{"id":1045,"date":"2019-03-23T16:57:55","date_gmt":"2019-03-23T08:57:55","guid":{"rendered":"https:\/\/0.mnihyc.com\/blog\/?p=1045"},"modified":"2020-02-09T03:00:05","modified_gmt":"2020-02-08T19:00:05","slug":"yzoj-p3846-2018%e7%9c%81%e9%98%9f%e9%9b%86%e8%ae%adyist","status":"publish","type":"post","link":"https:\/\/0.mnihyc.com\/blog\/archives\/1045","title":{"rendered":"YZOJ P3846 [2018\u7701\u961f\u96c6\u8bad]Yist"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P3846 [2018\u7701\u961f\u96c6\u8bad]Yist<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a1000MS \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>\u6709\u4e00\u4e2a \\(n\\) \u4e2a\u70b9 \\(m\\) \u6761\u8fb9\u7684\u65e0\u5411\u56fe\uff0c\u7ed3\u70b9\u4ece \\(1\\) \u5230 \\(n\\) \u6807\u53f7\uff0c\u70b9 \\(u\\) \u7684\u521d\u59cb\u6743\u503c\u4e3a \\(w_u\\)\u3002\u4f60\u53ef\u4ee5\u5bf9\u4efb\u610f\u7ed3\u70b9 \\(u\\) \u8fdb\u884c\u64cd\u4f5c\uff0c\u5c06\u4f60\u7684\u5f97\u5206\uff08\u521d\u59cb\u4e3a \\(0\\)\uff09\u52a0\u4e0a \\(\\sum_\\limits{(u,v) \\in E}w_v\\) \uff0c\u5e76\u5c06 \\(w_u\\) \u9664\u4ee5 \\(2\\) \u3002<\/p>\n<p>\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(k\\) \u7684\u7ed3\u70b9\u5e8f\u5217 \\(s_1,s_2,\\cdots,s_k\\) \uff08\\(1 \\leq s_i \\leq n\\)\uff09\uff0c\u5728\u4e00\u8f6e\u64cd\u4f5c\u4e2d\uff0c\u4f60\u9700\u8981\u4f9d\u6b21\u5bf9 \\(s_1,s_2,\\cdots,s_k\\) \u8fdb\u884c\u64cd\u4f5c\u3002\u4f60\u60f3\u77e5\u9053\uff0c\u5728\u8fdb\u884c\u4e86\u65e0\u9650\u8f6e\u64cd\u4f5c\u540e\uff0c\u4f60\u5f97\u5206\u7684\u6781\u9650\u662f\u591a\u5c11\u3002<\/p>\n<p>\u663e\u7136\u7b54\u6848\u4e00\u5b9a\u53ef\u4ee5\u8868\u793a\u6210 \\(P\/Q\\) \u7684\u5f62\u5f0f\uff0c\u4f60\u9700\u8981\u8f93\u51fa \\(P \\times Q^{-1}\\) \u5728\u6a21 \\(998244353\\) \u610f\u4e49\u4e0b\u7684\u503c\u3002\u7279\u522b\u7684\uff0c\u5982\u679c\u5f97\u5206\u5e76\u4e0d\u6536\u655b\uff0c\u8f93\u51fa \\(-1\\) \u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u672c\u9898\u6709\u591a\u7ec4\u6570\u636e\uff0c\u8bf7\u8bfb\u5165\u5230\u6587\u4ef6\u7ed3\u675f\u3002<\/p>\n<p>\u5bf9\u4e8e\u6bcf\u7ec4\u6570\u636e\uff0c\u7b2c\u4e00\u884c\u4e09\u4e2a\u6574\u6570 \\(n,m,k\\) \uff0c\u542b\u4e49\u5982\u9898\u6240\u8ff0\u3002<\/p>\n<p>\u7b2c\u4e8c\u884c \\(n\\) \u4e2a\u6574\u6570 \\(w_1,w_2,\\cdots,w_n\\)\uff0c\u8868\u793a\u7ed3\u70b9\u7684\u521d\u59cb\u6743\u503c\u3002<\/p>\n<p>\u7b2c\u4e09\u884c \\(k\\) \u4e2a\u6b63\u6574\u6570 \\(s_1,s_2,\\cdots,s_k\\) \u3002<\/p>\n<p>\u63a5\u4e0b\u6765 \\(m\\) \u884c\uff0c\u6bcf\u884c\u4e24\u4e2a\u6574\u6570 \\(u,v\\)\uff0c\u63cf\u8ff0\u4e86\u4e00\u6761\u65e0\u5411\u8fb9\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\u6570\u636e\uff0c\u8f93\u51fa\u4e00\u884c\u4e00\u4e2a\u6574\u6570\uff0c\u8868\u793a\u7b54\u6848\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u5165<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">4 3 4\r\n1 1 1 1\r\n1 2 3 4\r\n1 2\r\n2 3\r\n1 3<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">9<\/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 \\(20\\%\\) \u7684\u6570\u636e\uff0c\\(n,m \\leq 5\\)\uff0c\\(k \\leq 10\\)\uff1b<\/p>\n<p>\u5bf9\u4e8e \\(40\\%\\) \u7684\u6570\u636e\uff0c\\(n,m \\leq 1000\\)\uff0c\\(k \\leq 2000\\)\uff1b<\/p>\n<p>\u5bf9\u4e8e\u53e6\u5916 \\(20\\%\\) \u7684\u6570\u636e\uff0c\u6570\u636e\u4e3a\u968f\u673a\u751f\u6210\uff1b<\/p>\n<p>\u5bf9\u4e8e \\(100\\%\\) \u7684\u6570\u636e\uff0c\\(1 \\leq n,m \\leq 10^5\\)\uff0c\\(1 \\leq k \\leq 2 \\times 10^5\\)\uff0c \\(1 \\leq s_i \\leq n, 0 \\leq w_i &lt; 998244353\\)\uff0c\u4fdd\u8bc1\u539f\u56fe\u6ca1\u6709\u91cd\u8fb9\u548c\u81ea\u73af\uff0c\u6570\u636e\u7ec4\u6570\u4e0d\u8d85\u8fc7 \\(3\\) \u7ec4\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>\u8003\u573a\u4e0a\u60f3\uff1a\u8fd9\u4e0d\u662f\u7b80\u5355\u7684\u6781\u9650\u5417\uff1f\u7b54\u6848 \\(\\times 2 \\) \u4e0d\u5c31\u597d\u4e86\uff1f\\(60pts\\) \u5230\u624b\u4e86\uff01\u7136\u540e\u5c31\u7206\u96f6\u4e86\uff0c\u56e0\u4e3a \\(s_k\\) \u4e2d\u6709\u7684\u70b9\u662f\u91cd\u590d\u7684\u3002<\/p>\n<p>\u8003\u8651\u6bcf\u4e2a\u70b9\u5728\u7b2c\u4e00\u8f6e\u4e2d\u5bf9\u7b54\u6848\u7684\u8d21\u732e \\(sum\\)\uff0c\u82e5\u5b83\u5728 \\(s\\) \u4e2d\u51fa\u73b0 \\(cnt\\) \u6b21\uff0c\u90a3\u4e48\u5728\u7b2c\u4e8c\u8f6e\u4e2d\u8be5\u70b9\u5bf9\u7b54\u6848\u7684\u8d21\u732e\u4e3a \\(sum \\cdot 2^{-cnt}\\)\uff0c\u7b2c\u4e09\u8f6e\u4e2d\u4e3a \\(sum \\cdot 2^{-2cnt}\\)\uff0c\\(\\cdots\\)\uff0c\u7b2c \\(n\\) \u8f6e\u4e2d\u4e3a \\(sum \\cdot 2^{-(n-1)cnt}\\) \u3002<\/p>\n<p>\u90a3\u4e48\u505a\u65e0\u9650\u8f6e\u540e\uff0c\u5b83\u5bf9\u7b54\u6848\u7684\u8d21\u732e\u5c31\u662f\uff1a \\(sum \\cdot \\sum_\\limits{i=0}^{\\infty} {2^{-cnt}}^i = sum \\cdot \\frac{2^{cnt}}{2^{cnt}-1}\\) \u3002<\/p>\n<p>\u5173\u4e8e\u6536\u655b\u6027\u7684\u95ee\u9898\uff1a\u662f\u5426\u5b58\u5728\u4e00\u6761\u8fb9 \\((u,v)\\)\uff0c\u5176\u4e2d \\(u \\in s,v \\notin s\\) \u4e14 \\(w_v &gt; 0\\) \u3002\u5b58\u5728\u5219\u4e0d\u6536\u655b\uff0c\u5426\u5219\u6536\u655b\u3002<\/p>\n<p>\u73b0\u5728\u5c31\u5269\u5982\u4f55\u6c42\u51fa\u8fd9\u4e2a\u8d21\u732e\u4e86\u3002<\/p>\n<p>\u8003\u8651\u300c\u5c06\u5927\u70b9\u5ea6\u70b9\u7684\u590d\u6742\u5ea6<strong>\u644a\u7ed9<\/strong>\u5c0f\u70b9\u5ea6\u70b9\u300d\u3002<\/p>\n<p>\u600e\u4e48\u5b9e\u73b0\uff1f\u6309\u7167<strong>\u70b9\u5ea6<\/strong>\u5206\u5757\uff08\u62bd\u8c61\u610f\u4e49\u4e0a\u7684\u5206\u5757\uff09\u3002<\/p>\n<p>\u628a\u70b9\u5ea6\u4e0d\u5c0f\u4e8e \\(\\sqrt{N}\\) \u7684\u5206\u6210\u4e00\u5757\uff0c\u5269\u4e0b\u7684\u5206\u6210\u53e6\u5916\u4e00\u5757\uff0c\u8fd8\u662f\u6309\u7167 \\(s_1, s_2, \\cdots, s_k\\) \u7684\u987a\u5e8f \u4e00 \u4e00 \u5904\u7406\u3002<\/p>\n<p>\u505a\u5230\u5176\u4e2d\u7684\u67d0\u4e00\u4e2a\u70b9 \\(s_i\\) \u65f6\uff0c\u628a\u5b83\u8bbe\u4e3a \\(x\\) \uff0c\u73b0\u5728\u8981\u66f4\u65b0\u6240\u6709\u4e0e \\(x\\) \u76f4\u63a5\u76f8\u8fde\u7684\u70b9\u7684\u8d21\u732e\u3002<\/p>\n<p>\u5982\u679c \\(x\\) \u5728\u5757\u5185\u7684\u8bdd\uff0c\u90a3\u4e48\u76f4\u63a5\u66b4\u529b\u66f4\u65b0\u6240\u6709\u4e0e \\(x\\) \u76f8\u8fde\uff0c\u540c\u65f6\u4e5f\u5728\u5757\u5185\u7684\u70b9\u3002\u90a3\u4e48\u5bf9\u4e8e\u90a3\u4e9b\u4e0e \\(x\\) \u76f8\u8fde\uff0c\u540c\u65f6\u5728\u5757\u5916\u7684\u70b9\uff0c\u5982\u679c\u76f4\u63a5\u66b4\u529b\u66f4\u65b0\u7684\u8bdd\uff0c\u5f88\u663e\u7136\u590d\u6742\u5ea6\u5c31\u5f97\u4e0d\u5230\u4fdd\u8bc1\u3002\u6240\u4ee5\u53ef\u4ee5\u6709\u4e00\u4e2a\u7c7b\u4f3c\u4e8e \\(lazy\\_tag\\) \u7684\u601d\u60f3\uff0c\u5c31\u662f\u8bf4\u5f53\u524d\u4e0d\u76f4\u63a5\u66f4\u65b0\u90a3\u4e9b\u5728\u5757\u5916\u7684\u70b9\u3002\u8bbe \\(tag(x)\\) \u8868\u793a\u4e0e \\(x\\) \u76f8\u8fde\uff0c\u5e76\u4e14\u5728\u5757\u5916\u7684\u70b9\u7684\u8d21\u732e<strong>\u8fd8<\/strong>\u9700\u8981\u66f4\u65b0 \\(tag(x)\\) \u7684\u589e\u91cf \u6b21\uff0c\u90a3\u4e48\u53ea\u9700\u4ee4 <span class=\"lang:default decode:true  crayon-inline \">tag[x]++<\/span>\u00a0 \u5373\u53ef\u3002<\/p>\n<p>\u5982\u679c \\(x\\) \u5728\u5757\u5916\u7684\u8bdd\uff08\u70b9\u5ea6\u5c0f\u4e8e \\(\\sqrt{N}\\)\uff09\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u76f4\u63a5\u66b4\u529b\u66f4\u65b0\u6240\u6709\u4e0e \\(x\\) \u76f8\u8fde\u7684\u70b9\u4e86\u3002\u540c\u65f6\uff0c\u5728\u5757\u5916\u7684\u8fd9\u4e2a \\(x\\) \u8fd8\u53ef\u80fd\u4f1a\u6709\u6765\u81ea\u4e0e\u5b83\u76f8\u8fde\uff0c\u5e76\u4e14\u5728\u5757\u5185\u7684\u70b9\u7684\u201c\u8d21\u732e\u4fe1\u606f\u201d\uff08\u4e0a\u8ff0\u7684 \\(tag\\)\uff09\uff0c\u6240\u4ee5\u904d\u5386\u6240\u6709\u4e0e\u5b83\u76f8\u8fde\uff0c\u5e76\u4e14\u5728\u5757\u5185\u7684\u70b9\uff0c\u8ba1\u7b97\u5176\u5bf9\u81ea\u5df1\u7684\u8d21\u732e\u5e76\u4e14\u628a<strong>\u5bf9\u4e8e\u81ea\u5df1\u7684\u589e\u91cf<\/strong>\u6e05\u96f6\u5373\u53ef\u3002<\/p>\n<p>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\\(tag(x)\\) \u8868\u793a \\(x\\) \u5bf9\u5916<strong>\u6240\u6709<\/strong>\u4e0e\u5b83\u76f4\u63a5\u76f8\u8fde\uff0c\u5e76\u4e14\u4e0d\u5728\u5757\u5185\u7684\u70b9\u7684\u8d21\u732e\u4fe1\u606f\uff0c\u6240\u4ee5\u8bb0\u5f55\u589e\u91cf\u65f6<strong>\u4e0d\u80fd<\/strong>\u76f4\u63a5\u5728 \\(tag\\) \u4e0a\u4fee\u6539\uff0c\u5e94<strong>\u5206\u522b\u8bb0\u5f55<\/strong>\u6240\u6709\u8fd9\u4e9b\u70b9\u7684\u589e\u91cf\u3002<\/p>\n<p>\u53ef\u4ee5\u53d1\u73b0\uff0c\u4e0a\u9762\u300c\u4e0e \\(xxx\\) \u76f8\u8fde\uff0c\u5e76\u4e14\u5728\u5757\u5185\u7684\u70b9\u300d\u51fa\u73b0\u4e86\u5f88\u591a\u6b21\uff0c\u6240\u4ee5\u9884\u5904\u7406\u4e00\u4e0b\u5373\u53ef\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\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\n#define MOD 998244353\r\n#define REV2 499122177\r\n\r\ninline int _pow(register int base,register int b)\r\n{\r\n\tregister int ans=1;\r\n\twhile(b)\r\n\t{\r\n\t\tif(b&amp;1)\r\n\t\t\tans=(long long)ans*base%MOD;\r\n\t\tbase=(long long)base*base%MOD;\r\n\t\tb&gt;&gt;=1;\r\n\t}\r\n\treturn ans;\r\n}\r\n\r\nint ghead[105050],gnext[205050],gnode[205050],gcnt;\r\ninline void insertLine(register int s,register int t)\r\n{\r\n\tgnode[++gcnt]=t,gnext[gcnt]=ghead[s],ghead[s]=gcnt;\r\n\tgnode[++gcnt]=s,gnext[gcnt]=ghead[t],ghead[t]=gcnt;\r\n}\r\n\r\nint w[105050],s[205050],scnt[105050];\r\nint bs,d[105050],tag[105050],ans[105050];\r\n\r\nint ehead[105050],enext[205050],enode[205050],etag[205050],ecnt;\r\ninline void einsertLine(register int s,register int t,const int&amp;v)\r\n{\r\n\tenode[++ecnt]=t,enext[ecnt]=ehead[s],ehead[s]=ecnt,etag[ecnt]=v;\r\n}\r\n\r\nint main()\r\n{\r\nint N;\r\nwhile(~scanf(\"%d\",&amp;N))\r\n{\r\n\tmemset(d,0,sizeof(d)),memset(tag,0,sizeof(tag)),memset(ans,0,sizeof(ans)),memset(scnt,0,sizeof(scnt));\r\n\tgcnt=0,memset(ghead,0,sizeof(ghead));\r\n\tregister int M=getnum(),K=getnum();\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tw[i]=getnum();\r\n\tfor(register int k=1;k&lt;=K;k++)\r\n\t\tscnt[s[k]=getnum()]++;\r\n\tregister bool suc=true;\r\n\tfor(register int i=1;i&lt;=M;i++)\r\n\t{\r\n\t\tregister int u=getnum(),v=getnum();\r\n\t\tinsertLine(u,v);\r\n\t\td[u]++,d[v]++;\r\n\t\tif((scnt[u]&amp;&amp;!scnt[v]&amp;&amp;w[v]) || (scnt[v]&amp;&amp;!scnt[u]&amp;&amp;w[u]))\r\n\t\t\tsuc=false;\r\n\t}\r\n\tif(!suc)\r\n\t{\r\n\t\tprintf(\"%d\\n\",-1);\r\n\t\tcontinue;\r\n\t}\r\n\t\r\n\tbs=__builtin_sqrt(N);\r\n\tecnt=0,memset(ehead,0,sizeof(ehead));\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tfor(register int j=ghead[i];j;j=gnext[j])\r\n\t\t\tif(d[gnode[j]] &gt;= bs)\r\n\t\t\t\teinsertLine(i,gnode[j],0);\r\n\tfor(register int k=1;k&lt;=K;k++)\r\n\t{\r\n\t\tregister int x=s[k];\r\n\t\tif(d[x] &gt;= bs)\r\n\t\t{\r\n\t\t\ttag[x]++;\r\n\t\t\tfor(register int j=ehead[x];j;j=enext[j])\r\n\t\t\t\t((ans[enode[j]]+=w[enode[j]]) &gt;= MOD ? ans[enode[j]]-=MOD : 0);\r\n\t\t}\r\n\t\telse\r\n\t\t{\r\n\t\t\tfor(register int j=ghead[x];j;j=gnext[j])\r\n\t\t\t\t((ans[gnode[j]]+=w[gnode[j]]) &gt;= MOD ? ans[gnode[j]]-=MOD : 0);\r\n\t\t\tfor(register int j=ehead[x];j;j=enext[j])\r\n\t\t\t{\r\n\t\t\t\tans[x]=(ans[x]+(long long)w[x]*(tag[enode[j]]-etag[j])%MOD)%MOD;\r\n\t\t\t\tetag[j]=tag[enode[j]];\r\n\t\t\t}\r\n\t\t}\r\n\t\tw[x]=(long long)w[x]*REV2%MOD;\r\n\t}\r\n\t\r\n\tregister int tans=0;\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t{\r\n\t\tif(!(d[i] &gt;= bs))\r\n\t\t\tfor(register int j=ehead[i];j;j=enext[j])\r\n\t\t\t{\r\n\t\t\t\tans[i]=(ans[i]+(long long)w[i]*(tag[enode[j]]-etag[j])%MOD)%MOD;\r\n\t\t\t\tetag[j]=tag[enode[j]];\r\n\t\t\t}\r\n\t\tregister int tcnt=_pow(2,scnt[i]);\r\n\t\ttans=(tans+(long long)ans[i]*tcnt%MOD*_pow(tcnt-1,MOD-2))%MOD;\r\n\t}\r\n\tprintf(\"%d\\n\",tans);\r\n}\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 P3846 [2018\u7701\u961f\u96c6\u8bad]Yist \u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a524288K &hellip; <a href=\"https:\/\/0.mnihyc.com\/blog\/archives\/1045\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P3846 [2018\u7701\u961f\u96c6\u8bad]Yist<\/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":[37,68,72],"tags":[],"class_list":["post-1045","post","type-post","status-publish","format-standard","hentry","category-crazya","category-divideblock","category-expect"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - 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