\u3002\u3002\u5c31\u53ef\u4ee5\u76f4\u63a5\u7ed9\u7b54\u6848\u4e86\u3002\u3002<br \/>\u590d\u6742\u5ea6\u4e0d\u6e05\u695a\u3002\u3002\u4f460msAC\u4e86\u56e7\u3002\u3002\u3002 <\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5c3d\u7ba1\u6bd4\u8d5b\u7684\u65f6\u5019\u8fd8\u662f\u5f88\u591a\u9898\u4e0d\u4f1a\u505a\u3002\u3002\u4e0d\u8fc7\u4e0a\u4e86nimendongde\u8fd9\u4e2a\u53f7\u770b\u4e86lichao\u795e\u7287\u548cgaoxin\u795e\u7287\u7684\u7a0b\u5e8f\u4e4b\u540e\u3002\u3002\u603b\u7b97\u5168\u90e8\u90fd\u4f1a\u4e86\u56e7\u3002\u3002\u3002Orz Sro Orz gaoxin&amp;lichao\u795e\u7287A\uff0c\u7eaf\u6a21\u62df\u9898\u3002\u3002\u76f4\u63a5\u4e0a\u5c31\u597d\u4e86\u3002\u3002\u4f46\u662f\u6211\u4e00\u5f00\u59cb\u7528cin 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