{"id":1244,"date":"2019-08-13T12:37:39","date_gmt":"2019-08-13T04:37:39","guid":{"rendered":"https:\/\/0.mnihyc.com\/blog\/?p=1244"},"modified":"2020-02-09T02:17:06","modified_gmt":"2020-02-08T18:17:06","slug":"yzoj-p2967-%e6%94%b6%e5%89%b2","status":"publish","type":"post","link":"https:\/\/0.mnihyc.com\/blog\/archives\/1244","title":{"rendered":"YZOJ P2967 \u6536\u5272"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P2967 \u6536\u5272<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a4000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a524288KB<\/p>\n<p style=\"text-align: center;\">\u96be\u5ea6\uff1a<span style=\"color: #ff6600;\">\\(7.0\\)<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5154\u6709 \\(n\\) \u4e2a\u7518\u8517\uff0c\u5154\u5c06\u5b83\u4eec\u79cd\u6210\u4e00\u6392\u3002<\/p>\n<p>\u6bcf\u5929\u65e9\u4e0a\uff0c\u7b2c \\(i\\) \u4e2a\u7518\u8517\u4f1a\u957f\u9ad8 \\(a_i\\) \u7c73\uff0c\u4f46\u5982\u679c\u8fbe\u5230 \\(b_i\\) \u7c73\uff0c\u5c31\u4e0d\u4f1a\u7ee7\u7eed\u957f\u9ad8\uff0c\u800c\u662f\u7ef4\u6301\u5728 \\(b_i\\) \u7c73\u3002<\/p>\n<p>\u5154\u6536\u5272\u4e86 \\(m\\) \u6b21\u7518\u8517\uff0c\u7b2c \\(i\\) \u6b21\u6536\u5272\u5728\u7b2c \\(t_i\\) \u5929\u7684\u665a\u4e0a\uff0c\u4ed6\u6536\u5272\u4e86 \\([l_i, r_i]\\) \u4e2d\u7684\u6240\u6709\u7518\u8517\u3002\u6536\u5272\u540e\uff0c\u8fd9\u4e9b\u7518\u8517\u7684\u9ad8\u5ea6\u53d8\u4e3a \\(0\\) \u7c73\uff0c\u4f46\u7b2c\u4e8c\u5929\u8fd8\u4f1a\u7ee7\u7eed\u6309\u7167\u539f\u6765\u7684\u89c4\u5219\u751f\u957f\u3002<\/p>\n<p>\u8bf7\u4f60\u6c42\u51fa\u5154\u6bcf\u5929\u6536\u5272\u4e86\u591a\u5c11\u7518\u8517\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7b2c\u4e00\u884c \\(n, m\\) \uff1b<\/p>\n<p>\u63a5\u4e0b\u6765 \\(n\\) \u884c\uff0c\u6bcf\u4e00\u884c \\(a_i, b_i\\) \uff1b<\/p>\n<p>\u63a5\u4e0b\u6765 \\(m\\) \u884c\uff0c\u6bcf\u4e00\u884c \\(t_i, l_i, r_i\\)\uff0c\u4fdd\u8bc1\u8f93\u5165\u7684 \\(t_i\\) \u4e25\u683c\u9012\u589e\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u8f93\u51fa \\(m\\) \u884c\u8868\u793a\u5154\u6bcf\u6b21\u6536\u5272\u7684\u7518\u8517\u7684\u9ad8\u5ea6\u4e4b\u548c\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u5165<\/strong><\/h3>\n<\/li>\n<li>\n<pre class=\"lang:default decode:true\">3 2\r\n8 7\r\n3 9\r\n1 10\r\n6 1 3\r\n8 1 2<\/pre>\n<h3><strong> \u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"lang:default decode:true\">22\r\n13<\/pre>\n<ul>\n<li>\n<h3><strong>\u6570\u636e\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5b58\u5728 \\(30\\%\\) \u6570\u636e\uff0c\u4fdd\u8bc1\u6240\u6709\u7518\u8517\u90fd\u4e0d\u4f1a\u957f\u5230 \\(b_i\\) \u7c73\uff1b<\/p>\n<p>\u5b58\u5728 \\(30\\%\\) \u6570\u636e\uff0c\u4fdd\u8bc1\u6bcf\u6b21\u6536\u53d6\u7684\u662f\u6240\u6709\u841d\u535c\uff1b<\/p>\n<p>\u5b58\u5728 \\(60\\%\\) \u6570\u636e\uff0c\\(n \\leq 50000\\)\uff1b<\/p>\n<p>\u5bf9\u4e8e\u6240\u6709\u6570\u636e \\(n \\leq 300000\\) \uff0c\\(m \\leq 100000\\) \uff0c\\(t_i,a_i,b_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>&nbsp;<\/p>\n<p>\u9996\u5148\u9ebb\u70e6\u7684\u662f\u6bcf\u4e2a\uff08\u7518\u8517=\u841d\u535c\uff09\u7684\u751f\u957f\u72b6\u6001\u90fd\u662f\u4e0d\u4e00\u6837\u7684\uff0c\u53ef\u80fd\u6709\u7684\u5df2\u7ecf\u6210\u719f\u4f46\u662f\u6709\u7684\u624d\u521a\u88ab\u6536\u5272\uff0c\u76f4\u63a5\u7ef4\u62a4\u6709\u70b9\u9ebb\u70e6\u3002<span style=\"color: #ffffff;\">\uff08\u5176\u5b9e\u662f\u6211\u4e0d\u4f1a\uff09<\/span><\/p>\n<p>\u53d1\u73b0\u6bcf\u6b21\u64cd\u4f5c\u90fd\u4f1a\u628a\u4e00\u6bb5\u533a\u95f4\u5185\u7684\u7518\u8517\u5168\u90e8\u6536\u5272\uff0c\u4e5f\u5c31\u662f\u751f\u957f\u72b6\u6001\u6e05\u96f6\uff0c\u4e5f\u5c31\u662f<strong>\u533a\u95f4\u63a8\u5e73<\/strong>\uff08<strong>assign<\/strong>\uff09\u64cd\u4f5c\u3002<\/p>\n<p>\u90fd\u77e5\u9053\u533a\u95f4\u63a8\u5e73\u53ef\u4ee5\u4f7f\u7528 ODT \u6765\u7ef4\u62a4\uff0c\u4e5f\u5c31\u662f <code>std::set<\/code> \u7ef4\u62a4<strong>\u4e0a\u6b21\u6536\u5272\u65f6\u523b\u76f8\u540c<\/strong>\u7684\u533a\u95f4\uff0c\u6bcf\u6b21\u64cd\u4f5c\u7684\u65f6\u5019\u628a \\([l, r]\\) <strong>\u5206\u5272<\/strong>\uff08<strong>split<\/strong>\uff09\u6210\u82e5\u5e72\u6bb5<strong>\u5206\u522b<\/strong>\u8ba1\u7b97\u7b54\u6848\uff0c\u6700\u540e\u518d\u63a8\u5e73\u5373\u53ef\u3002<\/p>\n<p>\u5269\u4e0b\u7684\u95ee\u9898\u5c31\u53ea\u6709\u5982\u4f55\u6c42\u51fa\uff1a\u751f\u957f\u4e86\u4e00\u6bb5\u65f6\u95f4 \\(\\Delta t\\) \u540e\uff0c\u533a\u95f4\u5185\u7518\u8517\u7684\u9ad8\u5ea6\u603b\u548c\u3002<\/p>\n<p>\u8003\u8651 \\(\\lfloor \\frac{b_i}{a_i} \\rfloor\\) \uff0c\u5b83\u4ee3\u8868\u67d0\u4e00\u7518\u8517\u6210\u719f\u7684\u65f6\u523b\uff0c\u5728\u8fd9\u4e2a\u65f6\u523b<strong>\u53ca<\/strong>\u4e4b\u524d\u5b83\u7684\u9ad8\u5ea6\u662f \\(\\Delta t \\cdot a_i\\) \uff0c\u4e4b\u540e\u5b83\u7684\u9ad8\u5ea6\u662f \\(b_i\\) \u3002<\/p>\n<p>\u6240\u4ee5\u53ef\u4ee5\u5efa\u7acb<strong>\u6743\u503c\u7ebf\u6bb5\u6811<\/strong>\uff0c\u4e0b\u6807\u8868\u793a\u65f6\u523b<s>\uff08\u4e0d\u79bb\u6563\u5316\u5c31\u4f1a\u8dd1\u7684\u8ddf\u6211\u4e00\u6837\u6162\uff09<\/s>\uff0c\u8981\u627e\u5230<strong> \\(\\Delta t\\) \u65f6\u523b<\/strong>\u6240\u6709<strong>\u5728\u7ebf\u6bb5\u6811\u4e0a<\/strong>\u7684\u7518\u8517\u7684\u751f\u957f\u72b6\u6001\uff0c\u53ef\u4ee5\u5728\u4e0a\u9762\u4e8c\u5206\u67e5\u627e\u3002<\/p>\n<p>\u5bf9\u4e8e\u533a\u95f4 \\([l, r]\\) \uff1a\u82e5 \\(\\Delta t \\leq mid\\) \uff0c\u90a3\u4e48\u53f3\u533a\u95f4 \\((mid, r]\\) \u65f6\u523b\u5185\u7684\u7518\u8517\u90fd\u6ca1\u6210\u719f\uff0c\u5bf9 \\(QA\\) \u8d21\u732e\u53f3\u533a\u95f4\u5185 \\(a\\) \u7684\u548c\uff0c\u540c\u65f6\u9012\u5f52\u8fdb\u5de6\u533a\u95f4\u5904\u7406\uff1b\u82e5 \\(\\Delta t &gt; mid\\)\uff0c\u90a3\u4e48\u5de6\u533a\u95f4 \\([l, mid]\\) \u65f6\u523b\u5185\u7684\u7518\u8517\u90fd\u6210\u719f\u4e86\uff0c\u5bf9 \\(QB\\) \u8d21\u732e\u5de6\u533a\u95f4\u5185 \\(b\\) \u7684\u548c\uff0c\u540c\u65f6\u9012\u5f52\u8fdb\u53f3\u533a\u95f4\u5904\u7406\u3002<\/p>\n<p>\u7279\u522b\u6ce8\u610f\u7684\u662f \\(l = r = \\Delta t\\) \u7684\u60c5\u51b5\uff0c\u7531\u4e8e \\(\\lfloor \\frac{b_i}{a_i} \\rfloor \\leq \\frac{b_i}{a_i}\\) \uff0c\u6240\u4ee5\u90fd\u6309\u7167\u672a\u6210\u719f\u7684\u60c5\u51b5\u5bf9 \\(QA\\) \u8d21\u732e\u5b83\u7684 \\(a\\) \u3002<\/p>\n<p>\u6240\u4ee5\u672c\u6b21\u8be2\u95ee\u7684\u7b54\u6848\u5c31\u662f \\(\\Delta t \\cdot QA + QB\\) \u3002<\/p>\n<p>\u56e0\u4e3a\u8981\u6c42\u7684\u662f\u67d0\u4e00\u533a\u95f4\u5185\u7518\u8517\u7684\u751f\u957f\u9ad8\u5ea6\u548c\uff0c\u6240\u4ee5\u5efa\u7acb<strong>\u4e3b\u5e2d\u6811<\/strong>\uff08\u6216\u8005\u8bf4\u628a\u6743\u503c\u7ebf\u6bb5\u6811\u62ff\u53bb<strong>\u53ef\u6301\u4e45\u5316<\/strong>\uff09\u5373\u53ef\u3002<\/p>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u5927\u6982\u662f \\(O((n+m)\\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;ext\/pb_ds\/assoc_container.hpp&gt;\r\n#include &lt;ext\/pb_ds\/tree_policy.hpp&gt;\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\twhile(!(c&gt;='0' &amp;&amp; c&lt;='9'))\r\n\t\tc=getchar();\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 a;\r\n}\r\n\r\nstruct _node\r\n{\r\n\tint l,r,t;\r\n};\r\nstruct _comp\r\n{\r\n\tbool operator ()(const _node&amp;a,const _node&amp;b)\r\n\t{\r\n\t\treturn a.l &lt; b.l;\r\n\t}\r\n};\r\n\r\nint cnt,lson[10505050],rson[10505050];\r\nlong long mva[10505050],mvb[10505050];\r\n#define _LMAX (1e9+1)\r\n\r\nint MP,MA,MB;\r\nvoid ModifyTree(int &amp;o,register int oO,register int l=0,register int r=_LMAX)\r\n{\r\n\to=++cnt;\r\n\tlson[o]=lson[oO],rson[o]=rson[oO];\r\n\tif(l==r)\r\n\t{\r\n\t\t\/\/printf(\"modify %d %d with %d %d\\n\",l,r,MA,MB);\r\n\t\tmva[o]=mva[oO]+MA,mvb[o]=mvb[oO]+MB;\r\n\t\treturn;\r\n\t}\r\n\t\r\n\tregister int mid=(l+r)&gt;&gt;1;\r\n\tif(MP &lt;= mid)\r\n\t\tModifyTree(lson[o],lson[oO],l,mid);\r\n\telse\r\n\t\tModifyTree(rson[o],rson[oO],mid+1,r);\r\n\tmva[o]=mva[lson[o]]+mva[rson[o]],mvb[o]=mvb[lson[o]]+mvb[rson[o]];\r\n}\r\n\r\nint QP;\r\nlong long QA,QB;\r\nvoid QueryTree(register int o,register int oO,register int l=0,register int r=_LMAX)\r\n{\r\n\tif(!o &amp;&amp; !oO)\r\n\t\treturn;\r\n\tif(l==r)\r\n\t{\r\n\t\tQA+=mva[o]-mva[oO];\r\n\t\treturn;\r\n\t}\r\n\t\r\n\tregister int mid=(l+r)&gt;&gt;1;\r\n\tif(QP &lt;= mid)\r\n\t\tQA+=mva[rson[o]]-mva[rson[oO]],QueryTree(lson[o],lson[oO],l,mid);\r\n\telse\r\n\t\tQB+=mvb[lson[o]]-mvb[lson[oO]],QueryTree(rson[o],rson[oO],mid+1,r);\r\n}\r\n\r\nint a[305050],b[305050],t[305050];\r\n\r\nint root[305050];\r\ntypedef __gnu_pbds::tree&lt;_node,__gnu_pbds::null_type,_comp&gt; _tt;\r\ntypedef _tt::point_iterator _tit;\r\n_tt seg;\r\n\r\ninline _tit split(register int pos)\r\n{\r\n\t_tit it=seg.lower_bound((_node){pos,-1,0});\r\n\tif(it!=seg.end() &amp;&amp; it-&gt;l==pos)\r\n\t\treturn it;\r\n\t--it;\r\n\t\r\n\tregister int l=it-&gt;l,r=it-&gt;r,t=it-&gt;t;\r\n\tseg.erase(it);\r\n\t\r\n\tseg.insert((_node){l,pos-1,t});\r\n\treturn seg.insert((_node){pos,r,t}).first;\r\n}\r\n\r\nint main()\r\n{\r\n\tregister int N=getnum(),M=getnum();\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\ta[i]=getnum(),b[i]=getnum(),t[i]=(a[i] ? b[i]\/a[i] : _LMAX);\r\n\t\r\n\t\/\/printf(\"t[]= \");for(register int i=1;i&lt;=N;i++)\r\n\t\/\/\tprintf(\"%d \",t[i]);printf(\"\\n\");\r\n\t\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tMP=t[i],MA=a[i],MB=b[i],ModifyTree(root[i],root[i-1]);\r\n\tseg.insert((_node){1,N,0});\r\n\t\r\n\tfor(register int lp=1;lp&lt;=M;lp++)\r\n\t{\r\n\t\tlong long ans=0;\r\n\t\tregister int t=getnum(),l=getnum(),r=getnum();\r\n\t\t_tit itr=split(r+1),itl=split(l);\r\n\t\twhile(itl != itr)\r\n\t\t{\r\n\t\t\tregister int dt=t - itl-&gt;t;\r\n\t\t\t\/\/printf(\"update %d %d with %d\\n\",itl-&gt;l,itl-&gt;r,itl-&gt;t);\r\n\t\t\tQA=QB=0,QP=dt;\r\n\t\t\tQueryTree(root[itl-&gt;r],root[itl-&gt;l - 1]);\r\n\t\t\tans+=(long long)dt*QA+QB;\r\n\t\t\tseg.erase(itl++);\r\n\t\t}\r\n\t\tseg.insert((_node){l,r,t});\r\n\t\tprintf(\"%lld\\n\",ans);\r\n\t}\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 P2967 \u6536\u5272 \u65f6\u95f4\u9650\u5236\uff1a4000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a524288KB \u96be\u5ea6\uff1a \u9898\u76ee\u63cf\u8ff0 \u5154 &hellip; <a href=\"https:\/\/0.mnihyc.com\/blog\/archives\/1244\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P2967 \u6536\u5272<\/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":[37,63,76,71],"tags":[],"class_list":["post-1244","post","type-post","status-publish","format-standard","hentry","category-crazya","category-bindivide","category-persistentdstree","category-balancedtree"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>YZOJ P2967 \u6536\u5272 - mnihyc&#039;s Blog<\/title>\n<meta name=\"description\" content=\"YZOJ P2967 \u6536\u5272 \u65f6\u95f4\u9650\u5236\uff1a4000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a524288KB \u96be\u5ea6\uff1a 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