{"id":1151,"date":"2019-05-25T19:02:49","date_gmt":"2019-05-25T11:02:49","guid":{"rendered":"https:\/\/cf.mnihyc.com\/blog\/?p=1151"},"modified":"2020-04-22T11:40:00","modified_gmt":"2020-04-22T03:40:00","slug":"yzoj-p3195-noi2017%e6%b8%b8%e6%88%8f","status":"publish","type":"post","link":"https:\/\/cf.mnihyc.com\/blog\/archives\/1151","title":{"rendered":"YZOJ P3195 [NOI2017]\u6e38\u620f"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P3195 [NOI2017]\u6e38\u620f<\/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;\">\\(6.4\\)<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5c0f L \u8ba1\u5212\u8fdb\u884c \\(n\\) \u573a\u6e38\u620f\uff0c\u6bcf\u573a\u6e38\u620f\u4f7f\u7528\u4e00\u5f20\u5730\u56fe\uff0c\u5c0f L \u4f1a\u9009\u62e9\u4e00\u8f86\u8f66\u5728\u8be5\u5730\u56fe\u4e0a\u5b8c\u6210\u6e38\u620f\u3002<\/p>\n<p>\u5c0f L \u7684\u8d5b\u8f66\u6709\u4e09\u8f86\uff0c\u5206\u522b\u7528\u5927\u5199\u5b57\u6bcd \\(A\\)\u3001\\(B\\)\u3001\\(C\\) \u8868\u793a\u3002\u5730\u56fe\u4e00\u5171\u6709\u56db\u79cd\uff0c\u5206\u522b\u7528\u5c0f\u5199\u5b57\u6bcd \\(x\\)\u3001\\(a\\)\u3001\\(b\\)\u3001\\(c\\) \u8868\u793a\u3002\u5176\u4e2d\uff0c\u8d5b\u8f66 \\(A\\) \u4e0d\u9002\u5408\u5728\u5730\u56fe \\(a\\) \u4e0a\u4f7f\u7528\uff0c\u8d5b\u8f66 \\(B\\) \u4e0d\u9002\u5408\u5728\u5730\u56fe \\(b\\) \u4e0a\u4f7f\u7528\uff0c\u8d5b\u8f66 \\(C\\) \u4e0d\u9002\u5408\u5728\u5730\u56fe \\(c\\) \u4e0a\u4f7f\u7528\uff0c\u800c\u5730\u56fe \\(x\\) \u5219\u9002\u5408\u6240\u6709\u8d5b\u8f66\u53c2\u52a0\u3002\u9002\u5408\u6240\u6709\u8d5b\u8f66\u53c2\u52a0\u7684\u5730\u56fe\u5e76\u4e0d\u591a\u89c1\uff0c\u6700\u591a\u53ea\u4f1a\u6709 \\(d\\) \u5f20\u3002<\/p>\n<p>\\(n\\) \u573a\u6e38\u620f\u7684\u5730\u56fe\u53ef\u4ee5\u7528\u4e00\u4e2a\u5c0f\u5199\u5b57\u6bcd\u7ec4\u6210\u7684\u5b57\u7b26\u4e32\u63cf\u8ff0\u3002\u4f8b\u5982\uff1a\\(S=\\underline{\\mathrm{xaabxcbc}}\\) \u8868\u793a\u5c0f L \u8ba1\u5212\u8fdb\u884c \\(8\\) \u573a\u6e38\u620f\uff0c\u5176\u4e2d\u7b2c \\(1\\) \u573a\u548c\u7b2c \\(5\\) \u573a\u7684\u5730\u56fe\u7c7b\u578b\u662f \\(x\\)\uff0c\u9002\u5408\u6240\u6709\u8d5b\u8f66\uff0c\u7b2c \\(2\\) \u573a\u548c\u7b2c \\(3\\) \u573a\u7684\u5730\u56fe\u662f \\(a\\)\uff0c\u4e0d\u9002\u5408\u8d5b\u8f66 \\(A\\)\uff0c\u7b2c \\(4\\) \u573a\u548c\u7b2c \\(7\\) \u573a\u7684\u5730\u56fe\u662f \\(b\\)\uff0c\u4e0d\u9002\u5408\u8d5b\u8f66 \\(B\\)\uff0c\u7b2c \\(6\\) \u573a\u548c\u7b2c \\(8\\) \u573a\u7684\u5730\u56fe\u662f \\(c\\)\uff0c\u4e0d\u9002\u5408\u8d5b\u8f66 \\(C\\) \u3002<\/p>\n<p>\u5c0f L \u5bf9\u6e38\u620f\u6709\u4e00\u4e9b\u7279\u6b8a\u7684\u8981\u6c42\uff0c\u8fd9\u4e9b\u8981\u6c42\u53ef\u4ee5\u7528\u56db\u5143\u7ec4 \\((i,h_i,j,h_j)\\) \u6765\u63cf\u8ff0\uff0c\u8868\u793a\u82e5\u5728\u7b2c \\(i\\) \u573a\u4f7f\u7528\u578b\u53f7\u4e3a \\(h_i\\) \u7684\u8f66\u5b50\uff0c\u5219\u7b2c \\(j\\) \u573a\u6e38\u620f\u8981\u4f7f\u7528\u578b\u53f7\u4e3a \\(h_j\\) \u7684\u8f66\u5b50\u3002<\/p>\n<p>\u4f60\u80fd\u5e2e\u5c0f L \u9009\u62e9\u6bcf\u573a\u6e38\u620f\u4f7f\u7528\u7684\u8d5b\u8f66\u5417\uff1f\u5982\u679c\u6709\u591a\u79cd\u65b9\u6848\uff0c\u8f93\u51fa\u4efb\u610f\u4e00\u79cd\u65b9\u6848\u3002\u5982\u679c\u65e0\u89e3\uff0c\u8f93\u51fa \u201c\\(-1\\)\u201d\uff08\u4e0d\u542b\u53cc\u5f15\u53f7\uff09\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u8f93\u5165\u7b2c\u4e00\u884c\u5305\u542b\u4e24\u4e2a\u975e\u8d1f\u6574\u6570 \\(n,d\\) \u3002<\/p>\n<p>\u8f93\u5165\u7b2c\u4e8c\u884c\u4e3a\u4e00\u4e2a\u5b57\u7b26\u4e32 \\(S\\) \u3002<\/p>\n<p>\\(n,d,S\\) \u7684\u542b\u4e49\u89c1\u9898\u76ee\u63cf\u8ff0\uff0c\u5176\u4e2d \\(S\\) \u5305\u542b \\(n\\) \u4e2a\u5b57\u7b26\uff0c\u4e14\u5176\u4e2d\u6070\u597d \\(d\\) \u4e2a\u4e3a\u5c0f\u5199\u5b57\u6bcd \\(x\\) \u3002<\/p>\n<p>\u8f93\u5165\u7b2c\u4e09\u884c\u4e3a\u4e00\u4e2a\u6b63\u6574\u6570 \\(m\\)\uff0c\u8868\u793a\u6709 \\(m\\) \u6761\u7528\u8f66\u89c4\u5219\u3002\u63a5\u4e0b\u6765 \\(m\\) \u884c\uff0c\u6bcf\u884c\u5305\u542b\u4e00\u4e2a\u56db\u5143\u7ec4 \\(i,h_i,j,h_j\\) \uff0c\u5176\u4e2d \\(i,j\\) \u4e3a\u6574\u6570\uff0c\\(h_i,h_j\\) \u4e3a\u5b57\u7b26 \\(A\\) \u3001\\(B\\) \u6216 \\(C\\)\uff0c\u542b\u4e49\u89c1\u9898\u76ee\u63cf\u8ff0\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u8f93\u51fa\u4e00\u884c\u3002<\/p>\n<p>\u82e5\u65e0\u89e3\uff0c\u8f93\u51fa \u201c\\(-1\\)\u201d\uff08\u4e0d\u542b\u53cc\u5f15\u53f7\uff09\u3002<\/p>\n<p>\u82e5\u6709\u89e3\uff0c\u5219\u5305\u542b\u4e00\u4e2a\u957f\u5ea6\u4e3a \\(n\\) \u7684\u4ec5\u5305\u542b\u5927\u5199\u5b57\u6bcd \\(A\\)\u3001\\(B\\)\u3001\\(C\\) \u7684\u5b57\u7b26\u4e32\uff0c\u8868\u793a\u5c0f L \u5728\u8fd9 \\(n\\) \u573a\u6e38\u620f\u4e2d\u5982\u4f55\u5b89\u6392\u8d5b\u8f66\u7684\u4f7f\u7528\u3002\u5982\u679c\u5b58\u5728\u591a\u7ec4\u89e3\uff0c\u8f93\u51fa\u5176\u4e2d\u4efb\u610f\u4e00\u7ec4\u5373\u53ef\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 \">3 1\r\nxcc\r\n1\r\n1 A 2 B<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"\">ABA<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u89e3\u91ca<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5c0f L \u8ba1\u5212\u8fdb\u884c \\(3\\) \u573a\u6e38\u620f\uff0c\u5176\u4e2d\u7b2c \\(1\\) \u573a\u7684\u5730\u56fe\u7c7b\u578b\u662f \\(x\\)\uff0c\u9002\u5408\u6240\u6709\u8d5b\u8f66\uff0c\u7b2c \\(2\\) \u573a\u548c\u7b2c \\(3\\) \u573a\u7684\u5730\u56fe\u662f \\(c\\)\uff0c\u4e0d\u9002\u5408\u8d5b\u8f66 \\(C\\) \u3002<\/p>\n<p>\u5c0f L \u5e0c\u671b\uff1a\u82e5\u7b2c \\(1\\) \u573a\u6e38\u620f\u4f7f\u7528\u8d5b\u8f66 \\(A\\)\uff0c\u5219\u7b2c \\(2\\) \u573a\u6e38\u620f\u4f7f\u7528\u8d5b\u8f66 \\(B\\) \u3002<\/p>\n<p>\u90a3\u4e48\u4e3a\u8fd9 \\(3\\) \u573a\u6e38\u620f\u5206\u522b\u5b89\u6392\u8d5b\u8f66 \\(A\\)\u3001\\(B\\)\u3001\\(A\\) \u53ef\u4ee5\u6ee1\u8db3\u6240\u6709\u6761\u4ef6\u3002<\/p>\n<p>\u82e5\u4f9d\u6b21\u4e3a \\(3\\) \u573a\u6e38\u620f\u5b89\u6392\u8d5b\u8f66\u4e3a \\(BBB\\) \u6216 \\(BAA\\) \u65f6\uff0c\u4e5f\u53ef\u4ee5\u6ee1\u8db3\u6240\u6709\u6761\u4ef6\uff0c\u4e5f\u88ab\u89c6\u4e3a\u6b63\u786e\u7b54\u6848\u3002\u4f46\u4f9d\u6b21\u5b89\u6392\u8d5b\u8f66\u4e3a \\(AAB\\) \u6216 \\(ABC\\) \u65f6\uff0c\u56e0\u4e3a\u4e0d\u80fd\u6ee1\u8db3\u6240\u6709\u6761\u4ef6\uff0c\u6240\u4ee5\u4e0d\u88ab\u89c6\u4e3a\u6b63\u786e\u7b54\u6848\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6570\u636e\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\\(n \\leq 50000, m \\leq 100000, d \\leq 8\\)<\/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>\u6ce8\u610f\u5230 \\(d \\leq 8\\)\uff0c\u6240\u4ee5\u53ef\u4ee5 \\(O(2^d)\\)\uff08\u53bb\u6389\u91cd\u590d\u72b6\u6001\uff09\u679a\u4e3e\u5176\u5b57\u7b26\uff0c\u7136\u540e\u5c31\u662f\u4e00\u4e2a\u88f8\u7684 2-SAT \u3002<\/p>\n<p>\u6bcf\u573a\u6e38\u620f\u4e24\u4e2a\u70b9\u8868\u793a\u7b2c\u4e00\u4e2a\/\u7b2c\u4e8c\u4e2a\u53ef\u4ee5\u53d6\u7684\u5b57\u7b26\uff0c\u7136\u540e\u6309\u7167\u5957\u8def\u8fde\u8fb9\u3002<\/p>\n<p>\u8f93\u51fa\u65b9\u6848\u6570\u7684\u65f6\u5019\u53ef\u4ee5\u76f4\u63a5\u6309\u7167\u627e\u51fa\u5f3a\u8fde\u901a\u5757\u7684\u7f16\u53f7\u5927\u5c0f\u5224\u65ad\u53d6\u4e0d\u53d6\uff0c\u56e0\u4e3a Tarjan \u7f29\u51fa\u6765\u7684\u8fde\u901a\u5757\u7f16\u53f7\u5c31\u662f\u6309\u7167\u62d3\u6251\u9006\u5e8f\u7684\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\nint gcnt,ghead[105050],gnext[205050],gnode[205050];\r\ninline void insertLine(register int s,register int t)\r\n{\r\n\tgnext[++gcnt]=ghead[s],ghead[s]=gcnt,gnode[gcnt]=t;\r\n\t\/\/printf(\"%d -&gt; %d\\n\",s,t);\r\n}\r\n\r\nchar s[50505];\r\n\r\nint N;\r\ninline int ReverseIndex(register int x)\r\n{\r\n\treturn (x &gt; N ? x-N : x+N);\r\n}\r\n\r\n#define RoundNext(_x) (((_x)+1)%3)\r\ninline int GetIndex(register int x,register char c)\r\n{\r\n\tif(RoundNext(s[x]-'a') == c-'A')\r\n\t\treturn x;\r\n\telse\r\n\t\treturn x+N;\r\n}\r\n\r\nint cnt,dfn[105050],low[105050],belong[105050],bcnt;\r\nbool ins[105050];\r\nint stk[105050],top;\r\nvoid Tarjan(register int o)\r\n{\r\n\tdfn[o]=low[o]=++cnt;\r\n\tins[o]=true,stk[++top]=o;\r\n\tfor(register int j=ghead[o],t;j;j=gnext[j])\r\n\t\tif(!dfn[t=gnode[j]])\r\n\t\t\tTarjan(t),low[o]=_min(low[o],low[t]);\r\n\t\telse if(ins[t])\r\n\t\t\tlow[o]=_min(low[o],dfn[t]);\r\n\tif(dfn[o] == low[o])\r\n\t{\r\n\t\tregister int bo=++bcnt;\r\n\t\tins[o]=false,belong[o]=bo;\r\n\t\twhile(top &amp;&amp; stk[top]!=o)\r\n\t\t\tins[stk[top]]=false,belong[stk[top]]=bo,stk[top--]=0;\r\n\t\ttop--;\r\n\t}\r\n}\r\n\r\n\r\nint M,qi[105050],qj[105050];\r\nchar qhi[105050],qhj[105050];\r\ninline void Solve()\r\n{\r\n\tgcnt=0,memset(ghead,0,sizeof(ghead));\r\n\tfor(register int i=1,u,v;i&lt;=M;i++)\r\n\t\t\/\/ turn qi[i] can't select qhi[i]\r\n\t\tif(s[qi[i]]-'a' == qhi[i]-'A')\r\n\t\t\tcontinue;\r\n\t\t\/\/ turn qj[i] can't select qhj[i] and above\r\n\t\telse if(s[qj[i]]-'a' == qhj[i]-'A')\r\n\t\t\tu=GetIndex(qi[i],qhi[i]),insertLine(u,ReverseIndex(u));\r\n\t\t\/\/ standard 2-SAT\r\n\t\telse\r\n\t\t{\r\n\t\t\tu=GetIndex(qi[i],qhi[i]),v=GetIndex(qj[i],qhj[i]);\r\n\t\t\tinsertLine(u,v);\r\n\t\t\tinsertLine(ReverseIndex(v),ReverseIndex(u));\r\n\t\t}\r\n\t\r\n\tcnt=0,memset(dfn,0,sizeof(dfn)),memset(low,0,sizeof(low));\r\n\tbcnt=0,memset(belong,0,sizeof(belong)),top=0;\r\n\tfor(register int i=1;i&lt;=(N&lt;&lt;1);i++)\r\n\t\tif(!dfn[i])\r\n\t\t\tTarjan(i);\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tif(belong[i] == belong[ReverseIndex(i)])\r\n\t\t\treturn;\r\n\t\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tif(belong[i] &lt; belong[ReverseIndex(i)])\r\n\t\t\tputchar(RoundNext(s[i]-'a')+'A');\r\n\t\telse\r\n\t\t\tputchar(RoundNext(RoundNext(s[i]-'a'))+'A');\r\n\tputchar('\\n');\r\n\texit(0);\r\n}\r\n\r\nint xpos[10];\r\n\r\nint main()\r\n{\r\n\tint D;scanf(\"%d%d\",&amp;N,&amp;D);\r\n\tscanf(\"%s\",&amp;s[1]);\r\n\tregister int lx=0;\r\n\tfor(register int i=1;i&lt;=N;i++)\r\n\t\tif(s[i] == 'x')\r\n\t\t\txpos[++lx]=i;\r\n\tscanf(\"%d\",&amp;M);\r\n\tfor(register int i=1;i&lt;=M;i++)\r\n\t\tscanf(\"%d %c%d %c\",&amp;qi[i],&amp;qhi[i],&amp;qj[i],&amp;qhj[i]);\r\n\t\r\n\tif(!D)\r\n\t\tSolve();\r\n\telse\r\n\t\tfor(register int bin=0;bin&lt;(1&lt;&lt;(D-1));bin++)\r\n\t\t{\r\n\t\t\t\/\/printf(\"state %d\\n\",bin);\r\n\t\t\tregister int tbin=bin;\r\n\t\t\tfor(register int i=1;i&lt;=D;i++,tbin&gt;&gt;=1)\r\n\t\t\t\ts[xpos[i]]=((tbin&amp;1) ? 'b' : 'a');\r\n\t\t\tSolve();\r\n\t\t}\r\n\tprintf(\"%d\\n\",-1);\r\n\t\r\n\treturn 0;\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YZOJ P3195 [NOI2017]\u6e38\u620f \u65f6\u95f4\u9650\u5236\uff1a1000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a524288KB \u96be &hellip; <a href=\"https:\/\/cf.mnihyc.com\/blog\/archives\/1151\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P3195 [NOI2017]\u6e38\u620f<\/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":[97,41,65,96],"tags":[],"class_list":["post-1151","post","type-post","status-publish","format-standard","hentry","category-2sat","category-proa","category-enuma","category-tarjansepe"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>YZOJ P3195 [NOI2017]\u6e38\u620f - 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