{"id":1113,"date":"2019-05-11T17:11:58","date_gmt":"2019-05-11T09:11:58","guid":{"rendered":"https:\/\/0.mnihyc.com\/blog\/?p=1113"},"modified":"2020-02-09T02:52:34","modified_gmt":"2020-02-08T18:52:34","slug":"yzoj-p2358-zjoi-2012naive-matrix","status":"publish","type":"post","link":"https:\/\/0.mnihyc.com\/blog\/archives\/1113","title":{"rendered":"YZOJ P2358 [ZJOI 2012]Naive &#8211; Matrix"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P2358 [ZJOI 2012]Naive &#8211; Matrix<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a131072KB<\/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>\u7ed9\u51fa\u4e00\u4e2a \\(R \\times C\\) \u7684\u77e9\u9635\uff0c\u4e0a\u9762\u6709 \\(N\\) \u4e2a \\(0\\)\uff0c\u5176\u4ed6\u7684\u90fd\u662f \\(1\\)\uff0c\u73b0\u5728\u7ed9\u51fa\u8fd9\u4e9b \\(0\\) \u7684\u4f4d\u7f6e\uff0c\u8981\u6c42\u6c42\u51fa\u6709\u591a\u5c11\u4e2a\u5b50\u77e9\u9635<strong>\u5305\u542b<span style=\"text-decoration: underline;\">\u81f3\u5c11\u4e00\u4e2a<\/span><\/strong> \\(0\\) \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\u4e09\u4e2a\u6574\u6570 \\(R\\)\u3001\\(C\\)\u3001\\(N\\) \u3002<\/p>\n<p>\u63a5\u4e0b\u6765 \\(N\\) \u884c\uff0c\u6bcf\u884c\u4e24\u4e2a\u6574\u6570 \\(x\\)\u3001\\(y\\)\uff0c\u8868\u793a \\(0\\) \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\u4e00\u4e2a\u6570\u8868\u793a\u5b50\u77e9\u9635\u7684\u4e2a\u6570\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 \">5 5 3\r\n1 1\r\n1 4\r\n4 4\r\n<\/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 \">103<\/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\\(R, C \\leq 40000\\)\uff0c\\(N \\leq \\min\\{R \\times C,100000\\}\\)\uff0c\u6240\u6709 \\(0\\) \u7684\u4f4d\u7f6e\u4e24\u4e24\u4e0d\u540c\u4e14<strong>\u968f\u673a<\/strong>\u751f\u6210\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Source: BZOJ 2658<\/p>\n<p><!--more--><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>\u597d\u9898\uff01<\/p>\n<p>\u5f88\u663e\u7136\u7684\u662f\u8f6c\u6362\u300c\u81f3\u5c11\u5305\u542b\u4e00\u4e2a \\(0\\) \u5b50\u77e9\u5f62\u7684\u6570\u91cf\u300d\u4e3a\u300c<strong>\u4e0d\u5305\u542b<\/strong> \\(0\\) \u7684\u5b50\u77e9\u5f62\u7684\u6570\u91cf\u300d\uff0c\u7136\u540e\u5c31\u4e0d\u4f1a\u505a\u4e86\uff08\u3002<\/p>\n<p>\u60f3\u5230<strong>\u626b\u63cf\u7ebf<\/strong>\uff0c\u4ece\u4e0a\u5f80\u4e0b\u626b\u63cf\uff0c\u5904\u7406\u51fa\u6bcf\u4e00\u4e2a\u70b9\u5411\u5de6\u5411\u53f3<strong>\u5411\u4e0a<\/strong>\u80fd\u5230\u8fbe\u7684\u6700\u8fdc\u8ddd\u79bb\uff0c\u53d1\u73b0\u8fd9\u4e00\u6b65\u9aa4\u53ef\u4ee5\u4f7f\u7528<del>\u5355\u8c03\u6808\uff01<\/del><strong>\u7b1b\u5361\u5c14\u6811<\/strong>\u7ef4\u62a4\uff0c\u7b54\u6848\u5c31\u662f\u00a0<span style=\"font-size: 20px;\">\\(\\sum\\limits_{x}{\\frac{size_x \\times \\left(size_x+1\\right)}{2}\\times \\left(height_x-height_{fa}\\right)}\\)<\/span> \u3002<\/p>\n<p>\u6ce8\uff1a\u8fd9\u91cc\u6bcf\u4e2a\u8282\u70b9\u7ef4\u62a4\u7684\u662f\u5176<strong>\u5bf9\u7236\u4eb2\u8282\u70b9\u7684\u8d21\u732e<\/strong>\uff01<\/p>\n<p>\u8003\u8651\u5982\u4f55\u7531\u8fd9\u4e00\u5c42\u7684\u7b1b\u5361\u5c14\u6811\u8f6c\u6362\u81f3\u4e0b\u4e00\u5c42\u3002<\/p>\n<p>\u53d1\u73b0\u7b1b\u5361\u5c14\u6811\u5176\u5b9e\u548c \\(Treap\\) \u662f\u4e00\u6837\u7684\u4e1c\u897f\uff0c\u518d\u52a0\u4e0a\u672c\u9898\u7684\u6743\u503c \\(height\\) \u662f<strong>\u968f\u673a<\/strong>\u7684\uff0c\u6240\u4ee5\u5c31\u53ef\u4ee5\u7528 \\(Treap\\) \u7ef4\u62a4\u8fd9\u4e00\u64cd\u4f5c\u3002\u8df3\u5c42\u5176\u5b9e\u5c31\u662f\u628a\u6240\u6709\u8282\u70b9\u7684 \\(pri\\) \u90fd\u52a0\u4e0a \\(1\\) \uff0c\u7136\u540e\u628a\u5f53\u524d\u5c42\u6240\u6709\u503c\u4e3a \\(0\\) \u7684\u8282\u70b9\u7684 \\(pri\\) \u8bbe\u4e3a \\(0\\) \u5373\u53ef\u3002<\/p>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(NlogN+NlogC)\\) \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\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\nint root,pri[40505],size[40505],lson[40505],rson[40505];\r\nint tag[40505];\r\nlong long ans[40505];\r\n\r\ninline void PushUp(register int x)\r\n{\r\n\tsize[x]=size[lson[x]]+size[rson[x]]+1;\r\n\t\/\/ father[x] hasn't been defined yet!!!\r\n\t\/\/ans[x]=ans[lson[x]]+ans[rson[x]]+((long long)size[x]*(size[x]+1)&gt;&gt;1)*(pri[x]-pri[father[x]]);\r\n\tans[x]=0;\r\n\tif(lson[x])\r\n\t\tans[x]+=ans[lson[x]]+((long long)size[lson[x]]*(size[lson[x]]+1)&gt;&gt;1)*(pri[lson[x]]-pri[x]);\r\n\tif(rson[x])\r\n\t\tans[x]+=ans[rson[x]]+((long long)size[rson[x]]*(size[rson[x]]+1)&gt;&gt;1)*(pri[rson[x]]-pri[x]);\r\n}\r\n\r\ninline void PushDown(register int x)\r\n{\r\n\tif(tag[x])\r\n\t{\r\n\t\tif(lson[x])\r\n\t\t\ttag[lson[x]]+=tag[x],pri[lson[x]]+=tag[x];\r\n\t\tif(rson[x])\r\n\t\t\tpri[rson[x]]+=tag[x],tag[rson[x]]+=tag[x];\r\n\t\ttag[x]=0;\r\n\t}\r\n}\r\n\r\ninline int MergeTree(register int x,register int y)\r\n{\r\n\tif(!x || !y)\r\n\t\treturn x^y;\r\n\tPushDown(x),PushDown(y);\r\n\tif(pri[x] &lt; pri[y])\r\n\t{\r\n\t\trson[x]=MergeTree(rson[x],y);\r\n\t\treturn PushUp(x),x;\r\n\t}\r\n\telse\r\n\t{\r\n\t\tlson[y]=MergeTree(x,lson[y]);\r\n\t\treturn PushUp(y),y;\r\n\t}\r\n}\r\n\r\ninline void SplitTreeByOrder(register int o,register int k,int&amp;x,int&amp;y)\r\n{\r\n\tif(!o)\r\n\t{\r\n\t\tx=y=0;\r\n\t\treturn;\r\n\t}\r\n\tPushDown(o);\r\n\tif(k &lt;= size[lson[o]])\r\n\t\ty=o,SplitTreeByOrder(lson[o],k,x,lson[o]);\r\n\telse\r\n\t\tx=o,SplitTreeByOrder(rson[o],k-size[lson[o]]-1,rson[o],y);\r\n\tPushUp(o);\r\n}\r\n\r\ninline int BuildTree(register int l,register int r)\r\n{\r\n\tif(l&gt;r)\r\n\t\treturn 0;\r\n\tregister int mid=(l+r)&gt;&gt;1;\r\n\tlson[mid]=BuildTree(l,mid-1);\r\n\trson[mid]=BuildTree(mid+1,r);\r\n\treturn PushUp(mid),mid;\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}pnts[105050];\r\n\r\nint main()\r\n{\r\n\tregister int R=getnum(),C=getnum(),N=getnum();\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tpnts[i]=(_point){getnum(),getnum()};\r\n\tstd::sort(&amp;pnts[1],&amp;pnts[N+1]);\r\n\troot=BuildTree(1,C);\r\n\t\r\n\tlong long ans=((long long)R*(R+1)&gt;&gt;1)*((long long)C*(C+1)&gt;&gt;1);\r\n\tfor(register int x=1,j=1;x&lt;=R;x++)\r\n\t{\r\n\t\tpri[root]++,tag[root]++;\r\n\t\twhile(j&lt;=N &amp;&amp; pnts[j].x==x)\r\n\t\t{\r\n\t\t\tint a,b,c,d;\r\n\t\t\tSplitTreeByOrder(root,pnts[j].y-1,a,b);\r\n\t\t\tSplitTreeByOrder(b,1,c,d);\r\n\t\t\tpri[c]=0;\r\n\t\t\troot=MergeTree(a,MergeTree(c,d));\r\n\t\t\tj++;\r\n\t\t}\r\n\t\tans-=::ans[root]+((long long)size[root]*(size[root]+1)&gt;&gt;1)*pri[root];\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 P2358 [ZJOI 2012]Naive &#8211; Matrix \u65f6\u95f4\u9650\u5236\uff1a1000MS  &hellip; <a href=\"https:\/\/0.mnihyc.com\/blog\/archives\/1113\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P2358 [ZJOI 2012]Naive &#8211; Matrix<\/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":[37,71,86,84],"tags":[],"class_list":["post-1113","post","type-post","status-publish","format-standard","hentry","category-crazya","category-balancedtree","category-scanline","category-cartesiantree"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>YZOJ P2358 [ZJOI 2012]Naive - Matrix - mnihyc&#039;s Blog<\/title>\n<meta name=\"description\" content=\"YZOJ P2358 Naive - Matrix \u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a131072KB \u96be\u5ea6\uff1a \u9898\u76ee\u63cf\u8ff0 \u7ed9\u51fa\u4e00\u4e2a (R times C) \u7684\u77e9\u9635\uff0c\u4e0a\u9762\u6709 (N) \u4e2a (0)\uff0c\u5176\u4ed6\u7684\u90fd\u662f (1)\uff0c\u73b0\u5728\u7ed9\u51fa\u8fd9\u4e9b (0) \u7684\u4f4d\u7f6e\uff0c\u8981\u6c42\u6c42\u51fa\u6709\u591a\u5c11\u4e2a\u5b50\u77e9\u9635\u5305\u542b\u81f3\u5c11\u4e00\u4e2a\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/0.mnihyc.com\/blog\/archives\/1113\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"YZOJ P2358 [ZJOI 2012]Naive - Matrix - mnihyc&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"YZOJ P2358 Naive - Matrix \u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a131072KB \u96be\u5ea6\uff1a \u9898\u76ee\u63cf\u8ff0 \u7ed9\u51fa\u4e00\u4e2a (R times C) \u7684\u77e9\u9635\uff0c\u4e0a\u9762\u6709 (N) \u4e2a (0)\uff0c\u5176\u4ed6\u7684\u90fd\u662f (1)\uff0c\u73b0\u5728\u7ed9\u51fa\u8fd9\u4e9b (0) \u7684\u4f4d\u7f6e\uff0c\u8981\u6c42\u6c42\u51fa\u6709\u591a\u5c11\u4e2a\u5b50\u77e9\u9635\u5305\u542b\u81f3\u5c11\u4e00\u4e2a\" \/>\n<meta property=\"og:url\" content=\"https:\/\/0.mnihyc.com\/blog\/archives\/1113\" \/>\n<meta property=\"og:site_name\" content=\"mnihyc&#039;s Blog\" \/>\n<meta property=\"article:published_time\" content=\"2019-05-11T09:11:58+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-02-08T18:52:34+00:00\" \/>\n<meta name=\"author\" content=\"mnihyc\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@mnihyc\" \/>\n<meta name=\"twitter:site\" content=\"@mnihyc\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"mnihyc\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/0.mnihyc.com\/blog\/archives\/1113#article\",\"isPartOf\":{\"@id\":\"https:\/\/0.mnihyc.com\/blog\/archives\/1113\"},\"author\":{\"name\":\"mnihyc\",\"@id\":\"https:\/\/mnihyc.com\/blog\/#\/schema\/person\/61e167d6d591fdd20dcfee2cf848a751\"},\"headline\":\"YZOJ P2358 [ZJOI 2012]Naive &#8211; 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