{"id":1037,"date":"2019-03-23T16:23:14","date_gmt":"2019-03-23T08:23:14","guid":{"rendered":"https:\/\/0.mnihyc.com\/blog\/?p=1037"},"modified":"2020-04-22T11:41:16","modified_gmt":"2020-04-22T03:41:16","slug":"yzoj-p3367-%e9%ad%94%e6%9c%af%e5%b8%bd%e6%b8%b8%e6%88%8f","status":"publish","type":"post","link":"https:\/\/0.mnihyc.com\/blog\/archives\/1037","title":{"rendered":"YZOJ P3367 \u9b54\u672f\u5e3d\u6e38\u620f"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P3367 \u9b54\u672f\u5e3d\u6e38\u620f<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a1000MS\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0 \u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB<\/p>\n<p style=\"text-align: center;\">\u96be\u5ea6\uff1a<span style=\"color: #ff6600;\">\\(6.0\\)<\/span> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <span style=\"color: #000000;\">\u51fa\u9898\u4eba\uff1azzx<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u6709 \\(n\\) \u9876\u5916\u5f62\u76f8\u540c\u7684\u9b54\u672f\u5e3d\u548c\u4e00\u4e2a\u9b54\u672f\u7403\uff0c\u6bcf\u6b21\u6e38\u620f\u5f00\u59cb\u524d\uff0c\u9b54\u672f\u5e3d\u4f1a\u88ab\u5012\u6263\u653e\u7f6e\u6392\u6210\u4e00\u6392\uff0c\u8fd9\u4e9b\u9b54\u672f\u5e3d\u4ece\u5de6\u5230\u53f3\u4f9d\u6b21\u7f16\u53f7\u4e3a \\(1, 2, \\cdots , n\\) \u3002<\/p>\n<p>\u6bcf\u4e00\u5c40\u6e38\u620f\uff0c\u9b54\u672f\u7403\u4f1a\u88ab\u653e\u5728\u5176\u4e2d\u4e00\u9876\u9b54\u672f\u5e3d\u5e95\u4e0b\uff0c\u7136\u540e\u8fdb\u884c\u82e5\u5e72\u6b21\u4ea4\u6362\uff0c\u6bcf\u6b21\u4ea4\u6362\u65f6\u53ef\u4ee5\u9009\u51fa\u4e24\u9876\u9b54\u672f\u5e3d\uff0c\u4ea4\u6362\u5b83\u4eec\u7684\u4f4d\u7f6e\u3002\u6574\u4e2a\u8fc7\u7a0b\u5bf9\u4e8e\u5c0f\u670b\u53cb\u4eec\u800c\u8a00\u90fd\u662f\u53ef\u89c1\u7684\u3002\u4ea4\u6362\u7ed3\u675f\u540e\uff0c\u5c0f\u670b\u53cb\u4eec\u53ef\u4ee5\u6253\u5f00\u9b54\u672f\u5e3d\uff0c\u6b63\u786e\u627e\u5230\u9b54\u672f\u7403\u5219\u6e38\u620f\u80dc\u5229\u3002<\/p>\n<p>\u4e3a\u4e86\u8fdb\u884c\u591a\u5c40\u6e38\u620f\uff0c\u73b0\u6709\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(m\\) \u7684\u64cd\u4f5c\u5e8f\u5217 \\((a_1,b_1), (a_2,b_2), \\cdots ,(a_m,b_m)\\)\uff0c\u5176\u4e2d \\((a_i,b_i)\\) \u8868\u793a\u53cd\u8f6c \\(a_i\\) \u53f7\u548c \\(b_i\\) \u53f7\u9b54\u672f\u5e3d<strong>\u4e4b\u95f4<\/strong>\u7684\u9b54\u672f\u5e3d\u7684\u987a\u5e8f\uff08\u5982\u539f\u6765\u9b54\u672f\u5e3d\u4ece\u5de6\u5230\u53f3\u4e3a \\(a,b,c,d,e,f,g\\)\uff0c\u5219\u64cd\u4f5c \\((3,6)\\) \u8fdb\u884c\u540e\u987a\u5e8f\u53d8\u4e3a \\(a,b,f,e,d,c,g\\) \u3002\u4e4b\u540e\uff0c\u5c0f\u670b\u53cb\u4eec\u4f1a\u73a9 \\(q\\) \u5c40\u6e38\u620f\u3002\u5176\u4e2d\uff0c\u7b2c \\(j\\) \u8f6e\u6e38\u620f\uff0c\u9b54\u672f\u7403\u4f1a\u88ab\u653e\u5728 \\(x_j\\) \u53f7\u9b54\u672f\u5e3d\u4e0b\uff0c\u7136\u540e\u8fdb\u884c\u64cd\u4f5c\u5e8f\u5217\u4e2d \\([l_j,r_j]\\) \u8fd9\u4e2a\u7247\u6bb5\uff0c\u5373\u4f9d\u6b21\u8fdb\u884c\u53cd\u8f6c\u64cd\u4f5c \\((a_{l_j},b_{l_j}),(a_{l_j+1},b_{l_j+1}), \\cdots ,(a_{r_j},b_{r_j})\\) \u3002\u8bf7\u6c42\u51fa\u6bcf\u6b21\u6e38\u620f\u53cd\u8f6c\u64cd\u4f5c\u7ed3\u675f\u65f6\uff0c\u9b54\u672f\u7403\u4f4d\u4e8e\u5728\u54ea\u4e00\u9876\u9b54\u672f\u5e3d\u4e0b\u3002\u6ce8\u610f\uff1a\u8fd9\u91cc\u7684\u9b54\u672f\u5e3d\u7f16\u53f7\u59cb\u7ec8\u662f\u6309\u7167\u4f4d\u7f6e\u4ece\u5de6\u5230\u53f3\u7f16\u53f7\u7684\uff0c\u5373\u6bcf\u6b21\u4ea4\u6362\u9b54\u672f\u5e3d\u4e4b\u540e\uff0c\u6240\u6709\u9b54\u672f\u5e3d\u4f1a\u6309\u7167\u4ece\u5de6\u5230\u53f3\u7684\u987a\u5e8f\u91cd\u65b0\u7f16\u53f7\u4e3a \\(1,2,\\cdots,n\\) \u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7b2c\u4e00\u884c\u6709\u4e09\u4e2a\u6574\u6570 \\(n,m,q\\)\uff0c\u5176\u4e2d \\(n\\) \u4ee3\u8868\u9b54\u672f\u5e3d\u7684\u6570\u91cf\uff0c\\(m\\) \u4ee3\u8868\u64cd\u4f5c\u5e8f\u5217\u7684\u957f\u5ea6\uff0c\\(q\\) \u4ee3\u8868\u6e38\u620f\u6b21\u6570\u3002<\/p>\n<p>\u63a5\u4e0b\u6765 \\(m\\) \u884c\uff0c\u5176\u4e2d\u7b2c \\(i\\) \u884c\u4e24\u4e2a\u6574\u6570 \\(a_i,b_i\\)\uff0c\u8868\u793a\u64cd\u4f5c\u5e8f\u5217\u7684\u7b2c \\(i\\) \u9879\u3002\u63a5\u4e0b\u6765 \\(q\\) \u884c\uff0c\u5176\u4e2d\u7b2c \\(j\\) \u884c\u4e09\u4e2a\u6b63\u6574\u6570 \\(x_j,l_j,r_j\\)\uff0c\u8868\u793a\u7b2c \\(j\\) \u5c40\u6e38\u620f\u3002\u4fdd\u8bc1 \\(1 \\leq a_i \\leq b_i \\leq n\\)\uff0c\\(1 \\leq x_j \\leq n\\)\uff0c\\(1 \\leq l_j \\leq r_j \\leq m\\) \u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f <\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u8f93\u51fa \\(q\\) \u884c\uff0c\u6bcf\u884c\u4e00\u4e2a\u6574\u6570\uff0c\u7b2c \\(j\\) \u884c\u7684\u6574\u6570\u8868\u793a\u7b2c \\(j\\) \u5c40\u6e38\u620f\u7684\u4ea4\u6362\u7ed3\u675f\u540e\uff0c\u9b54\u672f\u7403\u6240\u5728\u7684\u9b54\u672f\u5e3d\u7f16\u53f7\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 \">5 5 3\r\n2 4\r\n1 4\r\n1 5\r\n3 4\r\n1 2\r\n2 1 3\r\n1 2 4\r\n2 3 5<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">5\r\n2\r\n3<\/pre>\n<ul>\n<li>\n<h3>\u6570\u636e\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/h3>\n<\/li>\n<\/ul>\n<p>\\(10\\%\\)\uff1a\\(n=2\\) \u3002<\/p>\n<p>\\(40\\%\\)\uff1a\\(n \\leq 15\\) \u3002<\/p>\n<p>\\(100\\%\\)\uff1a\\(1 \\leq n,m,q \\leq 100,000\\) \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>\u5148\u4e0d\u8003\u8651\u4ea4\u6362\u533a\u95f4\u7684\u64cd\u4f5c\u7684\u8bdd\uff0c\u53ef\u4ee5\u505a\u5230\u7ebf\u6027\u590d\u6742\u5ea6\u5904\u7406\u3002<\/p>\n<p>\u9996\u5148\u8003\u8651\u5bf9\u6240\u6709\u7684\u67e5\u8be2\u79bb\u7ebf\uff0c\u7136\u540e\u5206\u522b\u628a\u8fd9\u4e2a\u67e5\u8be2\u6302\u5230\u64cd\u4f5c\u533a\u95f4\u7684\u5de6\u7aef\u70b9\u548c\u53f3\u7aef\u70b9\u3002\u7531\u4e8e\u6bcf\u6b21\u4ea4\u6362\u9b54\u672f\u5e3d\u4e4b\u540e\uff0c\u6240\u6709\u9b54\u672f\u5e3d\u4f1a\u6309\u7167\u4ece\u5de6\u5230\u53f3\u7684\u987a\u5e8f\u91cd\u65b0\u7f16\u53f7\uff0c\u6240\u4ee5\u6211\u4eec\u5bf9\u4e8e\u6bcf\u5c40\u6e38\u620f\u53ea\u9700\u8981\u8bb0\u4f4f\u7403\u4e00\u5f00\u59cb\u653e\u5728\u54ea\u4e00\u4e2a\u9b54\u672f\u5e3d\uff0c\u7ed3\u675f\u65f6\u8fd9\u4e2a\u9b54\u672f\u5e3d\u5728\u54ea\u5c31\u884c\u4e86\u3002<\/p>\n<p>\u626b\u8fc7\u4e00\u904d\u64cd\u4f5c\u5e8f\u5217\uff0c\u82e5\u662f\u9047\u5230\u4e00\u4e2a\u70b9\u4e3a\u4e00\u4e2a\u67e5\u8be2\u7684\u5de6\u7aef\u70b9\uff0c\u5c31\u8bb0\u5f55\u4e0b\u5f53\u524d\u67e5\u8be2\u4f4d\u7f6e\u4e0a\u7684\u7f16\u53f7\uff0c\u9047\u5230\u53f3\u7aef\u70b9\u65f6\u627e\u5230\u8fd9\u4e2a\u7f16\u53f7\u73b0\u5728\u5728\u54ea\u4e00\u4e2a\u4f4d\u7f6e\uff0c\u5c31\u662f\u8fd9\u4e2a\u8be2\u95ee\u7684\u7b54\u6848\u4e86\u3002<\/p>\n<p>\u7531\u4e8e\u6709\u7ffb\u8f6c\u6574\u4e2a\u533a\u95f4\u7684\u64cd\u4f5c\uff0c\u4f7f\u7528\u5e73\u8861\u6811\u4f18\u5316\u3002<\/p>\n<p>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff08\u4f1a\u5199 Splay \u7684\u53ef\u4ee5\u8d70\u4e86orz\uff09\uff0c\u4f7f\u7528\u65e0\u65cb Treap \u7684\u65f6\u5019\uff0c\u7531\u4e8e\u6709\u533a\u95f4\u64cd\u4f5c\uff0c\u5fc5\u987b\u6309\u7167\u5b50\u6811\u5927\u5c0f <span class=\"lang:default decode:true  crayon-inline\">split()<\/span> \uff0c\u6240\u4ee5\u5728\u627e\u67d0\u4e00\u8282\u70b9\u7684 <code>order<\/code> \u65f6\u4e0d\u80fd\u76f4\u63a5\u5206\u6cbb\u3002\u5176\u5b9e\u53ea\u8981\u5728 <span class=\"lang:default decode:true  crayon-inline \">PushUp()<\/span> \u7684\u65f6\u5019\u987a\u4fbf\u8bb0\u5f55\u4e00\u4e0b\u6bcf\u4e2a\u8282\u70b9\u7684\u7236\u8282\u70b9\uff0c\u7136\u540e\u67e5\u8be2\u7684\u65f6\u5019\u4e0d\u65ad\u5f80\u4e0a\u8df3\uff0c\u82e5\u8fd9\u4e2a\u70b9\u4e3a\u5b83\u7236\u4eb2\u8282\u70b9\u7684\u53f3\u513f\u5b50\u90a3\u4e48\u8bf4\u660e\u5b83\u7684 <code>order<\/code> \u52a0\u4e0a\u5de6\u5b50\u6811\u5927\u5c0f\u52a0 1\u3002\u4e0d\u8981\u5fd8\u4e86 <span class=\"lang:default decode:true  crayon-inline \">PushDown()<\/span> \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;ctime&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\n\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{\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 g1head[105050],g1next[205050],g1node[205050],g1cnt;\r\nint g2head[105050],g2next[205050],g2node[205050],g2cnt;\r\n#define g1insertLine(_s,_t) \\\r\n\tg1node[++g1cnt]=_t,g1next[g1cnt]=g1head[_s],g1head[_s]=g1cnt;\r\n#define g2insertLine(_s,_t) \\\r\n\tg2node[++g2cnt]=_t,g2next[g2cnt]=g2head[_s],g2head[_s]=g2cnt;\r\n\r\nint N;\r\nint a[105050],b[105050],x[105050];\r\nint ansnode[105050],ans[105050];\r\n\r\nunsigned _seed,_ret;\r\n#define rnd() (_ret=_seed,_seed=_seed*7+23,_ret)\r\nint root,cnt,size[105050],lson[105050],rson[105050],val[105050],pri[105050],father[105050];\r\nbool rev[105050];\r\ninline int CreateNode(register int v)\r\n{\r\n\tsize[++cnt]=1;\r\n\tval[cnt]=v;\r\n\tpri[cnt]=rnd();\r\n\treturn cnt;\r\n}\r\n\r\ninline void PushUp(register int x)\r\n{\r\n\tsize[x]=size[lson[x]]+size[rson[x]]+1;\r\n\tfather[lson[x]]=father[rson[x]]=x;\r\n\t(x==root ? father[x]=0 : 0);\r\n}\r\n\r\ninline void PushDown(register int x)\r\n{\r\n\trev[x]^=1;\r\n\tlson[x]^=rson[x]^=lson[x]^=rson[x];\r\n\trev[lson[x]]^=1,rev[rson[x]]^=1;\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\tif(rev[x])\r\n\t\tPushDown(x);\r\n\tif(rev[y])\r\n\t\tPushDown(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\tif(rev[o])\r\n\t\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 void SegmentReverse(register int l,register int r)\r\n{\r\n\tint a=0,b=0,c=0,d=0;\r\n\tSplitTreeByOrder(root,r,a,b);\r\n\tSplitTreeByOrder(a,l-1,c,d);\r\n\trev[d]^=1;\r\n\troot=MergeTree(MergeTree(c,d),b);\r\n}\r\n\r\ninline int OrderOfKey(register int v)\r\n{\r\n\tstatic int stk[105050];\r\n\tregister int top=0;\r\n\tfor(register int x=v;father[x];x=father[x])\r\n\t\tstk[++top]=x;\r\n\tif(rev[root])\r\n\t\tPushDown(root);\r\n\tfor(register int i=top;i&gt;=1;i--)\r\n\t\tif(rev[stk[i]])\r\n\t\t\tPushDown(stk[i]);\r\n\tregister int s=size[lson[v]]+1;\r\n\tfor(register int x=v;father[x];x=father[x])\r\n\t\tif(x == rson[father[x]])\r\n\t\t\ts+=size[lson[father[x]]]+1;\r\n\treturn s;\r\n}\r\n\r\ninline int ValueOfOrder(register int x,register int k)\r\n{\r\n\tif(!x)\r\n\t\treturn -1;\r\n\tif(rev[x])\r\n\t\tPushDown(x);\r\n\tif(k == size[lson[x]]+1)\r\n\t\treturn val[x];\r\n\tif(k &lt;= size[lson[x]])\r\n\t\treturn ValueOfOrder(lson[x],k);\r\n\telse\r\n\t\treturn ValueOfOrder(rson[x],k-size[lson[x]]-1);\r\n}\r\n\r\ninline int BuildTree(register int l,register int r)\r\n{\r\n\tstatic int stk[105050];\r\n\tregister int top=0;\r\n\tfor(register int i=l;i&lt;=r;i++)\r\n\t{\r\n\t\tregister int x=CreateNode(i),last=0;\r\n\t\twhile(top &amp;&amp; pri[stk[top]] &gt; pri[x])\r\n\t\t\tPushUp(stk[top]),last=stk[top],stk[top--]=0;\r\n\t\tif(top)\r\n\t\t\trson[stk[top]]=x;\r\n\t\tlson[x]=last,stk[++top]=x;\r\n\t}\r\n\twhile(top)\r\n\t\tPushUp(stk[top--]);\r\n\treturn stk[1];\r\n}\r\n\r\nint main()\r\n{\r\nsrand(time(NULL));_seed=(unsigned)rand()*rand();\r\n\tregister int N=getnum(),M=getnum(),Q=getnum();\r\n\t::N=N;\r\n\tfor(register int i=1;i&lt;=M;i++)\r\n\t\ta[i]=getnum(),b[i]=getnum();\r\n\tfor(register int i=1;i&lt;=Q;i++)\r\n\t{\r\n\t\tx[i]=getnum();\r\n\t\tregister int l=getnum(),r=getnum();\r\n\t\tg1insertLine(l,i);g2insertLine(r,i);\r\n\t}\r\n\t\r\n\troot=BuildTree(1,N);\r\n\t\/\/printf(\"%d\\n\",0);\r\n\t\/\/printf(\"%d %d %d %d %d\\n\",ValueOfOrder(root,1),ValueOfOrder(root,2),ValueOfOrder(root,3),ValueOfOrder(root,4),ValueOfOrder(root,5));\r\n\t\/\/printf(\"pos: %d %d %d %d %d\\n\",OrderOfKey(1),OrderOfKey(2),OrderOfKey(3),OrderOfKey(4),OrderOfKey(5));\r\n\tfor(register int i=1;i&lt;=M;i++)\r\n\t{\r\n\t\tfor(register int j=g1head[i];j;j=g1next[j])\r\n\t\t\tansnode[j]=ValueOfOrder(root,x[g1node[j]]);\r\n\t\tSegmentReverse(a[i],b[i]);\r\n\t\t\/\/printf(\"%d\\n\",i);\r\n\t\t\/\/printf(\"%d %d %d %d %d\\n\",ValueOfOrder(root,1),ValueOfOrder(root,2),ValueOfOrder(root,3),ValueOfOrder(root,4),ValueOfOrder(root,5));\r\n\t\t\/\/printf(\"pos: %d %d %d %d %d\\n\",OrderOfKey(1),OrderOfKey(2),OrderOfKey(3),OrderOfKey(4),OrderOfKey(5));\r\n\t\tfor(register int j=g2head[i];j;j=g2next[j])\r\n\t\t\tans[g2node[j]]=OrderOfKey(ansnode[g2node[j]]);\r\n\t}\r\n\tfor(register int i=1;i&lt;=Q;i++)\r\n\t\tprintf(\"%d\\n\",ans[i]);\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 P3367 \u9b54\u672f\u5e3d\u6e38\u620f \u65f6\u95f4\u9650\u5236\uff1a1000MS\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0 \u00a0 \u5185\u5b58\u9650\u5236 &hellip; <a 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