{"id":1063,"date":"2019-05-11T13:22:16","date_gmt":"2019-05-11T05:22:16","guid":{"rendered":"https:\/\/mnihyc.com\/blog\/?p=1063"},"modified":"2020-02-09T02:57:07","modified_gmt":"2020-02-08T18:57:07","slug":"yzoj-p3361-%e6%a0%a1%e5%86%85%e8%ae%ad%e7%bb%8320171117%e6%95%b0%e7%82%b9%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/mnihyc.com\/blog\/archives\/1063","title":{"rendered":"YZOJ P3361 [\u6821\u5185\u8bad\u7ec320171117]\u6570\u70b9\u95ee\u9898"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P3361 [\u6821\u5185\u8bad\u7ec320171117]\u6570\u70b9\u95ee\u9898<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a2000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB<\/p>\n<p style=\"text-align: center;\">\u51fa\u9898\u4eba\uff1a<code>zzx<\/code> \u00a0\u00a0\u00a0\u00a0 \u96be\u5ea6\uff1a<span style=\"color: #ff6600;\">\\(6.0\\)<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\\(k\\) \u7ef4\u7a7a\u95f4\u5185\u6709\u4e24\u4e2a\u70b9\u96c6 \\(A=\\{X_1,X_2,\\ldots,X_m\\}\\)\uff0c\\(B=\\{Y_1,Y_2,\\ldots,Y_n\\}\\)\uff0c\u6bcf\u4e2a\u70b9\u7684\u5750\u6807\u662f\u4e00\u4e2a \\(k\\) \u5143\u7ec4 \\((x_1,x_2,\\ldots,x_k)\\)\u3002\u6211\u4eec\u79f0\u70b9 \\(X(x_1,x_2,\\ldots,x_k)\\) \u63a7\u5236\u70b9 \\(Y(y_1,y_2,\\ldots,y_k)\\) \u5f53\u4e14\u4ec5\u5f53 \\(\\forall 1\\le i\\le k,x_i&gt;y_i\\)\uff0c\u8bb0\u4e3a \\(X&gt;Y\\)\u3002\u6570\u70b9\u95ee\u9898\u662f\u8981\u6c42\u8ba1\u7b97\u70b9 \\(X_i\\) \u80fd\u63a7\u5236 \\(B\\) \u4e2d\u7684\u70b9\u6570 \\(c_i\\)\uff0c\u5373 \\(c_i=\\left| \\{Y \\in B\\ |\\ X_i &gt; Y\\} \\right|\\)\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u7f16\u7a0b\u4efb\u52a1<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u70b9\u96c6 \\(A\\) \u548c \\(B\\)\uff0c\u6c42\u51fa\u5bf9\u4e8e\u6240\u6709 \\(1\\le i\\le m\\) \u7684 \\(c_i\\) \u7684\u503c\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\u6b63\u6574\u6570\\(m\\)\u3001\\(n\\) \u548c \\(k\\)\uff0c\u5206\u522b\u8868\u793a\u96c6\u5408 \\(A\\) \u548c \\(B\\) \u7684\u57fa\u6570\u53ca\u7ef4\u6570\u3002\u63a5\u4e0b\u6765\u7684 \\(m+n\\) \u884c\u4f9d\u6b21\u7ed9\u51fa\u70b9 \\(X_1 , X_2 ,\\ldots, X_m ,Y_1 ,Y_2 ,\\ldots,Y_n\\)\uff0c\u6bcf\u4e2a\u70b9\u7684\u5750\u6807\u7528\u4e00\u884c \\(k\\) \u4e2a\u6574\u6570 \\(x_1 , x_2 ,\\ldots, x_k\\) \u63cf\u8ff0\uff0c\u6240\u6709\u5750\u6807\u5728 \\(int\\) \u8303\u56f4\u5185\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5c06\u8ba1\u7b97\u51fa\u7684 \\(c_1 ,c_2 ,\\ldots,c_m\\) \u4f9d\u6b21\u8f93\u51fa\u5230\u6587\u4ef6\u4e2d\uff0c\u6bcf\u4e2a \\(c_i\\) \u8f93\u51fa \\(1\\) \u884c\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u5165<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">3 3 2\r\n4 6\r\n3 3\r\n6 4\r\n1 1\r\n2 5\r\n5 2<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">2\r\n1\r\n2<\/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\u6570\u636e\u70b9 \\(1\\)\uff0c\\(n,m\\le 200,000\\)\uff0c\\(k=1\\)<\/p>\n<p>\u5bf9\u4e8e\u6570\u636e\u70b9 \\(2\\)\u3001\\(3\\)\u3001\\(4\\)\uff0c\\(n,m\\le 150,000\\)\uff0c\\(k=2\\)<\/p>\n<p>\u5bf9\u4e8e\u6570\u636e\u70b9 \\(5\\)\u3001\\(6\\)\u3001\\(7\\)\uff0c\\(n,m\\le 100,000\\)\uff0c\\(k=3\\)<\/p>\n<p>\u5bf9\u4e8e\u6570\u636e\u70b9 \\(8\\)\u3001\\(9\\)\u3001\\(10\\)\uff0c\\(n,m\\le 20,000\\)\uff0c\\(k\\le 10\\)<\/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><del>\u6076\u5fc3\u7684<\/del>\u56db\u5408\u4e00\u597d\u9898\uff1f<\/p>\n<p>\u9898\u610f\u5c31\u662f\u8981\u6c42 \\(k\\) \u7ef4\u504f\u5e8f\u7684\u4e2a\u6570\u3002<\/p>\n<p>\u5bf9\u4e8e \\(k=1\\) \u7684\u70b9\uff0c\u76f4\u63a5 <span class=\"lang:default decode:true  crayon-inline \">std::sort()<\/span> \u548c<span class=\"lang:default decode:true  crayon-inline \">std::upper_bound()<\/span> \u3002<\/p>\n<p>\u5bf9\u4e8e \\(k=2\\) \u7684\u70b9\uff0c\u5c31\u662f\u7ecf\u5178\u7684\u4e8c\u7ef4\u504f\u5e8f\uff0c\u6811\u72b6\u6570\u7ec4\u89e3\u51b3\u3002<\/p>\n<p>\u5bf9\u4e8e \\(k=3\\) \u7684\u70b9\uff0c\u5c31\u662f\u7ecf\u5178\u7684\u4e09\u7ef4\u504f\u5e8f\uff0cCDQ\u5206\u6cbb\u89e3\u51b3\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1064\" src=\"https:\/\/mnihyc.com\/blog\/wp-content\/uploads\/2019\/05\/QQ\u622a\u56fe20190511131700.png\" alt=\"\" width=\"651\" height=\"302\" srcset=\"https:\/\/mnihyc.com\/blog\/wp-content\/uploads\/2019\/05\/QQ\u622a\u56fe20190511131700.png 651w, https:\/\/mnihyc.com\/blog\/wp-content\/uploads\/2019\/05\/QQ\u622a\u56fe20190511131700-300x139.png 300w\" sizes=\"auto, (max-width: 651px) 100vw, 651px\" \/><\/p>\n<p>\u4e8e\u662f\u5c31\u53ea\u80fd\u8003\u8651\u5176\u4ed6\u7b97\u6cd5\u3002<\/p>\n<p>\u53d1\u73b0 \\(n\\) \u53d8\u5c0f\u4e86\uff0c\u6240\u4ee5\u53ef\u4ee5\u8003\u8651\u5e73\u65b9\u7ea7\u522b\u7684\u7b97\u6cd5\u3002<\/p>\n<p>\u66b4\u529b\u679a\u4e3e\u6240\u6709\u7684\u7ef4\u5ea6\uff0c\u6309\u8be5\u7ef4\u5ea6\u6392\u5e8f\uff0c\u8fd9\u6837\u6bcf\u4e2a\u8be2\u95ee\u70b9\u6240\u80fd\u63a7\u5236\u7684\u70b9\u5c31\u53ef\u4ee5\u7528\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u4e8c\u8fdb\u5236\u6570\u8868\u793a\uff0c\u6700\u540e\u5bf9\u4e8e\u6bcf\u4e2a\u8be2\u95ee\u70b9\u628a\u5b83\u5728\u6bcf\u4e2a\u7ef4\u5ea6\u4e0b\u80fd\u63a7\u5236\u7684\u70b9\u6c42\u4ea4\u96c6\uff0c\u7b54\u6848\u5c31\u662f\u4e8c\u8fdb\u5236\u6570\u4e0a \\(1\\) \u7684\u4e2a\u6570\u3002<\/p>\n<p>\u6ce8\u610f\u5230 \\(n^2k \\approx 4 \\times 10^9\\) \u65e0\u6cd5\u901a\u8fc7\u672c\u9898\u3002<\/p>\n<p>\u4e8e\u662f\uff0c\u56e0\u4e3a\u662f\u4e8c\u8fdb\u5236\uff0c\u6240\u4ee5\u4f7f\u7528 <span class=\"lang:default decode:true  crayon-inline \">std::bitset<\/span> \u4f18\u5316\u3002<\/p>\n<p>\u590d\u6742\u5ea6 \\(O(\\frac{n^2k}{\\omega} \\approx 10^8)\\) \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;bitset&gt;\r\n#include &lt;algorithm&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\ninline int getnum()\r\n{\r\n\tregister char c=0;\r\n\tregister bool neg=false;\r\n\twhile(!(c&gt;='0' &amp;&amp; c&lt;='9'))\r\n\t\tc=getchar(),neg|=(c=='-');\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 (neg?-1:1)*a;\r\n}\r\n\r\ninline void PrintNum(register int a)\r\n{\r\n\tstatic int buf[32];buf[0]=0;\r\n\tregister int lb=0;\r\n\twhile(a&gt;9)\r\n\t\tbuf[++lb]=a%10,a\/=10;\r\n\tbuf[++lb]=a;\r\n\tfor(register int i=lb;i&gt;=1;i--)\r\n\t\tputchar('0'+buf[i]);\r\n\tputchar('\\n');\r\n}\r\n\r\nint M,N,K;\r\nint x[10][200001],_y[10][200001],y[10][200001],yb[10][451];\r\nint idx[10][200001];\r\n\r\nint _k;\r\nstruct _comp\r\n{\r\n\tbool operator ()(const int&amp;a,const int&amp;b)const\r\n\t{\r\n\t\tif(_y[_k][a]!=_y[_k][b])\r\n\t\t\treturn _y[_k][a]&lt;_y[_k][b];\r\n\t\treturn a&lt;b;\r\n\t}\r\n};\r\n\r\nint f[305050];\r\n#define _lowbit(_o_) ((_o_)&amp;-(_o_))\r\ninline void update(register int o,const int&amp;val)\r\n{\r\n\twhile(o&lt;=N+M)\r\n\t{\r\n\t\tf[o]+=val;\r\n\t\to+=_lowbit(o);\r\n\t}\r\n}\r\n\r\ninline int query(register int o)\r\n{\r\n\tregister int ans=0;\r\n\twhile(o)\r\n\t{\r\n\t\tans+=f[o];\r\n\t\to-=_lowbit(o);\r\n\t}\r\n\treturn ans;\r\n}\r\n\r\nstruct _res\r\n{\r\n\tint y1,y2,y3,idx;\r\n\tbool operator &lt; (const _res&amp;o)const\r\n\t{\r\n\t\tif(y1!=o.y1)\r\n\t\t\treturn y1&lt;o.y1;\r\n\t\treturn idx&gt;o.idx;\r\n\t}\r\n}res[305050],tres[305050];\r\n\r\nstruct _compy2\r\n{\r\n\tbool operator()(const _res&amp;a,const _res&amp;b)const\r\n\t{\r\n\t\tif(a.y2!=b.y2)\r\n\t\t\treturn a.y2&lt;b.y2;\r\n\t\treturn a.idx&gt;b.idx;\r\n\t}\r\n};\r\n\r\nint ans[155050];\r\nvoid CDQ_Divide(register int l,register int r)\r\n{\r\n\tif(l==r)\r\n\t\treturn;\r\n\tregister int mid=(l+r)&gt;&gt;1,tl=l,tr=mid+1;\r\n\t\r\n\tCDQ_Divide(l,mid),CDQ_Divide(mid+1,r);\r\n\t\r\n\tregister int j=l;\r\n\tfor(register int i=mid+1;i&lt;=r;i++)\r\n\t{\r\n\t\twhile(j&lt;=mid &amp;&amp; res[j].y3&lt;res[i].y3)\r\n\t\t{\r\n\t\t\tif(!res[j].idx)\r\n\t\t\t\tupdate(res[j].y2,1);\r\n\t\t\tj++;\r\n\t\t}\r\n\t\tif(res[i].idx)\r\n\t\t\tans[res[i].idx]+=query(res[i].y2-1);\r\n\t}\r\n\tfor(register int i=l;i&lt;j;i++)\r\n\t\tif(!res[i].idx)\r\n\t\t\tupdate(res[i].y2,-1);\r\n\t\r\n\tfor(register int i=l;i&lt;=r;i++)\r\n\t\tif(tr&gt;r || (tl&lt;=mid &amp;&amp; res[tl].y3&lt;res[tr].y3))\r\n\t\t\ttres[i]=res[tl++];\r\n\t\telse\r\n\t\t\ttres[i]=res[tr++];\r\n\tfor(register int i=l;i&lt;=r;i++)\r\n\t\tres[i]=tres[i];\r\n}\r\n\r\ninline void PreAKT()\r\n{\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tres[i]=(_res){y[0][i],y[1][i],y[2][i],0};\r\n\tfor(register int i=1;i&lt;=M;i++)\r\n\t\tres[N+i]=(_res){x[0][i],x[1][i],x[2][i],i};\r\n\tstd::sort(&amp;res[1],&amp;res[N+M+1],_compy2());\r\n\tregister int ly2=0;\r\n\tfor(register int i=1;i&lt;=N+M;i++)\r\n\t\tif(res[i].y2 != res[i-1].y2)\r\n\t\t\tres[i].y2=++ly2;\r\n\t\telse\r\n\t\t\tres[i].y2=res[i-1].y2;\r\n\tstd::sort(&amp;res[1],&amp;res[N+M+1]);\r\n}\r\n\r\n\/\/ \r\n#pragma GCC optimize(3)\r\n__attribute__((optimize(\"-O3\"))) int main()\r\n{\r\n\tM=getnum(),N=getnum(),K=getnum();\r\n\tfor(register int i=1;i&lt;=M;i++)\r\n\t\tfor(register int k=0;k&lt;K;k++)\r\n\t\t\tx[k][i]=getnum();\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tfor(register int k=0;k&lt;K;k++)\r\n\t\t\ty[k][i]=_y[k][i]=getnum();\r\n\t\r\n\tif(N&gt;20000)\r\n\t\tif(N&gt;100000)\r\n\t\t\tif(N&gt;150000)\r\n\t\t\t{\r\n\t\t\t\tstd::sort(&amp;y[0][1],&amp;y[0][N+1]);\r\n\t\t\t\tfor(register int i=1;i&lt;=M;i++)\r\n\t\t\t\t\tif(x[0][i]-1&lt;y[0][1])\r\n\t\t\t\t\t\tPrintNum(0);\r\n\t\t\t\t\telse\r\n\t\t\t\t\t\tPrintNum(std::upper_bound(&amp;y[0][1],&amp;y[0][N+1],x[0][i]-1)-&amp;y[0][1]);\r\n\t\t\t}\r\n\t\t\telse\r\n\t\t\t{\r\n\t\t\t\tPreAKT();\r\n\t\t\t\tregister int j=1;\r\n\t\t\t\tfor(register int i=1;i&lt;=N+M;i++)\r\n\t\t\t\t{\r\n\t\t\t\t\tif(!res[i].idx)\r\n\t\t\t\t\t\tcontinue;\r\n\t\t\t\t\twhile(j&lt;=N+M &amp;&amp; res[j].y1&lt;res[i].y1)\r\n\t\t\t\t\t{\r\n\t\t\t\t\t\tif(!res[j].idx)\r\n\t\t\t\t\t\t\tupdate(res[j].y2,1);\r\n\t\t\t\t\t\tj++;\r\n\t\t\t\t\t}\r\n\t\t\t\t\tans[res[i].idx]=query(res[i].y2-1);\r\n\t\t\t\t}\r\n\t\t\t\tfor(register int i=1;i&lt;=M;i++)\r\n\t\t\t\t\tPrintNum(ans[i]);\r\n\t\t\t}\r\n\t\telse\r\n\t\t{\r\n\t\t\tPreAKT();\r\n\t\t\tCDQ_Divide(1,N+M);\r\n\t\t\tfor(register int i=1;i&lt;=M;i++)\r\n\t\t\t\tPrintNum(ans[i]);\r\n\t\t}\r\n\telse\r\n\t{\r\n\t\tregister int BlockSize=__builtin_sqrt(N),BlockNum=N\/BlockSize+(N%BlockSize!=0);\r\n\t\tstatic int _bpos[105050],_bleft[350],_bright[350];\r\n\t\t#define GetBlockPos(_p_) (_bpos[_p_])\r\n\t\t#define GetBlockLeft(_w_) (_bleft[_w_])\r\n\t\t#define GetBlockRight(_w_) (_bright[_w_])\r\n\t\t_bleft[1]=1,_bright[BlockNum]=N;\r\n\t\tfor(register int i=1,tb=1;i&lt;=N+1;i++)\r\n\t\t{\r\n\t\t\t_bpos[i]=tb;\r\n\t\t\tif(i%BlockSize == 0)\r\n\t\t\t\t_bright[tb++]=i,_bleft[tb]=i+1;\r\n\t\t}\r\n\t\t_bpos[0]=1,_bleft[0]=N+1,_bright[BlockNum+1]=-1;\r\n\t\t\r\n\t\tstatic std::bitset&lt;20001&gt;ans[10][151];\r\n\t\tstatic std::bitset&lt;20001&gt;tans,tsans;\r\n\t\tfor(register int k=0;k&lt;K;k++)\r\n\t\t{\r\n\t\t\tfor(register int i=1;i&lt;=N;i++)\r\n\t\t\t\tidx[k][i]=i;\r\n\t\t\t_k=k,std::sort(&amp;idx[k][1],&amp;idx[k][N+1],_comp());\r\n\t\t\tans[k][0].reset(),ans[k][1].reset();\r\n\t\t\tfor(register int i=1;i&lt;=N;i++)\r\n\t\t\t{\r\n\t\t\t\ty[k][i]=_y[k][idx[k][i]];\r\n\t\t\t\tregister int tbi=GetBlockPos(i),tbp=GetBlockPos(i-1);\r\n\t\t\t\tyb[k][tbi]=_y[k][idx[k][i]];\r\n\t\t\t\tif(tbi != tbp)\r\n\t\t\t\t\tans[k][tbi]=ans[k][tbp];\r\n\t\t\t\tans[k][tbi].set(idx[k][i]);\r\n\t\t\t}\r\n\t\t}\r\n\t\t\r\n\t\tfor(register int j=1;j&lt;=M;j++)\r\n\t\t{\r\n\t\t\tfor(register int k=0;k&lt;K;k++)\r\n\t\t\t{\r\n\t\t\t\tregister int tbpos=std::upper_bound(&amp;yb[k][1],&amp;yb[k][BlockNum+1],x[k][j]-1)-&amp;yb[k][0];\r\n\t\t\t\ttsans=ans[k][tbpos-1];\r\n\t\t\t\tregister int lpos=GetBlockLeft(tbpos),rpos=GetBlockRight(tbpos);\r\n\t\t\t\tfor(register int i=lpos;y[k][i]&lt;x[k][j] &amp;&amp; i&lt;=rpos;i++)\r\n\t\t\t\t\ttsans.set(idx[k][i]);\r\n\t\t\t\tif(!k)\r\n\t\t\t\t\ttans=tsans;\r\n\t\t\t\telse\r\n\t\t\t\t\ttans&amp;=tsans;\r\n\t\t\t}\r\n\t\t\tPrintNum(tans.count());\r\n\t\t}\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 P3361 [\u6821\u5185\u8bad\u7ec320171117]\u6570\u70b9\u95ee\u9898 \u65f6\u95f4\u9650\u5236\uff1a2000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262 &hellip; <a href=\"https:\/\/mnihyc.com\/blog\/archives\/1063\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P3361 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