{"id":1233,"date":"2019-07-02T17:30:41","date_gmt":"2019-07-02T09:30:41","guid":{"rendered":"https:\/\/cf.mnihyc.com\/blog\/?p=1233"},"modified":"2020-02-09T02:18:23","modified_gmt":"2020-02-08T18:18:23","slug":"yzoj-p2050-fjoi2013%e5%9c%86%e5%bd%a2%e6%b8%b8%e6%88%8f","status":"publish","type":"post","link":"https:\/\/cf.mnihyc.com\/blog\/archives\/1233","title":{"rendered":"YZOJ P2050 [FJOI2013]\u5706\u5f62\u6e38\u620f"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P2050 [FJOI2013]\u5706\u5f62\u6e38\u620f<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a8000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB<\/p>\n<p style=\"text-align: center;\">\u96be\u5ea6\uff1a<span style=\"color: #ff0000;\">\\(8.0\\)<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5728\u4e00\u4e2a\u65e0\u7a77\u5927\u7684\u684c\u9762\u4e0a\u6709 \\(n\\) \u4e2a\u5706\u5f62\uff0c\u4fdd\u8bc1\u4efb\u610f\u4e24\u4e2a\u5706\u76f8\u79bb\u6216\u8005\u76f8\u542b\uff0c\u4e0d\u5b58\u5728\u76f8\u5207\u6216\u76f8\u4ea4\u3002\u73b0\u5728 Alice \u548c Bob \u5728\u73a9\u4e00\u4e2a\u5706\u5f62\u6e38\u620f\uff0c\u4ee5 Alice \u4e3a\u5148\u624b\uff0c\u53cc\u65b9\u4ee5\u5982\u4e0b\u6b65\u9aa4\u8f6e\u6d41\u6e38\u620f\uff1a<\/p>\n<p>1\uff0c\u9009\u5b9a\u4e00\u4e2a\u5706 \\(A\\)\uff0c\u628a \\(A\\) \u4ee5\u53ca\u6240\u6709\u5b8c\u5168\u5728 \\(A\\) \u5185\u90e8\u7684\u5706\u90fd\u5220\u9664\uff1b<\/p>\n<p>2\uff0c\u5982\u679c\u5728\u81ea\u5df1\u56de\u5408\u65e0\u6cd5\u627e\u5230\u53ef\u5220\u9664\u7684\u5706\uff0c\u5219\u8f93\u6389\u6bd4\u8d5b\u3002<\/p>\n<p>\u5047\u8bbe Alice \u548c Bob \u90fd\u975e\u5e38\u806a\u660e\uff0c\u8bf7\u95ee\u6700\u7ec8\u8c01\u80fd\u591f\u53d6\u5f97\u80dc\u5229\uff1f\u8bf7\u7f16\u7a0b\u8f93\u51fa\u6700\u7ec8\u83b7\u80dc\u7684\u4eba\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u8f93\u5165\u6570\u636e\u7684\u7b2c\u4e00\u884c\u4e3a\u4e00\u4e2a\u6b63\u6574\u6570 \\(T\\)\uff0c\u8868\u793a\u6570\u636e\u7ec4\u6570\u3002<\/p>\n<p>\u63a5\u4e0b\u6765 \\(T\\) \u7ec4\u6570\u636e\uff0c\u5bf9\u4e8e\u6bcf\u7ec4\u6570\u636e\uff0c\u7b2c\u4e00\u884c\u5305\u542b \\(1\\) \u4e2a\u6b63\u6574\u6570 \\(n\\)\uff0c\u8868\u793a\u5706\u5f62\u7684\u4e2a\u6570\u3002<\/p>\n<p>\u4e4b\u540e \\(n\\) \u884c\uff0c\u6bcf\u884c\u4e3a \\(3\\) \u4e2a\u6574\u6570 \\(x\\)\u3001\\(y\\) \u548c \\(r\\) \uff0c\u5206\u522b\u8868\u793a\u5706\u5f62\u7684\u5706\u5fc3\u5750\u6807\u4ee5\u53ca\u5706\u7684\u534a\u5f84\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5047\u8bbe Alice \u6700\u540e\u83b7\u80dc\uff0c\u5219\u8f93\u51fa\u4e00\u884c \u201cAlice\u201d\uff08\u4e0d\u5305\u62ec\u5f15\u53f7\uff09\uff0c\u5426\u5219\u8f93\u51fa \u201cBob\u201d \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 \">2\r\n1\r\n0 0 1\r\n6\r\n-100 0 90\r\n-50 0 1\r\n-20 0 1\r\n100 0 90\r\n47 0 1\r\n23 0 1<\/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\">Alice\r\nBob<\/pre>\n<ul>\n<li>\n<h3><strong>\u6570\u636e\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\\(100\\%\\) \u7684\u6570\u636e\u6ee1\u8db3 \\(T \\leq 100\\)\uff0c\\(n \\leq m20000\\)\uff0c\\(\\left|x\\right|, \\left|y\\right|, r \\leq 10^8\\) \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>\u4e09\u00b7\u539f\u9898\u5957\u5728\u4e00\u8d77wwwww<\/p>\n<p>\u9996\u5148\u628a \\(n\\) \u4e2a\u5706\u6309\u7167\u534a\u5f84\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\uff0c\u90a3\u4e48\u5bf9\u4e8e\u7b2c \\(i\\) \u4e2a\u5706\uff0c\u5728\u534a\u5f84\u6bd4\u5b83\u5927\u7684\u5706\u4e2d\u627e\u5230\u7b2c\u4e00\u4e2a\u5305\u542b\u5b83\u7684\u5706 \\(j\\) \uff0c\\(i \\rightarrow\\) \u8fde\u8fb9\uff0c\u90a3\u4e48\u6b64\u65f6\u4f1a\u8fde\u6210\u4e00\u4e2a\u68ee\u6797\u3002<\/p>\n<p>\u82e5\u518d\u6dfb\u52a0\u4e00\u4e2a \\(x=0, y=0, r=\\infty\\) \u7684 \\(0\\) \u53f7\u5706\uff0c\u90a3\u4e48\u6b64\u65f6\u4f1a\u8fde\u6210\u4e00\u68f5\u4ee5 \\(0\\) \u4e3a\u6839\u8282\u70b9\u7684\u6811\u3002<\/p>\n<p>\u7136\u540e\u5c31\u662f\u4e00\u4e2a SG\u51fd\u6570 \u5566\uff0c\u5728\u4e0a\u9762 DP \u4e00\u4e0b\uff0c\u6709 \\(f_o = (f_{s_1}+1) \\oplus (f_{s_2}+1) \\oplus \\cdots\\) \uff0c\u82e5 \\(o\\) \u4e3a\u53f6\u5b50\u7ed3\u70b9\u5219 \\(f_o=0\\) \u3002<del>\uff08\u5176\u5b9e\u6211\u4e5f\u4e0d\u77e5\u9053\u4e3a\u4ec0\u4e48<\/del><\/p>\n<p>\u8fd9\u6837\u8f6c\u79fb\u662f \\(O(n)\\) \u7684\uff0c\u4f46\u662f\u5efa\u6811\u5374\u662f \\(O(n^2)\\) \u7684\uff0c\u60f3\u529e\u6cd5\u4f18\u5316\u3002<\/p>\n<p>\u5176\u5b9e\u53ef\u4ee5\u4f7f\u7528\u626b\u63cf\u7ebf\u7ef4\u62a4\u8fd9\u4e9b\u5706\u7684\u4f4d\u7f6e\u5173\u7cfb\u3002<\/p>\n<p>\u628a\u5706\u62c6\u6210\u4e24\u4e2a\u4e8b\u4ef6\uff0c\\(x-r\\) \u63d2\u5165\u4e14 \\(x+r\\) \u5f39\u51fa\uff0c\u5e76\u4e14\u628a\u8fd9\u4e2a\u5706\u62c6\u6210\u4e0a\u534a\u5706\u548c\u4e0b\u534a\u5706\uff0c\u8fd1\u4f3c\u770b\u6210\u53f3\u62ec\u53f7\u548c\u5de6\u62ec\u53f7\uff0c\u90a3\u4e48\u5176\u5b9e\u5c31\u662f\u8981\u52a8\u6001\u7ef4\u62a4\u4e00\u4e2a\u62ec\u53f7\u5e8f\u5217\u3002<\/p>\n<p>\u5e76\u4e14\u5728 \u63d2\u5165\/\u5f39\u51fa \u524d\u5706\u7684\u4f4d\u7f6e\u5173\u7cfb\u90fd\u662f\u4e0d\u4f1a\u53d1\u751f\u6539\u53d8\u7684\u3002<\/p>\n<p>\u8fd9\u6837\uff0c\u4f8b\u5982 <code>(())<\/code>\u5c31\u662f\u5305\u542b\u5173\u7cfb\uff0c<code>()()<\/code>\u5c31\u662f\u76f8\u79bb\u5173\u7cfb\u3002<\/p>\n<p>\u8981\u627e\u51fa\u5f53\u524d\u5706\u88ab\u54ea\u4e00\u4e2a\u5706\u5b8c\u5168\u5305\u542b\uff0c\u5c31\u662f\u627e\u5f53\u524d\u5de6\u62ec\u53f7\u7684\u524d\u9a71\uff1a\u82e5\u4e3a\u5de6\u62ec\u53f7\u5219\u88ab\u5176\u5305\u542b\uff0c\u82e5\u4e3a\u53f3\u62ec\u53f7\u5219\u5b83\u4eec\u540c\u65f6\u88ab\u53e6\u4e00\u4e2a\u5706\u5305\u542b\u3002<\/p>\n<p>\u53d1\u73b0\u53ef\u4ee5\u4f7f\u7528\u5e73\u8861\u6811\u7ef4\u62a4\u62ec\u53f7\u5e8f\u5217\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n \\log n)\\) \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#include &lt;ext\/pb_ds\/assoc_container.hpp&gt;\r\n#include &lt;ext\/pb_ds\/tree_policy.hpp&gt;\r\n\r\n#define _max(_a_,_b_) ((_a_)&gt;(_b_)?(_a_):(_b_))\r\n\r\n#ifdef ONLINE_JUDGE\r\n\tchar __B[1&lt;&lt;15],*__S=__B,*__T=__B;\r\n\t#define getchar() (__S==__T&amp;&amp;(__T=(__S=__B)+fread(__B,1,1&lt;&lt;15,stdin),__S==__T)?EOF:*__S++)\r\n#endif\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\n#pragma pack(1)\r\nstruct _event\r\n{\r\n\tint x,id;\r\n\tbool ins;\r\n\tbool operator &lt; (const _event&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 ins &gt; o.ins;\r\n\t}\r\n}event[40505];\r\nint le,x[20505],y[20505],r[20505];\r\n\r\nint _curx;\r\nstruct _node\r\n{\r\n\tint id;\r\n\tbool type;\r\n\tbool operator &lt; (const _node&amp;o)const\r\n\t{\r\n\t\tif(id == o.id)\r\n\t\t\treturn type &lt; o.type;\r\n\t\t#define _sqr(_x) ((long long)(_x)*(_x))\r\n\t\tregister long long p=_sqr(r[id])-_sqr(_curx-x[id]);\r\n\t\tregister long long p1=_sqr(r[o.id])-_sqr(_curx-x[o.id]);\r\n\t\treturn (type ? 1 : -1)*__builtin_sqrtl(p)+y[id] \\\r\n\t\t\t&lt; (o.type ? 1 : -1)*__builtin_sqrtl(p1)+y[o.id];\r\n\t}\r\n};\r\ntypedef __gnu_pbds::tree&lt;_node,__gnu_pbds::null_type&gt; _t;\r\ntypedef _t::point_iterator _tit;\r\n_t tree;\r\n_tit itp[40505];\r\n\r\nint father[20505];\r\nint gcnt,ghead[20505],gnext[40505],gnode[40505];\r\ninline void insertLine(register int s,register int t)\r\n{\r\n\tgnext[++gcnt]=ghead[s],ghead[s]=gcnt,gnode[gcnt]=t;\r\n\tgnext[++gcnt]=ghead[t],ghead[t]=gcnt,gnode[gcnt]=s;\r\n}\r\n\r\nint f[20505];\r\nvoid DFS(register int o,register int fa)\r\n{\r\n\tf[o]=0;\r\n\tfor(register int j=ghead[o],t;j;j=gnext[j])\r\n\t\tif((t=gnode[j]) != fa)\r\n\t\t{\r\n\t\t\tDFS(t,o);\r\n\t\t\tf[o]^=(f[t]+1);\r\n\t\t}\r\n}\r\n\r\nint main()\r\n{\r\nregister int _T=getnum();\r\nwhile(_T--)\r\n{\r\n\tregister int N=getnum();\r\n\tle=0;\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t{\r\n\t\tx[i]=getnum(),y[i]=getnum(),r[i]=getnum();\r\n\t\tevent[++le].x=x[i]-r[i],event[le].id=i,event[le].ins=true;\r\n\t\tevent[++le].x=x[i]+r[i],event[le].id=i,event[le].ins=false;\r\n\t}\r\n\tstd::sort(&amp;event[1],&amp;event[le+1]);\r\n\t\r\n\ttree.clear(),r[N+1]=INT_MAX&gt;&gt;1;\r\n\t\r\n\ttree.insert((_node){N+1,1}),tree.insert((_node){N+1,0});\r\n\t_tit it;\r\n\tfor(register int i=1;i&lt;=le;i++)\r\n\t{\r\n\t\t_curx=event[i].x;\r\n\t\tif(event[i].ins)\r\n\t\t{\r\n\t\t\ttree.insert((_node){event[i].id,1}).first;\r\n\t\t\tit=tree.insert((_node){event[i].id,0}).first;\r\n\t\t\tif((--it)-&gt;type == 0)\r\n\t\t\t\tfather[event[i].id]=it-&gt;id;\r\n\t\t\telse\r\n\t\t\t\tfather[event[i].id]=father[it-&gt;id];\r\n\t\t}\r\n\t\telse\r\n\t\t{\r\n\t\t\ttree.erase(tree.find((_node){event[i].id,1}));\r\n\t\t\ttree.erase(tree.find((_node){event[i].id,0}));\r\n\t\t}\r\n\t}\r\n\t\r\n\tgcnt=0,memset(ghead,0,sizeof(ghead));\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tinsertLine(i,father[i]);\r\n\tDFS(N+1,0);\r\n\tprintf(\"%s\\n\",(f[N+1] ? \"Alice\" : \"Bob\"));\r\n}\r\n\treturn 0;\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YZOJ P2050 [FJOI2013]\u5706\u5f62\u6e38\u620f \u65f6\u95f4\u9650\u5236\uff1a8000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144K &hellip; <a href=\"https:\/\/cf.mnihyc.com\/blog\/archives\/1233\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P2050 [FJOI2013]\u5706\u5f62\u6e38\u620f<\/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":[37,108,71,86],"tags":[],"class_list":["post-1233","post","type-post","status-publish","format-standard","hentry","category-crazya","category-gametheory","category-balancedtree","category-scanline"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>YZOJ P2050 [FJOI2013]\u5706\u5f62\u6e38\u620f - mnihyc&#039;s Blog<\/title>\n<meta name=\"description\" content=\"YZOJ P2050 \u5706\u5f62\u6e38\u620f \u65f6\u95f4\u9650\u5236\uff1a8000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB \u96be\u5ea6\uff1a \u9898\u76ee\u63cf\u8ff0 \u5728\u4e00\u4e2a\u65e0\u7a77\u5927\u7684\u684c\u9762\u4e0a\u6709 (n) \u4e2a\u5706\u5f62\uff0c\u4fdd\u8bc1\u4efb\u610f\u4e24\u4e2a\u5706\u76f8\u79bb\u6216\u8005\u76f8\u542b\uff0c\u4e0d\u5b58\u5728\u76f8\u5207\u6216\u76f8\u4ea4\u3002\u73b0\u5728 Alice \u548c Bob \u5728\u73a9\u4e00\u4e2a\u5706\u5f62\u6e38\u620f\uff0c\u4ee5 Alice \u4e3a\u5148\u624b\uff0c\u53cc\u65b9\u4ee5\u5982\u4e0b\u6b65\u9aa4\u8f6e\u6d41\u6e38\u620f\uff1a\" \/>\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\/1233\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"YZOJ P2050 [FJOI2013]\u5706\u5f62\u6e38\u620f - mnihyc&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"YZOJ P2050 \u5706\u5f62\u6e38\u620f \u65f6\u95f4\u9650\u5236\uff1a8000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB \u96be\u5ea6\uff1a 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