{"id":446,"date":"2018-08-11T00:08:14","date_gmt":"2018-08-10T16:08:14","guid":{"rendered":"https:\/\/mnihyc.tk\/blog\/?p=446"},"modified":"2019-01-06T11:33:34","modified_gmt":"2019-01-06T03:33:34","slug":"bzoj-1041-yzoj-3460-%e5%9c%86%e8%a7%84%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/cf.mnihyc.com\/blog\/archives\/446","title":{"rendered":"BZOJ 1041 (YZOJ 3460) \u5706\u89c4\u95ee\u9898"},"content":{"rendered":"<h1 style=\"text-align: center;\">\u5706\u89c4\u95ee\u9898<\/h1>\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u65f6\u95f4\u9650\u5236\uff1a1000MS       \u5185\u5b58\u9650\u5236\uff1a262144KB<\/span><\/p>\n<ul>\n<li>\n<h3>\u95ee\u9898\u63cf\u8ff0<\/h3>\n<\/li>\n<\/ul>\n<p><span style=\"color: black;\">\u5c0f C \u6709\u4e00\u4e2a\u5706\u89c4\uff0c\u4ed6\u7ecf\u5e38\u7528\u5706\u89c4\u5728\u7eb8\u4e0a\u4f5c\u56fe\u3002<\/span><\/p>\n<p><span style=\"color: black;\">\u6709\u4e00\u5929\uff0c\u5c0f C \u51c6\u5907\u5728\u4e00\u4e2a\u5355\u4f4d\u7f51\u683c\u7eb8\u4e0a\u4f5c\u4e00\u4e2a\u5706\u3002\u4ed6\u4ee5\u67d0\u4e2a\u683c\u70b9\u4e3a\u5706\u5fc3\uff0c\u4f5c\u4e86\u4e00\u4e2a\u534a\u5f84\u4e3a <\/span><span style=\"color: black;\">\\(R\\) \u7684\u5706\u3002\u63a5\u7740\uff0c\u4ed6\u5c06\u5706\u7ecf\u8fc7\u7684\u6240\u6709\u683c\u5b50\u6d82\u6210\u9ed1\u8272\u3002\u6ce8\u610f\uff1a\u53ea\u6709\u5706\u7ecf\u8fc7\u4e86\u4e00\u4e2a\u683c\u5b50\u7684\u5185\u90e8\u624d\u80fd\u6d82\u9ed1\uff0c\u53ea\u7ecf\u8fc7\u683c\u5b50\u7684\u8fb9\u754c\u4e0d\u6d82\u9ed1\u3002\u5c0f C \u7684\u95ee\u9898\u662f\uff1a\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u534a\u5f84\u4e3a \\(R\\)<\/span><span style=\"color: black;\"> \u7684\u5706\uff0c\u5171\u6709\u591a\u5c11\u4e2a\u683c\u5b50\u88ab\u6d82\u9ed1\uff1f<\/span><\/p>\n<p>\u8fd9\u662f\u4e00\u4e2a \\(R=10\\)\u7684\u5b9e\u4f8b\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-447\" src=\"https:\/\/cf.mnihyc.com\/blog\/wp-content\/uploads\/2018\/08\/3460-compass-description.png\" alt=\"\" width=\"902\" height=\"454\" srcset=\"https:\/\/cf.mnihyc.com\/blog\/wp-content\/uploads\/2018\/08\/3460-compass-description.png 902w, https:\/\/cf.mnihyc.com\/blog\/wp-content\/uploads\/2018\/08\/3460-compass-description-300x151.png 300w, https:\/\/cf.mnihyc.com\/blog\/wp-content\/uploads\/2018\/08\/3460-compass-description-768x387.png 768w\" sizes=\"auto, (max-width: 902px) 100vw, 902px\" \/><\/p>\n<p><span style=\"color: black;\">\u5de6\u56fe\u4e3a\u5c0f C \u4f5c\u7684\u5706\uff0c\u53f3\u56fe\u662f\u5c06\u5706\u7ecf\u8fc7\u7684\u683c\u5b50\u6d82\u9ed1\u540e\u7684\u56fe\u3002\u53ef\u4ee5\u770b\u51fa\uff0c\\(R=10\\)\u65f6\uff0c\u5171\u6709 68<\/span><span style=\"color: black;\"> \u4e2a\u683c\u5b50\u88ab\u6d82\u9ed1\u3002<\/span><\/p>\n<p><span style=\"color: black;\">\u7ed9\u5b9a\\(N\\)\uff0c\u8ba1\u7b97\u88ab\u6d82\u9ed1\u7684\u683c\u5b50\u6570\u76ee\u3002<\/span><\/p>\n<ul>\n<li>\n<h3>\u8f93\u5165\u683c\u5f0f<\/h3>\n<\/li>\n<\/ul>\n<p><span style=\"color: black;\">\u8f93\u5165\u6587\u4ef6\u5305\u542b\u4e00\u4e2a\u6574\u6570\\(R\\)\uff0c\\(1 \\leq R \\leq 2,000,000,000\\)<\/span><\/p>\n<ul>\n<li>\n<h3>\u8f93\u51fa\u683c\u5f0f<\/h3>\n<\/li>\n<\/ul>\n<p><span style=\"color: black;\">\u5c06\u88ab\u6d82\u9ed1\u7684\u683c\u5b50\u6570\u76ee\u8f93\u51fa\u5230\u6587\u4ef6\u4e2d\u3002<\/span><\/p>\n<ul>\n<li>\u6837\u4f8b\u8f93\u5165<\/li>\n<\/ul>\n<pre>10<\/pre>\n<ul>\n<li> \u6837\u4f8b\u8f93\u51fa<\/li>\n<\/ul>\n<pre>68<\/pre>\n<p>\n<!--more--><\/p>\n<p>&nbsp;<\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-449\" src=\"https:\/\/cf.mnihyc.com\/blog\/wp-content\/uploads\/2018\/08\/QQ\u622a\u56fe20180810235106.png\" alt=\"\" width=\"765\" height=\"123\" srcset=\"https:\/\/cf.mnihyc.com\/blog\/wp-content\/uploads\/2018\/08\/QQ\u622a\u56fe20180810235106.png 765w, https:\/\/cf.mnihyc.com\/blog\/wp-content\/uploads\/2018\/08\/QQ\u622a\u56fe20180810235106-300x48.png 300w\" sizes=\"auto, (max-width: 765px) 100vw, 765px\" \/><\/p>\n<p>\u4e0d\u9519\uff0c\u53ef\u60dc\u8fd9\u4e2a\u662f\u4eba\u5bb6\u5927\u795e\u7684\u505a\u6cd5\uff0c\u6211\u7684\u8bdd\u7edd\u5bf9\u60f3\u4e0d\u51fa\u6765\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u7136\u540e\uff0c\u6211\u60f3\u8d77\u4e86\u4e00\u4e2a\u4e24\u5e74\u524d\u770b\u5230\u7684\u89c6\u9891<\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=NaL_Cb42WyY\">https:\/\/www.youtube.com\/watch?v=NaL_Cb42WyY<\/a><\/p>\n<p>Translated: <a href=\"https:\/\/www.bilibili.com\/video\/av12131743\">https:\/\/www.bilibili.com\/video\/av12131743<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>\u9996\u5148\u5b9a\u4e49      \\(\\chi (n) = \\left\\{ {\\begin{array}{*{20}{c}}<br \/>\n0&amp;{n\\bmod 2 \\equiv 0}\\\\<br \/>\n1&amp;{n\\bmod 4 \\equiv 1}\\\\<br \/>\n{ &#8211; 1}&amp;{n\\bmod 4 \\equiv &#8211; 1}<br \/>\n\\end{array}} \\right.\\)<\/p>\n<p>\u7136\u540e\uff0c\u5bf9\u4e8e\u534a\u5f84\u4e3a\\(\\sqrt{R}\\)\u7684\u5706\uff0c\u5176\u7ecf\u8fc7\u6574\u70b9\u4e2a\u6570\u4e3a\\(4 \\cdot \\sum\\limits_{i|R} {\\chi (i)} \\)<\/p>\n<p>\u6709\u4e86\u8fd9\u4e2a\u7ed3\u8bba\uff0c\u7a0b\u5e8f\u5c31\u4e0d\u96be\u5b9e\u73b0\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u53ea\u9700\u8981\u628a\\(R\\)\u8fdb\u884c\u8d28\u56e0\u6570\u5206\u89e3\uff0c\u4e00\u822c\u8d28\u56e0\u6570\u5206\u89e3\u6700\u5dee\u60c5\u51b5\u4e0b\\(O(R)\\)\u5f53\u4e14\u4ec5\u5f53R\u4e3a\u8d28\u6570\uff0c\u7279\u5224\u4e00\u4e0b\u5373\u53ef\u505a\u5230\\(O(\\sqrt{R})\\)<\/p>\n<p>\u7136\u540eDFS\u51fa\\(R^2\\)\u7684\u6240\u6709\u56e0\u6570\uff08\u904d\u5386\\(R\\)\u7684\u8d28\u56e0\u6570\u65f6\uff0c\u628a\u5176\u6307\u6570\u6269\u5927\u4e00\u500d\u904d\u5386\u5373\u53ef\uff09\uff0c\u56e0\u4e3a\\(4 \\cdot 10^{18}\\)\u7684\u56e0\u6570\u4e2a\u6570\u4ec5\u4e3a\\(399\\)\uff0c\u6240\u4ee5\u7406\u8bba\u4e0b\u4e0d\u5b58\u5728\u98ce\u9669\u3002<\/p>\n<p>&nbsp;<\/p>\n<pre class=\"lang:default decode:true \">#include &lt;cstdio&gt;\r\n#include &lt;cstdlib&gt;\r\n#include &lt;cstring&gt;\r\n\r\nint kai(const int&amp;a)\r\n{\r\n\tif(a%2==0)\r\n\t\treturn 0;\r\n\telse if(a%4==1)\r\n\t\treturn 1;\r\n\telse\r\n\t\treturn -1;\r\n}\r\n\r\nstruct _prm\r\n{\r\n\tint val;int num;\r\n}prm[1050+1];\r\nint base[1050+1][1050+1];\r\nint lprm;\r\n\r\nint ans,nde;\r\nvoid DFS(int step)\r\n{\r\n\tif(step&gt;lprm)\r\n\t{\r\n\t\t\/\/printf(\"-----%d %d\\n\",nde,kai(nde));\r\n\t\t\/\/printf(\"%d,\",nde);\r\n\t\tans+=kai(nde);\r\n\t\treturn;\r\n\t}\r\n\tfor(register int i=0;i&lt;=2*prm[step].num;i++)\r\n\t{\r\n\t\tif(base[step][i]==0)\r\n\t\t\tbase[step][i]=base[step][i-1]*prm[step].val%4;\r\n\t\t\/\/printf(\"%d -&gt; %d %d ... %d = %d\\n\",step,prm[step].val,prm[step].num,i,base[step][i]);\r\n\t\tint bnde=nde;\r\n\t\tnde*=base[step][i];\r\n\t\tnde%=4;\r\n\t\tDFS(step+1);\r\n\t\tnde=bnde;\r\n\t}\r\n}\r\n\r\nint main()\r\n{\r\n\tfor(register int i=0;i&lt;=1050;i++)\r\n\t\tbase[i][0]=1;\r\n\t\r\n\tint R;scanf(\"%d\",&amp;R);\r\n\tregister int Rs=R;\r\n\t\r\n\tint nj=2;\r\n\twhile(Rs&gt;1)\r\n\t\tif(Rs%nj==0)\r\n\t\t{\r\n\t\t\tRs\/=nj;\r\n\t\t\tif(prm[lprm].val!=nj)\r\n\t\t\t\tprm[++lprm].val=nj;\r\n\t\t\tprm[lprm].num++;\r\n\t\t}\r\n\t\telse\r\n\t\t\tnj++;\r\n\t\r\n\tnde=1;\r\n\tDFS(1);\r\n\t\r\n\t\/\/printf(\"%d %d --- R\\n\",nde,ans,R);\r\n\tprintf(\"%lld\\n\",4*(long long)((long long)R*2-ans));\r\n\t\r\n\treturn 0;\r\n}\r\n\r\n<\/pre>\n<p>&nbsp;<\/p>\n<p>base[][]\u6ca1\u4ec0\u4e48\u7528\uff0c\u5ffd\u7565\u5427<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5706\u89c4\u95ee\u9898 \u65f6\u95f4\u9650\u5236\uff1a1000MS \u5185\u5b58\u9650\u5236\uff1a262144KB \u95ee\u9898\u63cf\u8ff0 \u5c0f C \u6709\u4e00\u4e2a\u5706\u89c4\uff0c\u4ed6\u7ecf\u5e38\u7528\u5706\u89c4\u5728\u7eb8\u4e0a &hellip; <a href=\"https:\/\/cf.mnihyc.com\/blog\/archives\/446\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">BZOJ 1041 (YZOJ 3460) \u5706\u89c4\u95ee\u9898<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[23],"tags":[],"class_list":["post-446","post","type-post","status-publish","format-standard","hentry","category-math"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>BZOJ 1041 (YZOJ 3460) \u5706\u89c4\u95ee\u9898 - mnihyc&#039;s Blog<\/title>\n<meta name=\"description\" content=\"\u5706\u89c4\u95ee\u9898 \u65f6\u95f4\u9650\u5236\uff1a1000MS \u5185\u5b58\u9650\u5236\uff1a262144KB \u95ee\u9898\u63cf\u8ff0 \u5c0f C \u6709\u4e00\u4e2a\u5706\u89c4\uff0c\u4ed6\u7ecf\u5e38\u7528\u5706\u89c4\u5728\u7eb8\u4e0a\u4f5c\u56fe\u3002 \u6709\u4e00\u5929\uff0c\u5c0f C \u51c6\u5907\u5728\u4e00\u4e2a\u5355\u4f4d\u7f51\u683c\u7eb8\u4e0a\u4f5c\u4e00\u4e2a\u5706\u3002\u4ed6\u4ee5\u67d0\u4e2a\u683c\u70b9\u4e3a\u5706\u5fc3\uff0c\u4f5c\u4e86\u4e00\u4e2a\u534a\u5f84\u4e3a\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cf.mnihyc.com\/blog\/archives\/446\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"BZOJ 1041 (YZOJ 3460) \u5706\u89c4\u95ee\u9898 - mnihyc&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"\u5706\u89c4\u95ee\u9898 \u65f6\u95f4\u9650\u5236\uff1a1000MS \u5185\u5b58\u9650\u5236\uff1a262144KB \u95ee\u9898\u63cf\u8ff0 \u5c0f C 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