{"id":1017,"date":"2019-02-23T18:01:50","date_gmt":"2019-02-23T10:01:50","guid":{"rendered":"https:\/\/cf.mnihyc.com\/blog\/?p=1017"},"modified":"2020-04-22T11:41:55","modified_gmt":"2020-04-22T03:41:55","slug":"yzoj-p3484-%e5%ad%90%e6%a0%91%e6%b1%82%e5%92%8c","status":"publish","type":"post","link":"https:\/\/cf.mnihyc.com\/blog\/archives\/1017","title":{"rendered":"YZOJ P3484 \u5b50\u6811\u6c42\u548c"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P3484 \u5b50\u6811\u6c42\u548c<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a2000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB\u00a0\u00a0\u00a0\u00a0\u00a0 \u51fa\u9898\u4eba\uff1a<code>lgj<\/code><\/p>\n<p style=\"text-align: center;\">\u96be\u5ea6\uff1a <span style=\"color: #ff9900;\">\\(6.0\\)<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5df2\u77e5\u4e00\u68f5\u6811\u6709 \\(n\\) \u4e2a\u8282\u70b9\uff0c\u5e76\u4e14\u6839\u8282\u70b9\u662f\u56fa\u5b9a\u7684\u3002<\/p>\n<p>\u6bcf\u4e2a\u8282\u70b9\u4e0a\u90fd\u6709\u4e00\u4e2a\u6743\u503c \\(w_i\\) \uff0c\u8bb0 \\(s_i\\) \u4e3a \u4ee5 \\(i\\) \u4e3a\u6839\u7684<strong>\u5b50\u6811<\/strong>\u4e2d\uff0c<strong>\u6240\u6709\u8282\u70b9<\/strong>\u7684 \\(w_i\\) \u7684\u548c\u3002<\/p>\n<p>\u7531\u4e8e\u8be2\u95ee \\(s_i\\) \u592a\u7b80\u5355\u4e86\uff0c\u4e0d\u80fd\u5c06 <code>AKIOI<\/code> \u7684\u4f60\u7684\u9ad8\u667a\u5546\u4f53\u73b0\u51fa\u6765\uff0c\u6240\u4ee5\u6bcf\u6b21\u8be2\u95ee\u7ed9\u5b9a \\(l, r\\) \uff0c\u6c42 \\(\\sum\\limits_{i=l}^{r}{s_i}\\) \u3002<\/p>\n<p>\u4e3a\u4e86\u907f\u514d\u6b64\u9898\u96be\u5ea6\u592a\u4f4e\uff0c\u4e0d\u80fd\u5c06 <code>AKIOI<\/code> \u7684\u4f60\u7684\u9ad8\u667a\u5546\u4f53\u73b0\u51fa\u6765\uff0c\u6240\u4ee5\u7684\u8be2\u95ee\u7684\u8fc7\u7a0b\u4e2d\u8fd8\u53ef\u80fd\u4fee\u6539\u67d0\u4e2a\u8282\u70b9\u7684 \\(w_i\\) \u3002<\/p>\n<p>\u4e3a\u4e86\u5c06 <code>AKIOI<\/code> \u7684\u4f60\u7684\u9ad8\u667a\u5546\u4f53\u73b0\u51fa\u6765\uff0c\u4f60\u8981\u5199\u4e00\u4e2a\u7a0b\u5e8f\u6765\u5b9e\u65f6\u7ed9\u51fa\u8be2\u95ee\u7684\u7b54\u6848\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7b2c\u4e00\u884c\u4e3a\u4e24\u4e2a\u6574\u6570 \\(n\\) \u548c \\(q\\)\uff0c\u5206\u522b\u8868\u793a\u8282\u70b9\u6570\u548c\u64cd\u4f5c\u7684\u6b21\u6570\uff1b<\/p>\n<p>\u7b2c\u4e8c\u884c \\(n\\) \u4e2a\u6b63\u6574\u6570\uff0c\u8868\u793a\u5e8f\u5217 \\(w\\) \uff1b<\/p>\n<p>\u63a5\u4e0b\u6765 \\(n\\) \u884c\uff0c\u7b2c \\(i\\) \u884c\u4e24\u4e2a\u6b63\u6574\u6570 \\(u_i\\) \u548c \\(v_i\\)\uff0c\u63cf\u8ff0\u4e00\u6761\u6811\u4e0a\u7684\u8fb9\u3002\u7279\u522b\u5730\uff0c\\(u_i=0\\) \u65f6\uff0c\u8868\u793a \\(v_i\\) \u4e3a\u6811\u7684\u6839\u8282\u70b9\uff1b<\/p>\n<p>\u63a5\u4e0b\u6765 \\(q\\) \u884c\uff0c\u6bcf\u884c\u4e09\u4e2a\u6b63\u6574\u6570 \\(op, l, r\\) \u3002\u63cf\u8ff0 \\(q\\) \u7ec4\u64cd\u4f5c\u3002 \\(op=1\\) \u8868\u793a \\(w_l\\) \u4fee\u6539\u4e3a \\(r\\)\uff0c\\(op=2\\) \u8868\u793a\u8be2\u95ee \\(\\sum\\limits_{i=l}^{r}{s_i}\\) \u7684\u503c\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e\u6bcf\u7ec4\u8be2\u95ee\u64cd\u4f5c\uff0c\u4f60\u9700\u8981\u4f9d\u636e\u5f53\u524d\u6811\u7684\u60c5\u51b5\u8f93\u51fa\u8be5\u7ec4\u8be2\u95ee\u7684\u6807\u51c6\u7b54\u6848\uff0c\u6bcf\u6b21\u8be2\u95ee\u7684\u7b54\u6848\u72ec\u5360\u4e00\u884c\u3002<\/p>\n<p><!--more--><\/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 6\r\n7 4 3 4 9 1\r\n4 2\r\n0 1\r\n2 1\r\n2 3\r\n5 3\r\n6 5\r\n2 1 3\r\n1 1 1\r\n2 3 6\r\n2 3 5\r\n1 3 5\r\n2 6 6<\/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 \">62\r\n28\r\n27\r\n1<\/pre>\n<p><del>\uff08\u5047\u6837\u4f8b\uff09<\/del><\/p>\n<ul>\n<li>\n<h3><strong>\u6570\u636e\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e \\(40\\%\\) \u7684\u6570\u636e\uff0c\\(n, q \\leq 3000\\) \uff1b<\/p>\n<p>\u5bf9\u4e8e\u53e6\u5916 \\(15\\%\\) \u7684\u6570\u636e\uff0c\u6240\u6709 \\(op=2\\) \u7684\u64cd\u4f5c \\(l=r\\) \uff1b<\/p>\n<p>\u5bf9\u4e8e \\(100\\%\\) \u7684\u6570\u636e\uff0c\\(n, q \\leq 100000\\)\uff0c\\( w_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\u628a\u6bcf\u4e2a\u8282\u70b9\u7684 dfn \u6c42\u51fa\u6765\uff0c\u90a3\u4e48\u4e00\u4e2a\u8282\u70b9\u7684\u5b50\u6811\u5c31\u5bf9\u4e8e\u5176\u4e2d\u8fde\u7eed\u7684\u4e00\u6bb5\u533a\u95f4\u3002\u5dee\u5206\u9884\u5904\u7406\u4fee\u6539\u6bcf\u4e2a\u70b9\u4f1a\u5bf9\u5176\u4ed6\u8282\u70b9\u9020\u6210\u591a\u5c11\u7684\u5f71\u54cd\uff0c\u5206\u5757\u7ef4\u62a4 dfn \u5e8f\u5217\uff0c\u7531\u4e8e\u67e5\u8be2\u6bd4\u8f83\u591a\uff08\u6bcf\u6b21\u67e5\u8be2\u4e00\u4e2a\u7f16\u53f7\u90fd\u4f1a\u5bf9\u5e94\u67e5\u8be2\u8fd9\u91cc\u7684\u4e00\u6bb5\u533a\u95f4\uff09\uff0c\u6240\u4ee5\u524d\u7f00\u548c\u7ef4\u62a4\u5206\u5757\u3002\u540c\u65f6\u5206\u5757\u7ef4\u62a4\u7f16\u53f7\u5e8f\u5217\uff0c\u7531\u4e8e\u6bcf\u6b21\u53ea\u4f1a\u4fee\u6539\u4e00\u4e2a\u7f16\u53f7\uff0c\u6240\u4ee5\u4f7f\u7528\u666e\u901a\u7684\u5206\u5757\u5373\u53ef\u3002<\/p>\n<p>\u4fee\u6539\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7f16\u53f7 \\(O(1)\\)\uff0cdfn \\(O(\\sqrt n)\\) \uff1b<\/p>\n<p>\u67e5\u8be2\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff1a\u7f16\u53f7 \\(O(\\sqrt n)\\) \uff0c dfn \\(O(1)\\) \uff1b<\/p>\n<p>\u603b\u65f6\u95f4\u590d\u6742\u5ea6 \\(O(n\\sqrt 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\r\n#define _min(_a_,_b_) ((_a_)&lt;(_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\n\r\ninline int getnum()\r\n{\r\n\tregister char c=getchar();\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{\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\nstruct _node\r\n{\r\n\tint o;\r\n\tint next;\r\n}graph[105050];\r\nint gcnt;\r\n_node glist[205050];\r\n\r\ninline void insertLine(const int&amp;s,const int&amp;t)\r\n{\r\n\t_node*n=&amp;graph[s];\r\n\t_node*nw=&amp;glist[++gcnt];\r\n\tnw-&gt;o=t,nw-&gt;next=n-&gt;next;\r\n\tn-&gt;next=gcnt;\r\n}\r\n\r\nint w[105050];long long s[105050];\r\n\r\nint size[105050],dfn[105050],rdfn[105050],ldfn;\r\nvoid DFS(register int o,register int father)\r\n{\r\n\tdfn[++ldfn]=o,rdfn[o]=ldfn;\r\n\ts[o]+=w[o],size[o]++;\r\n\t_node*n=&amp;graph[o];\r\n\twhile(n-&gt;next)\r\n\t{\r\n\t\tn=&amp;glist[n-&gt;next];\r\n\t\tif(n-&gt;o!=father)\r\n\t\t{\r\n\t\t\tDFS(n-&gt;o,o);\r\n\t\t\ts[o]+=s[n-&gt;o],size[o]+=size[n-&gt;o];\r\n\t\t}\r\n\t}\r\n}\r\n\r\nint N;\r\nint BlockSize,BlockNum;\r\nlong long BlockPSumW[350],BlockSumS[350];\r\nlong long BlockPW[105050];\r\n\/\/int ContWtoS[105050][350];\r\nint ContWtoS[350][105050]; \r\n#define GetBlockPos(_p_) (((_p_)-1)\/BlockSize+1)\r\n#define GetBlockLeft(_w_) (((_w_)-1)*BlockSize+1)\r\n#define GetBlockRight(_w_) _min((_w_)*BlockSize,N)\r\n\r\ninline void InitializeBlocks()\r\n{\r\n\tBlockSize=__builtin_sqrt(N),BlockNum=N\/BlockSize+(N%BlockSize!=0);\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t{\r\n\t\tBlockSumS[GetBlockPos(i)]+=s[i];\r\n\t\tif(GetBlockPos(i) == GetBlockPos(i-1))\r\n\t\t\tBlockPW[i]=BlockPW[i-1]+w[dfn[i]];\r\n\t\telse\r\n\t\t\tBlockPW[i]=w[dfn[i]];\r\n\t}\r\n\tfor(register int i=1;i&lt;=BlockNum;i++)\r\n\t\tBlockPSumW[i]=BlockPSumW[i-1]+BlockPW[GetBlockRight(i)];\r\n\t\r\n\tfor(register int si=1;si&lt;=BlockNum;si++)\r\n\t{\r\n\t\tregister int left=GetBlockLeft(si),right=GetBlockRight(si);\r\n\t\tfor(register int i=left;i&lt;=right;i++)\r\n\t\t\tContWtoS[si][rdfn[i]]++,ContWtoS[si][rdfn[i]+size[i]]--;\r\n\t\tfor(register int i=1;i&lt;=N;i++)\r\n\t\t\tContWtoS[si][i]+=ContWtoS[si][i-1];\r\n\t}\r\n}\r\n\r\ninline void EditBlockW(const int&amp;pos,const int&amp;val)\r\n{\r\n\tregister int bi=GetBlockPos(pos),right=GetBlockRight(bi);\r\n\t\/\/printf(\"editW: %d(%d) %d\\n\",pos,bi,val);\r\n\tfor(register int i=pos;i&lt;=right;i++)\r\n\t\tBlockPW[i]+=val;\r\n\tfor(register int i=bi;i&lt;=BlockNum;i++)\r\n\t\tBlockPSumW[i]=BlockPSumW[i-1]+BlockPW[GetBlockRight(i)];\r\n\t\r\n\tfor(register int i=1;i&lt;=BlockNum;i++)\r\n\t\tBlockSumS[i]+=(long long)ContWtoS[i][pos]*val;\r\n}\r\n\r\ninline long long QueryBlockSumW(const int&amp;lpos,const int&amp;rpos)\r\n{\r\n\tregister int bl=GetBlockPos(lpos),br=GetBlockPos(rpos);\r\n\t\/\/printf(\"queryW: %d(%d) %d(%d)\\n\",lpos,bl,rpos,br);\r\n\tlong long ans=BlockPSumW[br]-BlockPSumW[bl-1];\r\n\tif(lpos != GetBlockLeft(bl))\r\n\t\tans-=BlockPW[lpos-1];\r\n\tif(rpos != GetBlockRight(br))\r\n\t\tans-=(BlockPW[GetBlockRight(br)]-BlockPW[rpos]);\r\n\treturn ans;\r\n}\r\n\r\ninline long long QueryBlockSumS(const int&amp;lpos,const int&amp;rpos)\r\n{\r\n\tregister int bl=GetBlockPos(lpos),br=GetBlockPos(rpos);\r\n\t\/\/printf(\"queryS: %d(%d) %d(%d)\\n\",lpos,bl,rpos,br);\r\n\tlong long ans=0;\r\n\tfor(register int i=bl;i&lt;=br;i++)\r\n\t\tans+=BlockSumS[i];\r\n\tfor(register int i=GetBlockLeft(bl);i&lt;=lpos-1;i++)\r\n\t\tans-=QueryBlockSumW(rdfn[i],rdfn[i]+size[i]-1);\r\n\tregister int right=GetBlockRight(br);\r\n\tfor(register int i=rpos+1;i&lt;=right;i++)\r\n\t\tans-=QueryBlockSumW(rdfn[i],rdfn[i]+size[i]-1);\r\n\treturn ans;\r\n}\r\n\r\nint main()\r\n{\r\n\tN=getnum();register int Q=getnum();\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tw[i]=getnum();\r\n\t\r\n\tregister int root=0;\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t{\r\n\t\tregister int u=getnum(),v=getnum();\r\n\t\tif(!u)\r\n\t\t\troot=v;\r\n\t\telse\r\n\t\t\tinsertLine(u,v),insertLine(v,u);\r\n\t}\r\n\tDFS(root,0);\r\n\t\r\n\tInitializeBlocks();\r\n\tfor(register int lp=1;lp&lt;=Q;lp++)\r\n\t{\r\n\t\tregister int op=getnum(),l=getnum(),r=getnum();\r\n\t\tif(op==2)\r\n\t\t\tprintf(\"%lld\\n\",QueryBlockSumS(l,r));\r\n\t\telse\r\n\t\t\tEditBlockW(rdfn[l],r-w[l]),w[l]=r;\r\n\t}\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 P3484 \u5b50\u6811\u6c42\u548c \u65f6\u95f4\u9650\u5236\uff1a2000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB\u00a0\u00a0\u00a0\u00a0\u00a0 \u51fa\u9898\u4eba &hellip; <a href=\"https:\/\/cf.mnihyc.com\/blog\/archives\/1017\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P3484 \u5b50\u6811\u6c42\u548c<\/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":[41,68],"tags":[],"class_list":["post-1017","post","type-post","status-publish","format-standard","hentry","category-proa","category-divideblock"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>YZOJ P3484 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