{"id":976,"date":"2019-02-14T00:59:43","date_gmt":"2019-02-13T16:59:43","guid":{"rendered":"https:\/\/0self.mnihyc.com\/blog\/?p=976"},"modified":"2020-02-09T03:02:24","modified_gmt":"2020-02-08T19:02:24","slug":"fjwc2019-day2-%e7%9b%b4%e5%be%84","status":"publish","type":"post","link":"https:\/\/0self.mnihyc.com\/blog\/archives\/976","title":{"rendered":"[FJWC2019 Day2] \u76f4\u5f84"},"content":{"rendered":"<h1 style=\"text-align: center;\">[FJWC2019 Day2] \u76f4\u5f84<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a524288KB<\/p>\n<p style=\"text-align: center;\">\u96be\u5ea6\uff1a <span style=\"color: #ffff00;\">\\(4.0\\)<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u4f60\u9700\u8981\u6784\u9020\u4e00\u68f5\u81f3\u5c11\u6709\u4e24\u4e2a\u9876\u70b9\u7684\u6811\uff0c\u6811\u4e0a\u7684\u6bcf\u6761\u8fb9\u6709\u4e00\u4e2a\u975e\u8d1f\u6574\u6570\u8fb9\u6743\u3002\u6811\u4e0a\u4e24\u70b9 \\(i,j\\) \u7684\u8ddd\u79bb \\(dis(i,j)\\) \u5b9a\u4e49\u4e3a\u6811\u4e0a\u8fde\u63a5 \\(i\\) \u548c \\(j\\) \u8fd9\u4e24\u70b9\u7684\u7b80\u5355\u8def\u5f84\u4e0a\u7684\u8fb9\u6743\u548c\u3002<\/p>\n<p>\u6211\u4eec\u5b9a\u4e49\u8fd9\u68f5\u6811\u7684\u76f4\u5f84\u4e3a\uff0c\u6240\u6709\u6ee1\u8db3 \\(1 \\leq i &lt; j \\leq n\\) \u7684 \\((i,j)\\) \u4e2d\uff0c\\(dis(i,j)\\) \u6700\u5927\u7684\u3002\u5982\u679c\u6709\u591a\u4e2a\u8fd9\u6837\u7684 \\((i,j)\\)\uff0c\u90a3\u4e48\u5747\u4e3a\u76f4\u5f84\u3002<\/p>\n<p>\u4f5c\u4e3a\u4e00\u4e2a\u6784\u9020\u9898\uff0c\u4f60\u9700\u8981\u6784\u9020\u4e00\u4e2a<strong>\u6070\u6709 \\(k\\) \u4e2a\u76f4\u5f84<\/strong>\u7684<strong>\u6811<\/strong>\u3002\u53ef\u4ee5\u8bc1\u660e\u5728\u7ed9\u5b9a\u7684\u9650\u5236\u4e0b\u4e00\u5b9a\u6709\u89e3\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u4e00\u884c\u4e00\u4e2a\u6b63\u6574\u6570 \\(k\\)\uff0c\u8868\u793a\u4f60\u9700\u8981\u6784\u9020\u51fa\u4e00\u4e2a\u6070\u6709 \\(k\\) \u4e2a\u76f4\u5f84\u7684\u6811\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7b2c\u4e00\u884c\u4e00\u4e2a\u6b63\u6574\u6570 \\(n\\)\uff0c\u8868\u793a\u4f60\u6784\u9020\u7684\u6811\u7684\u70b9\u6570\u3002<\/p>\n<p>\u63a5\u4e0b\u6765 \\(n-1\\) \u884c\uff0c\u6bcf\u884c\u4e09\u4e2a\u6574\u6570 \\(i,j,w\\)\uff0c\u8868\u793a\u4e00\u6761\u8fde\u63a5\u70b9 \\(i\\) \u548c \\(j\\) \uff08\u70b9\u7684\u7f16\u53f7\u4e3a \\(1,2, \\cdots, n\\)\uff09\u7684\u6811\u8fb9\uff0c\u8fb9\u6743\u4e3a \\(w\\) \u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u5165<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">3<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">5\r\n1 2 2\r\n3 2 2\r\n2 5 3\r\n4 2 2<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8bf4\u660e<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u8fd9\u53ea\u662f\u4e00\u79cd\u7b26\u5408\u9898\u610f\u7684\u8f93\u51fa\uff0c\u53ef\u80fd\u8fd8\u6709\u5176\u4ed6\u8f93\u51fa\u3002\u5728\u8fd9\u4e2a\u8f93\u51fa\u4e2d\uff0c\u76f4\u5f84\u4e3a \\((1,5),(3,5),(4,5)\\) \u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6570\u636e\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u6ce8\u610f\uff0c\u4f60\u9700\u8981\u6784\u9020\u51fa\u7684\u6811\u5fc5\u987b<strong>\u6ee1\u8db3 \\(2 \\leq n \\leq 5000, 0 \\leq w \\leq 10^5\\)<\/strong> \uff01<\/p>\n<p>\u5bf9\u4e8e \\(30pts\\) \u7684\u6570\u636e\uff0c\\(1\\leq k \\leq 2000\\) \uff1b<\/p>\n<p>\u5bf9\u4e8e \\(100pts\\) \u7684\u6570\u636e\uff0c\\(1\\leq k \\leq 5 \\times 10^6\\) \u3002<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>YZOJ P4260<\/p>\n<p><!--more--><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>\u5927\u90e8\u5206\u4eba\u90fd\u5f53\u573a\u5207\u6389\u4e86\uff0c\u6211\u6ca1\u6709\u4e00\u4e2a\u6e05\u9192\u7684\u601d\u8def\u5c31\u6ca1\u6709\u6784\u9020\u51fa\u6765\u3002\u3002\u3002<\/p>\n<p>\u9996\u5148\uff0c\u6837\u4f8b\u662f\u4e00\u4e2a\u83ca\u82b1\u3002\u53ef\u4ee5\u5f88\u5bb9\u6613\u53d1\u73b0\uff0c\u8981\u6784\u9020\u51fa \\(k\\) \u6761\u76f4\u5f84\uff0c\u53ea\u9700\u8981\u6309\u7167\u4e0b\u56fe\u7684\u65b9\u6848\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-977\" src=\"https:\/\/0self.mnihyc.com\/blog\/wp-content\/uploads\/2019\/02\/\u65e0\u6807\u9898.png\" alt=\"\" width=\"396\" height=\"323\" srcset=\"https:\/\/0self.mnihyc.com\/blog\/wp-content\/uploads\/2019\/02\/\u65e0\u6807\u9898.png 396w, https:\/\/0self.mnihyc.com\/blog\/wp-content\/uploads\/2019\/02\/\u65e0\u6807\u9898-300x245.png 300w\" sizes=\"auto, (max-width: 396px) 100vw, 396px\" \/><\/p>\n<p>\u8fd9\u6837\u5c31\u662f\u7528 \\(k+2\\) \u4e2a\u70b9\u6784\u9020\u51fa\u4e00\u4e2a\u83ca\u82b1\uff0c\u663e\u7136\u6709 \\(k\\) \u6761\u6700\u957f\u94fe\uff0c\u62ff\u5230 \\(30pts\\) \u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u56e0\u4e3a \\(2 \\leq n \\leq 5000\\) \uff0c\\(k\\) \u5f88\u5927\uff0c\u6240\u4ee5\u8003\u8651\u5c06 \\(k\\) \u8fdb\u884c\u5206\u89e3\u3002\u6211\u5f53\u65f6\u5c31\u60f3\u5230\u53ef\u4ee5\u5f80\u70b9\u5916\u8fde \\(a\\) \u6761\u8fb9\u6743\u4e3a \\(1\\) \uff0c \\(b\\) \u6761\u8fb9\u6743\u4e3a \\(2\\) \u5f62\u6210\u7684\u83ca\u82b1\uff0c\u8fd9\u6837\u7b54\u6848\u5c31\u662f \\(k=a \\times b\\) \uff0c\u53ef\u4ee5\u628a \\(k\\) \u53d8\u5c0f\u3002\u4f46\u662f\u8fd9\u6837\u505a\u7684\u8bdd\u4e07\u4e00 \\(k\\) \u662f\u4e2a\u5927\u8d28\u6570\uff0c\u90a3\u53c8\u5b8c\u86cb\u4e86\uff0c\u6ca1\u6709\u529e\u6cd5\u5206\u89e3\u3002<\/p>\n<p>\u7136\u800c\u5230\u8fd9\u91cc\u6211\u5c31\u60f3\u4e0d\u4e0b\u53bb\u4e86\u3002\u5176\u5b9e\u79bb\u6b63\u89e3\u53ea\u5dee\u4e00\u6b65\u4e4b\u9065\uff1a\\(k\\) \u5206\u89e3\u7684\u8fd8\u4e0d\u591f\u3002<\/p>\n<p>\u8003\u8651\u5411\u5916\u8fde\u4e09\u4e2a\u83ca\u82b1\uff08\u5982\u4e0b\u56fe\uff09\uff0c\u8fd9\u6837 \\(k=ab+ac+bc\\) \u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-978\" src=\"https:\/\/0self.mnihyc.com\/blog\/wp-content\/uploads\/2019\/02\/\u65e0\u6807\u9898-1.png\" alt=\"\" width=\"396\" height=\"366\" srcset=\"https:\/\/0self.mnihyc.com\/blog\/wp-content\/uploads\/2019\/02\/\u65e0\u6807\u9898-1.png 396w, https:\/\/0self.mnihyc.com\/blog\/wp-content\/uploads\/2019\/02\/\u65e0\u6807\u9898-1-300x277.png 300w\" sizes=\"auto, (max-width: 396px) 100vw, 396px\" \/><\/p>\n<p>\u8fd9\u6837\u5b50\u5c31\u6709\u529e\u6cd5\u5206\u89e3\u4e86\uff01<\/p>\n<p>\\(k=ab+ac+bc=a(b+c)+bc\\) \uff0c\u5373 \\(a=\\frac{k-bc}{b+c}\\) \u3002\u7531\u4e8e \\(a+b+c \\leq n-4\\) \uff0c\u6240\u4ee5\u53ef\u4ee5\u76f4\u63a5\u66b4\u529b<strong>\u679a\u4e3e \\(b, c\\)<\/strong> \u7136\u540e<strong>\u7b97\u51fa\u5408\u6cd5\u7684 \\(a\\)<\/strong> \uff0c\u8fd9\u6837\u5c31\u5f97\u5230\u4e86\u4e00\u7ec4\u5408\u6cd5\u7684\u6784\u9020\u65b9\u6848\u4e86\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n^2)\\) \u3002<\/p>\n<p>\u6b64\u5916\uff0c\u672c\u9898\u8fd8\u53ef\u4ee5\u5229\u7528\u8fb9\u6743\u4e3a \\(0\\) \u7684\u6027\u8d28\u6302\u94fe\uff0c\u6216\u8005\u5176\u4ed6\u4e00\u4e9b\u5947\u5947\u602a\u602a\u7684\u505a\u6cd5\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#include &lt;climits&gt;\r\n\r\n#define MXN 5000\r\n\r\nint main()\r\n{\r\n\/\/freopen(\"diameter.in\",\"r\",stdin);freopen(\"diameter.out\",\"w\",stdout);\r\n\tint k;scanf(\"%d\",&amp;k);\r\n\t\r\n\tfor(register int b=1;b&lt;=MXN-4;b++)\r\n\t\tfor(register int c=1;b+c&lt;=MXN-4;c++)\r\n\t\t\tif(k&gt;=b*c &amp;&amp; (k-b*c)%(b+c)==0)\r\n\t\t\t{\r\n\t\t\t\tregister int a=(k-b*c)\/(b+c);\r\n\t\t\t\tif(a+b+c&gt;MXN-4)\r\n\t\t\t\t\tcontinue;\r\n\t\t\t\t\r\n\t\t\t\tprintf(\"%d\\n\",a+b+c+4);\r\n\t\t\t\tprintf(\"%d %d %d\\n\",1,2,1);\r\n\t\t\t\tprintf(\"%d %d %d\\n\",1,3,1);\r\n\t\t\t\tprintf(\"%d %d %d\\n\",1,4,1);\r\n\t\t\t\t\r\n\t\t\t\tregister int l=4;\r\n\t\t\t\tfor(register int i=1;i&lt;=a;i++)\r\n\t\t\t\t\tprintf(\"%d %d %d\\n\",2,++l,1);\r\n\t\t\t\tfor(register int i=1;i&lt;=b;i++)\r\n\t\t\t\t\tprintf(\"%d %d %d\\n\",3,++l,1);\r\n\t\t\t\tfor(register int i=1;i&lt;=c;i++)\r\n\t\t\t\t\tprintf(\"%d %d %d\\n\",4,++l,1);\r\n\t\t\t\t\r\n\t\t\t\treturn 0;\r\n\t\t\t}\r\n\t\r\n\treturn 0;\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[FJWC2019 Day2] \u76f4\u5f84 \u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a524288KB \u96be\u5ea6\uff1a \u9898 &hellip; <a href=\"https:\/\/0self.mnihyc.com\/blog\/archives\/976\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">[FJWC2019 Day2] \u76f4\u5f84<\/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":[52,65],"tags":[],"class_list":["post-976","post","type-post","status-publish","format-standard","hentry","category-mediuma","category-enuma"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>[FJWC2019 Day2] \u76f4\u5f84 - mnihyc&#039;s Blog<\/title>\n<meta name=\"description\" content=\"\u76f4\u5f84 \u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a524288KB \u96be\u5ea6\uff1a \u9898\u76ee\u63cf\u8ff0 \u4f60\u9700\u8981\u6784\u9020\u4e00\u68f5\u81f3\u5c11\u6709\u4e24\u4e2a\u9876\u70b9\u7684\u6811\uff0c\u6811\u4e0a\u7684\u6bcf\u6761\u8fb9\u6709\u4e00\u4e2a\u975e\u8d1f\u6574\u6570\u8fb9\u6743\u3002\u6811\u4e0a\u4e24\u70b9 (i,j) \u7684\u8ddd\u79bb (dis(i,j)) \u5b9a\u4e49\u4e3a\u6811\u4e0a\u8fde\u63a5 (i) \u548c (j) \u8fd9\u4e24\u70b9\u7684\u7b80\u5355\u8def\u5f84\u4e0a\u7684\u8fb9\u6743\u548c\u3002\" \/>\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\/976\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[FJWC2019 Day2] \u76f4\u5f84 - mnihyc&#039;s Blog\" 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