{"id":1220,"date":"2019-07-02T16:45:05","date_gmt":"2019-07-02T08:45:05","guid":{"rendered":"https:\/\/cf.mnihyc.com\/blog\/?p=1220"},"modified":"2020-02-09T02:40:02","modified_gmt":"2020-02-08T18:40:02","slug":"yzoj-p3056-%e4%b8%89%e8%a7%92%e5%bd%a2%e6%9c%80%e5%a4%a7%e9%9d%a2%e7%a7%af","status":"publish","type":"post","link":"https:\/\/cf.mnihyc.com\/blog\/archives\/1220","title":{"rendered":"YZOJ P3056 \u4e09\u89d2\u5f62\u6700\u5927\u9762\u79ef"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P3056 \u4e09\u89d2\u5f62\u6700\u5927\u9762\u79ef<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB<\/p>\n<p style=\"text-align: center;\">\u51fa\u9898\u4eba\uff1achj2001\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u96be\u5ea6\uff1a<span style=\"color: #ffcc00;\">\\(4.5\\)<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7ed9\u5b9a\u5e73\u9762\u4e0a \\(n\\) \u4e2a\u70b9\uff0c\u5b9a\u4e49 \\(f(A,B,C)=\\frac{1}{2} \\left| x_A(y_B-y_C)+x_B(y_C-y_A)+x_C(y_A-y_B) \\right|\\) \u3002<\/p>\n<p>\u6bcf\u6b21\u64cd\u4f5c\u90fd\u4f1a\u5c06\u5750\u6807\u7cfb\u987a\u65f6\u9488\u65cb\u8f6c \\(\\frac{\\pi}{9}\\) \u5f27\u5ea6\uff0c\u76f4\u5230\u4e0e\u539f\u5750\u6807\u7cfb\u91cd\u5408\u3002<\/p>\n<p>\u8ba1\u7b97\u6bcf\u6b21\u64cd\u4f5c\u524d \\(f\\) \u7684\u6700\u5927\u503c\uff0c\u5e76\u8f93\u51fa\u6240\u6709\u6700\u5927\u503c\u7684\u603b\u548c\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7b2c\u4e00\u884c\u8f93\u5165\u4e00\u4e2a\u6b63\u6574\u6570 \\(n\\)\uff0c\u8868\u793a\u70b9\u7684\u6570\u91cf\uff1b<\/p>\n<p>\u63a5\u4e0b\u6765 \\(n\\) \u884c\uff0c\u6bcf\u884c\u4e24\u4e2a\u6574\u6570 \\(x_i, y_i\\) \u8868\u793a\u6700\u5f00\u59cb\u5efa\u7acb\u7684\u5750\u6807\u7cfb\u4e0b\u70b9\u7684\u5750\u6807\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u8f93\u51fa\u6240\u6709 \\(f\\) \u6700\u5927\u503c\u7684\u603b\u548c\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u5165<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"lang:default decode:true \">6\r\n0 0\r\n1 3\r\n3 1\r\n1 9\r\n9 1\r\n9 9<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"lang:default decode:true \">720<\/pre>\n<ul>\n<li>\n<h3><strong>\u6570\u636e\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e \\(100\\%\\) \u7684\u6570\u636e\uff0c\\(3 \\leq n \\leq 10000, -10000 \\leq x_i, y_i \\leq 10000\\) \u3002<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><!--more--><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>\u628a \\(f\\) \u90a3\u4e00\u5806\u4e1c\u897f\u5c55\u5f00\u7136\u540e\u53c9\u79ef\u5408\u5e76\u4e00\u4e0b\uff0c\u5176\u5b9e\u5c31\u662f\u6c42 \\(A, B, C\\) \u4e09\u70b9\u56f4\u6210\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u3002<\/p>\n<p>\u90a3\u672c\u9898\u5176\u5b9e\u6c42\u7684\u5c31\u662f \\(n\\) \u4e2a\u70b9\u56f4\u6210\u4e09\u89d2\u5f62\u9762\u79ef\u7684\u6700\u5927\u503c\u3002<\/p>\n<p>\u5f88\u663e\u7136\u8fd9\u4e9b\u70b9\u4e00\u5b9a\u90fd\u4f1a\u5728\u51f8\u5305\u4e0a\uff0c\u6240\u4ee5\u628a\u51f8\u5305\u8dd1\u51fa\u6765\uff0c\u7136\u540e\u518d \\(O(n^3)\\) \u66b4\u529b\u5c31\u80fd\u8fc7\u3002\u3002\u3002\u3002\u3002\u3002\u3002\u3002\u3002\u3002<\/p>\n<p>\u597d\u5427\uff0c\u5f88\u663e\u7136\u8fd9\u4e2a\u505a\u6cd5\u5f88\u5bb9\u6613\u4f1a\u88ab\u5361\u6389\u3002<\/p>\n<p>\u6ce8\u610f\u5230\u56fa\u5b9a\u4e24\u4e2a\u70b9\u65f6\uff0c\u79fb\u52a8\u5176\u4e2d\u4e00\u4e2a\u70b9\uff0c\u6700\u5927\u503c\u5bf9\u5e94\u7684\u7b2c\u4e09\u4e2a\u70b9\u7684\u79fb\u52a8\u4e5f\u662f\u5355\u8c03\u7684\u3002<\/p>\n<p>\u4e8e\u662f\u5c31\u53ef\u4ee5\u8dd1\u4e00\u4e2a\u65cb\uff08xu\u00e1n\uff09\u8f6c\uff08zhu\u01cen\uff09\u5361\uff08qi\u01ce\uff09\u58f3\uff08k\u00e9\uff09\uff0c\u672c\u8d28\u4e0a\u5c31\u662f\u7ef4\u62a4\u7b2c\u4e09\u4e2a\u70b9\u7684<strong>\u5355\u8c03\u79fb\u52a8<\/strong>\u3002<\/p>\n<p>\u7136\u540e\u5c31\u662f \\(O(n^2)\\) \u4e86\uff0c\u8c8c\u4f3cxx\u8bba\u6587\uff08\u56fd\u96c6\uff1f\uff09\u91cc\u6709\u8bc1\u660e\uff1a\u5e73\u9762\u5185\u5750\u6807\u8303\u56f4\u5728 \\([0, r]\\) \u5185\u7684\u70b9\u6784\u6210\u7684\u51f8\u5305\u70b9\u6570\u4e3a \\(O(r^{\\frac{2}{3}})\\)\uff0c\u7136\u540e\u5c31\u80fd\u8fc7\u4e86\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#include &lt;algorithm&gt;\r\n\r\ntypedef long long LLONG;\r\n#define _max(_a_,_b_) ((_a_)&gt;(_b_)?(_a_):(_b_))\r\n\r\ninline int getnum()\r\n{\r\n\tregister char c=0;\r\n\tregister bool neg=false;\r\n\twhile(!(c&gt;='0' &amp;&amp; c&lt;='9'))\r\n\t\tc=getchar(),neg|=(c=='-');\r\n\tregister int a=0;\r\n\twhile(c&gt;='0' &amp;&amp; c&lt;='9')\r\n\t\ta=a*10+c-'0',c=getchar();\r\n\treturn (neg?-1:1)*a;\r\n}\r\n\r\nstruct _point\r\n{\r\n\tint x,y;\r\n\tbool operator &lt; (const _point&amp;o)const\r\n\t{\r\n\t\tif(x != o.x)\r\n\t\t\treturn x&lt;o.x;\r\n\t\treturn y&lt;o.y;\r\n\t}\r\n\tinline int operator * (const _point&amp;o)const\r\n\t{\r\n\t\treturn x*o.y - y*o.x;\r\n\t}\r\n\tinline _point operator - (const _point&amp;o)const\r\n\t{\r\n\t\treturn (_point){x-o.x, y-o.y};\r\n\t}\r\n}p[10505];\r\nint stk[10505],lst[10505],llst;\r\nbool vis[10505];\r\n\r\nint main()\r\n{\r\n\tregister int N=getnum();\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tp[i].x=getnum(),p[i].y=getnum();\r\n\t\r\n\tstd::sort(&amp;p[1],&amp;p[N+1]);\r\n\t\r\n\tregister int top=0;\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t{\r\n\t\twhile(top&gt;=2 &amp;&amp; (p[stk[top]]-p[stk[top-1]])*(p[i]-p[stk[top-1]])&gt;=0)\r\n\t\t\ttop--;\r\n\t\tstk[++top]=i;\r\n\t}\r\n\twhile(top)\r\n\t\tlst[++llst]=stk[top],vis[stk[top]]=true,top--;\r\n\t\r\n\tfor(register int i=N;i&gt;=1;i--)\r\n\t{\r\n\t\twhile(top&gt;=2 &amp;&amp; (p[stk[top]]-p[stk[top-1]])*(p[i]-p[stk[top-1]])&gt;=0)\r\n\t\t\ttop--;\r\n\t\tstk[++top]=i;\r\n\t}\r\n\twhile(top)\r\n\t\t(!vis[stk[top]] ? lst[++llst]=stk[top], vis[stk[top]]=true : 0),top--;\r\n\t\r\n\tregister int ans=0;\r\n\tfor(register int i=1;i&lt;llst-1;i++)\r\n\t\tfor(register int j=i+1,k=j;j&lt;llst;j++)\r\n\t\t{\r\n\t\t\treju:\r\n\t\t\tregister int t=(p[lst[k]]-p[lst[i]])*(p[lst[j]]-p[lst[i]]);\r\n\t\t\tif(t&lt;0)\r\n\t\t\t\tt=-t;\r\n\t\t\tregister int t1=(p[lst[k+1]]-p[lst[i]])*(p[lst[j]]-p[lst[i]]);\r\n\t\t\tif(t1&lt;0)\r\n\t\t\t\tt1=-t1;\r\n\t\t\tif(t1&gt;t)\r\n\t\t\t{\r\n\t\t\t\tk++,t=t1;\r\n\t\t\t\tgoto reju;\r\n\t\t\t}\r\n\t\t\tans=_max(ans,t);\r\n\t\t}\r\n\tprintf(\"%lld\\n\",(long long)ans*9);\r\n\t\r\n\treturn 0;\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YZOJ P3056 \u4e09\u89d2\u5f62\u6700\u5927\u9762\u79ef \u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB \u51fa\u9898\u4eba\uff1ac &hellip; <a href=\"https:\/\/cf.mnihyc.com\/blog\/archives\/1220\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P3056 \u4e09\u89d2\u5f62\u6700\u5927\u9762\u79ef<\/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":[52,105,104],"tags":[],"class_list":["post-1220","post","type-post","status-publish","format-standard","hentry","category-mediuma","category-convexhull","category-rotatingcalipersalgorithm"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>YZOJ P3056 \u4e09\u89d2\u5f62\u6700\u5927\u9762\u79ef - mnihyc&#039;s Blog<\/title>\n<meta name=\"description\" content=\"YZOJ P3056 \u4e09\u89d2\u5f62\u6700\u5927\u9762\u79ef \u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB \u51fa\u9898\u4eba\uff1achj2001\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u96be\u5ea6\uff1a \u9898\u76ee\u63cf\u8ff0 \u7ed9\u5b9a\u5e73\u9762\u4e0a (n) \u4e2a\u70b9\uff0c\u5b9a\u4e49 (f(A,B,C)=frac{1}{2} left|\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/0self.mnihyc.com\/blog\/archives\/1220\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"YZOJ P3056 \u4e09\u89d2\u5f62\u6700\u5927\u9762\u79ef - mnihyc&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"YZOJ P3056 \u4e09\u89d2\u5f62\u6700\u5927\u9762\u79ef \u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB \u51fa\u9898\u4eba\uff1achj2001\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u96be\u5ea6\uff1a \u9898\u76ee\u63cf\u8ff0 \u7ed9\u5b9a\u5e73\u9762\u4e0a (n) \u4e2a\u70b9\uff0c\u5b9a\u4e49 (f(A,B,C)=frac{1}{2} left|\" \/>\n<meta property=\"og:url\" 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