{"id":1059,"date":"2019-05-11T13:03:51","date_gmt":"2019-05-11T05:03:51","guid":{"rendered":"https:\/\/0self.mnihyc.com\/blog\/?p=1059"},"modified":"2020-02-09T02:57:19","modified_gmt":"2020-02-08T18:57:19","slug":"yzoj-p3216-%e8%a1%8c%e5%95%86","status":"publish","type":"post","link":"https:\/\/0self.mnihyc.com\/blog\/archives\/1059","title":{"rendered":"YZOJ P3216 \u884c\u5546"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P3216 \u884c\u5546<\/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;\">\u96be\u5ea6\uff1a<span style=\"color: #ffcc00;\">\\(4.0\\)<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u6709 \\(n\\) \u4e2a\u8d27\u7269\uff0c\u6bcf\u4e2a\u8d27\u7269\u90fd\u6709\u5404\u81ea\u7684\u91cd\u91cf \\(w_i\\) \u548c\u4ef7\u503c \\(c_i\\)\uff0c\u4f46\u662f\u8f7d\u91cd\u91cf\u4ec5\u4e3a \\(m\\) \u3002<\/p>\n<p>\u6311\u9009\u51fa\u4e00\u4e9b\u8d27\u7269\uff0c\u603b\u91cd\u91cf\u4e0d\u8d85\u8fc7 \\(m\\)\uff0c\u4f7f\u4ef7\u503c\u4e4b\u548c\u6700\u5927\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7b2c\u4e00\u884c\uff0c\u4e24\u4e2a\u6574\u6570 \\(n\\)\uff0c\\(m\\)\uff1b<\/p>\n<p>\u63a5\u4e0b\u6765 \\(n\\) \u884c\uff0c\u6bcf\u884c\u4e24\u4e2a\u6574\u6570 \\(w_i\\)\uff0c\\(c_i\\) \u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u4e00\u4e2a\u6574\u6570 \\(ans\\) \u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u5165<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">4 3\r\n3 10\r\n2 7\r\n2 8\r\n1 1<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">10<\/pre>\n<ul>\n<li>\n<h3><strong>\u6570\u636e\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u00a0\\(1 \\leq n \\leq 10^6\\)\uff0c\\(1 \\leq m \\leq 4^{31}\\)\uff0c\\(1 \\leq w_i \\leq 3\\)\uff0c\\(1 \\leq c_i \\leq 10^9\\) \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>\u9996\u5148 \\(w\\) \u8fd9\u4e48\u5c0f\uff0c\u80af\u5b9a\u662f\u628a \\(3\\) \u79cd\u60c5\u51b5\u5206\u5f00\u8003\u8651\u3002<\/p>\n<p>\u5c06\u8d27\u7269\u6309\u7167 \\(w\\) \u5206\u4e3a \\(3\\) \u7c7b\uff0c\u5206\u522b\u6309\u4ece\u5927\u5230\u5c0f\u8fdb\u884c\u6392\u5e8f\uff0c\u7136\u540e\u987a\u4fbf\u8bb0\u4e2a\u524d\u7f00\u548c \\(sum\\) \u3002<\/p>\n<p>\u53d1\u73b0\u5982\u679c\u5148\u4e0d\u8003\u8651 \\(w=3\\) \u7684\u60c5\u51b5\uff0c\u90a3\u4e48\u6709\uff1a\u9009 \\(i\\) \u4ef6\u8d27\u7269\u65f6\uff0c\u6709 \\(f_i = sum2_i + sum1_{m &#8211; 2i}\\) \u3002<\/p>\n<p>\u53ef\u4ee5\u53d1\u73b0 \\(sum2\\) \u662f\u4e00\u4e2a\u5355\u8c03\u4e0a\u5347\u5e76\u4e14\u4e8c\u9636\u5bfc\u6570 \\(&lt;0\\) \u7684\u6574\u70b9\u51fd\u6570\uff0c\\(sum1_{m &#8211; 2i}\\) \u662f\u4e00\u4e2a\u5355\u8c03\u4e0b\u964d\u5e76\u4e14\u4e8c\u9636\u5bfc\u6570 \\(&gt;0\\) \u7684\u6574\u70b9\u51fd\u6570\u3002<\/p>\n<p>\u7ecf\u8fc7\u7b80\u5355\u7684\u6570\u5b66\u63a8\u7406\uff0c\u53ef\u4ee5\u53d1\u73b0\u5b83\u4eec\u76f8\u52a0\uff0c\u7ed3\u679c\u4f1a\u662f\u4e00\u4e2a\u5355\u5cf0\u51fd\u6570\u3002<\/p>\n<p>\u8fd9\u6837\u5c31\u679a\u4e3e \\(w=3\\) \u53d6\u7684\u6570\u91cf\uff0c\u7136\u540e\u4e09\u5206\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(nlogn)\\) \u3002<\/p>\n<p>\uff08p.s. \\(m \\leq 4^{31}\\) \u770b\u4f3c\u5f88\u5927\uff0c\u4f46\u662f\u5f53 \\(m \\geq 3n\\) \u6240\u6709\u7684\u8d27\u7269\u90fd\u53ef\u4ee5\u88c5\u7684\u4e0b\uff0c\u6240\u4ee5\u5e76\u6ca1\u6709\u4ec0\u4e48\u7528\uff09<\/p>\n<p>\uff08\u8c8c\u4f3c\u8fd8\u6709\u4e00\u79cd DP \u7684\u505a\u6cd5\uff09<\/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;functional&gt;\r\n\r\n#define _min(_a_,_b_) ((_a_)&lt;(_b_)?(_a_):(_b_))\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\ntemplate&lt;class T&gt;\r\ninline T getnum()\r\n{\r\n\tregister char c=0;\r\n\twhile(!(c&gt;='0' &amp;&amp; c&lt;='9'))\r\n\t\tc=getchar();\r\n\tregister T a=0;\r\n\twhile(c&gt;='0' &amp;&amp; c&lt;='9')\r\n\t{\r\n\t\ta*=10,a+=c-'0';\r\n\t\tc=getchar();\r\n\t}\r\n\treturn a;\r\n}\r\n\r\nint lc1,lc2,lc3;\r\nlong long nc1[1050505],nc2[1050505],nc3[1050505];\r\n\r\nint main()\r\n{\r\n\tregister int N=getnum&lt;int&gt;();\r\n\tregister long long M=getnum&lt;long long&gt;(),tc=0;\r\n\tregister int tw=0;\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t{\r\n\t\tregister int w=getnum&lt;int&gt;();\r\n\t\tif(w==1)\r\n\t\t\tnc1[++lc1]=getnum&lt;int&gt;(),tc+=nc1[lc1];\r\n\t\telse if(w==2)\r\n\t\t\tnc2[++lc2]=getnum&lt;int&gt;(),tc+=nc2[lc2];\r\n\t\telse\r\n\t\t\tnc3[++lc3]=getnum&lt;int&gt;(),tc+=nc3[lc3];\r\n\t\ttw+=w;\r\n\t}\r\n\tif(tw&lt;=M)\r\n\t{\r\n\t\tprintf(\"%lld\\n\",tc);\r\n\t\treturn 0;\r\n\t}\r\n\t\r\n\tstd::sort(&amp;nc1[1],&amp;nc1[lc1+1],std::greater&lt;int&gt;());\r\n\tstd::sort(&amp;nc2[1],&amp;nc2[lc2+1],std::greater&lt;int&gt;());\r\n\tstd::sort(&amp;nc3[1],&amp;nc3[lc3+1],std::greater&lt;int&gt;());\r\n\tfor(register int i=1;i&lt;=lc1;i++)\r\n\t\tnc1[i]+=nc1[i-1];\r\n\tfor(register int i=1;i&lt;=lc2;i++)\r\n\t\tnc2[i]+=nc2[i-1];\r\n\tfor(register int i=1;i&lt;=lc3;i++)\r\n\t\tnc3[i]+=nc3[i-1];\r\n\t\r\n\tlong long ans=0;\r\n\tfor(register int s3=0;s3&lt;=lc3;s3++)\r\n\t{\r\n\t\tregister int sl=M-3*s3;\r\n\t\tif(sl&lt;0)\r\n\t\t\tbreak;\r\n\t\t\/\/printf(\"s3: %d    left: %d\\n\",s3,sl);\r\n\t\tif((lc2&lt;&lt;1)+lc1 &lt;= sl)\r\n\t\t\tans=_max(ans,nc2[lc2]+nc1[lc1]+nc3[s3]);\r\n\t\telse\r\n\t\t{\r\n\t\t\t#define AnsPoint(_x) \\\r\n\t\t\t\tnc2[_x]+nc1[_min(sl-((_x)&lt;&lt;1),lc1)]\r\n\t\t\tregister int l=0,r=_min(sl&gt;&gt;1,lc2);\r\n\t\t\twhile(l+1&lt;r)\r\n\t\t\t{\r\n\t\t\t\t\/\/printf(\"divide %d %d\\n\",l,r);\r\n\t\t\t\tregister int lmid=(l+r)&gt;&gt;1,rmid=(lmid+r)&gt;&gt;1;\r\n\t\t\t\t\/\/printf(\"lmid %d(%d)  rmid %d(%d)\\n\",lmid,sl-(lmid&lt;&lt;1),rmid,sl-(rmid&lt;&lt;1));\r\n\t\t\t\tregister long long ansl=AnsPoint(lmid),ansr=AnsPoint(rmid);\r\n\t\t\t\t\/\/printf(\"ansl %lld  ansr %lld\\n\",ansl,ansr);\r\n\t\t\t\tif(ansl&gt;ansr)\r\n\t\t\t\t\tr=rmid;\r\n\t\t\t\telse\r\n\t\t\t\t\tl=lmid;\r\n\t\t\t}\r\n\t\t\tans=_max(ans,_max(AnsPoint(l),AnsPoint(r))+nc3[s3]);\r\n\t\t}\r\n\t}\r\n\tprintf(\"%lld\\n\",ans);\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>YZOJ P3216 \u884c\u5546 \u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB \u96be\u5ea6\uff1a \u9898\u76ee\u63cf\u8ff0 \u6709 &hellip; <a href=\"https:\/\/0self.mnihyc.com\/blog\/archives\/1059\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P3216 \u884c\u5546<\/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":[52,74],"tags":[],"class_list":["post-1059","post","type-post","status-publish","format-standard","hentry","category-mediuma","category-bbindivide"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>YZOJ P3216 \u884c\u5546 - mnihyc&#039;s Blog<\/title>\n<meta name=\"description\" content=\"YZOJ P3216 \u884c\u5546 \u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB 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