{"id":843,"date":"2019-04-02T22:20:26","date_gmt":"2019-04-02T14:20:26","guid":{"rendered":"http:\/\/SmokeyDays.top\/wordpress\/?p=843"},"modified":"2019-04-02T22:20:26","modified_gmt":"2019-04-02T14:20:26","slug":"lp3690-%e3%80%90%e6%a8%a1%e6%9d%bf%e3%80%91link-cut-tree-%ef%bc%88%e5%8a%a8%e6%80%81%e6%a0%91%ef%bc%89","status":"publish","type":"post","link":"http:\/\/SmokeyDays.top\/wordpress\/2019\/04\/02\/lp3690-%e3%80%90%e6%a8%a1%e6%9d%bf%e3%80%91link-cut-tree-%ef%bc%88%e5%8a%a8%e6%80%81%e6%a0%91%ef%bc%89\/","title":{"rendered":"lp3690 \u3010\u6a21\u677f\u3011Link Cut Tree 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fd9\u65f6\u5019\u6211\u4eec\u9700\u8981\u6362\u6839\u64cd\u4f5c\u3002<br>\n\u9996\u5148\uff0c\u6211\u4eec\u5c06\u6839\u8282\u70b9\u5230\u5c06\u8981\u6210\u4e3a\u6839\u7684\u8282\u70b9X\u7f6e\u4e8e\u540c\u4e00\u6761\u5b9e\u94fe\u4e0a\u2014\u2014\u8fd9\u53ef\u4ee5\u901a\u8fc7access\u6765\u8fbe\u6210\u3002<br>\n\u5728access\u540e\uff0cX\u4fbf\u662fX\u6240\u5728\u7684Splay\u4e2d\u539f\u6811\u6df1\u5ea6\u6700\u6d45\u7684\u8282\u70b9\uff0c\u4e5f\u5c31\u662f\u6700\u53f3\u7684\u8282\u70b9\u3002\u8fd9\u65f6\u5019\uff0c\u5018\u82e5\u5c06X\u65cb\u5230\u5176\u6240\u5728\u7684Splay\u7684\u6839\uff0c\u7136\u540e\u7ffb\u8f6cX\uff0c\u90a3\u4e48\u6574\u6761\u94fe\u5c31\u4e0a\u4e0b\u5012\u8f6c\u4e86\u3002<\/p>\n\n\n\n<p>qryrt(X)<br>\n\u5728\u786e\u8ba4\u8fde\u901a\u6027\u7684\u65f6\u5019\uff0c\u6211\u4eec\u9700\u8981\u8be2\u95ee\u67d0\u4e2a\u70b9X\u6240\u5728\u7684\u6811\u7684\u6839\u3002<br>\n\u663e\u7136\uff0c\u8fd9\u8981\u6c42\u7684\u5c31\u662faccess\u4e4b\u540eX\u6240\u5728\u7684Splay\u7684\u6700\u5de6\u7aef\u8282\u70b9\u3002<\/p>\n\n\n\n<p>split(X,Y)<br>\n\u5728\u5904\u7406\u5177\u4f53\u64cd\u4f5c\u7684\u65f6\u5019\uff0c\u6211\u4eec\u53ef\u80fd\u4f1a\u9700\u8981\u5c06\u67d0\u4e00\u6761\u94fe\u6458\u79bb\u51fa\u6765\u3002<br>\n\u5982\u679c\u5b83\u4eec\u8fde\u901a\uff0c\u53ea\u9700\u8981\u6362\u6839\u5230\u4e00\u8005\uff0c\u7136\u540eaccess\u53e6\u4e00\u8005\u5373\u53ef\u3002<\/p>\n\n\n\n<p>link(X,Y)<br> \u4eceX\u5230Y\u8fde\u8fb9\u3002<br> \u65b9\u6cd5\u5f88\u7b80\u5355\uff0c\u5c06X\u4f5c\u4e3a\u5b83\u6240\u5728\u7684\u6811\u7684\u6839\uff0c\u7136\u540e\u76f4\u63a5\u8fde\u4e00\u6761\u865a\u8fb9\u5373\u53ef\u3002<\/p>\n\n\n\n<p>cut(X,Y)<br>\n\u5220\u9664X\u548cY\u4e4b\u95f4\u7684\u8fb9\u3002<br>\n\u5018\u82e5\u4fdd\u8bc1X\u548cY\u4e4b\u95f4\u672c\u6765\u662f\u6709\u8fde\u8fb9\u7684\uff0c\u90a3\u5012\u662f\u5bb9\u6613\u4e86\uff0c\u76f4\u63a5split\u51fa\u6765\u4e4b\u540e\u5206\u79bb\u4e24\u8005\u5373\u53ef\u3002<br>\n\u73b0\u5728\u6211\u4eec\u9700\u8981\u8003\u8651\u4e24\u8005\u6ca1\u6709\u8fde\u8fb9\u7684\u60c5\u51b5\u3002<br>\n\u9996\u5148\uff0c\u6211\u4eec\u5c06X\u53d8\u4e3a\u6839\uff0c\u7136\u540e\u5bfb\u627eY\u7684\u6839\u3002<br>\n\u8003\u8651Splay\u64cd\u4f5c\u7684\u5f71\u54cd\uff0c\u6211\u4eec\u77e5\u9053\uff0c\u8fd9\u6837\u64cd\u4f5c\u4e4b\u540e\uff0c\u5728Splay\u6811\u4e0a\uff0cY\u8282\u70b9\u4e00\u5b9a\u5728X\u8282\u70b9\u7684\u53f3\u513f\u5b50\u7684\u4f4d\u7f6e\u3002<br>\n\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5982\u679cY\u7684\u6839\u4e0d\u662fX\uff0c\u90a3\u4e48\u663e\u7136\u4e24\u8005\u4e0d\u8fde\u901a\u3002\u5982\u679cY\u4e0d\u662fX\u7684\u540e\u7ee7\uff0c\u90a3\u4e48\u663e\u7136\u4e24\u8005\u4e4b\u95f4\u6709\u9694\u7740\u70b9\uff0c\u4e5f\u5c31\u4e0d\u662f\u7236\u5b50\u5173\u7cfb\u3002<\/p>\n\n\n\n<p>\u6ce8\u610f\uff1a<br>\n\u4e00\uff1a\u5173\u4e8eSplay\uff1a\u5728LCT\u4e2d\uff0c\u6211\u4e60\u60ef\u4f7f\u7528\u7684SplayOne\u7684\u65b9\u6cd5\u5e76\u4e0d\u662f\u7279\u522b\u6709\u6548\uff0c\u8fd9\u662f\u56e0\u4e3a\u5728LCT\u4e2d\u5b58\u5728\u865a\u8fb9\u3002<br>\n\u4e8c\uff1a\u5728\u65cb\u8f6c\u7684\u65f6\u5019\uff0c\u9700\u8981\u7279\u522b\u6ce8\u610f\u5224\u65adC\u662f\u7a7a\u8282\u70b9\u548cY\u662f\u6839\u8282\u70b9\u7684\u60c5\u51b5\u3002\u5728\u8fd9\u4e24\u79cd\u60c5\u51b5\u4e0b\u6709\u4e24\u53e5\u8bdd\u662f\u4e0d\u5e94\u8be5\u5199\u7684\u3002 <\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>#include&lt;iostream>\n#include&lt;cstdio>\n#include&lt;cstring>\n#include&lt;algorithm>\n#include&lt;queue>\n#include&lt;vector>\n\ninline void Swap(int &amp;A,int &amp;B){\n\tA^=B^=A^=B;\n}\nconst int N=300005;\nint fa[N],ch[N][2],rev[N],sm[N],val[N];\n\ninline bool isrt(int X){\n\treturn ch[fa[X]][0]!=X&amp;&amp;ch[fa[X]][1]!=X;\n}\ninline void updt(int X){\n\tsm[X]=sm[ch[X][0]]^sm[ch[X][1]]^val[X];\n}\ninline void flp(int X){\n\tSwap(ch[X][0],ch[X][1]);\n\trev[X]^=1;\n}\ninline void pshd(int X){\n\tif(rev[X]){\n\t\tif(ch[X][0]){\n\t\t\tflp(ch[X][0]);\n\t\t}\n\t\tif(ch[X][1]){\n\t\t\tflp(ch[X][1]);\n\t\t}\n\t\trev[X]=0;\n\t}\n}\ninline int fndD(int X){\n\treturn ch[fa[X]][1]==X;\n}\ninline void splayOne(int X){\n\/\/\tint D=fndD(X),D2=fndD(fa[X]);\n\/\/\tfa[ch[X][D^1]]=fa[X],ch[fa[X]][D]=ch[X][D^1];\n\/\/\tch[X][D^1]=fa[X],fa[X]=fa[ch[X][D^1]];\n\/\/\tch[fa[X]][D2]=X,fa[ch[X][D^1]]=X;\n\/\/\tupdt(ch[X][D^1]),updt(X);\n\/\/\t\u5728LCT\u4e2d\uff0c\u6211\u4e60\u60ef\u4f7f\u7528\u7684SplayOne\u7684\u65b9\u6cd5\u5e76\u4e0d\u662f\u7279\u522b\u6709\u6548\uff0c\u8fd9\u662f\u56e0\u4e3a\u5728LCT\u4e2d\u5b58\u5728\u865a\u8fb9\u3002\n\tint Y=fa[X],Z=fa[Y],D=fndD(X),D2=fndD(fa[X]),C=ch[X][D^1];\n\tif(!isrt(Y)){\n\t\tch[Z][D2]=X;\n\t}\n\tch[X][D^1]=Y,ch[Y][D]=C;\n\tif(C){\n\t\tfa[C]=Y;\n\t}\n\tfa[X]=Z,fa[Y]=X;\n\tupdt(Y),updt(X);\n}\nint st[N];\ninline void splay(int X){\n\tint Y=X,Z=0;\n\tst[++Z]=Y;\n\twhile(!isrt(Y)){\n\t\tY=fa[Y];\n\t\tst[++Z]=Y;\n\t}\n\twhile(Z){\n\t\tpshd(st[Z--]);\n\t}\n\twhile(!isrt(X)){\n\t\tY=fa[X],Z=fa[Y];\n\t\tif(!isrt(Y)){\n\t\t\tsplayOne((fndD(X)^fndD(Y))?X:Y);\n\t\t}\n\t\tsplayOne(X);\n\t}\n}\ninline void access(int X){\n\tfor(int Y=0;X;Y=X,X=fa[X]){\n\t\tsplay(X),ch[X][1]=Y,updt(X);\n\t}\n}\ninline void chgrt(int X){\n\taccess(X),splay(X),flp(X);\n}\ninline int qryrt(int X){\n\taccess(X),splay(X);\n\twhile(ch[X][0]){\n\t\tpshd(X);\n\t\tX=ch[X][0];\n\t}\n\tsplay(X);\n\treturn X;\n} \ninline void split(int X,int Y){\n\tchgrt(X);\n\taccess(Y),splay(Y);\n} \ninline bool link(int X,int Y){\n\tchgrt(X);\n\tif(qryrt(Y)==X){\n\t\treturn 0;\n\t}\n\tfa[X]=Y;\n\treturn 1;\n}\ninline bool cut(int X,int Y){\n\tsplit(X,Y);\n\tif(ch[Y][0]!=X||ch[X][1]){\n\t\treturn 0;\n\t}\n\tfa[X]=ch[Y][0]=0;\n\treturn 1;\n}\nint n,q;\nvoid init(){\n\tscanf(\"%d%d\",&amp;n,&amp;q);\n\tfor(int i=1;i&lt;=n;++i){\n\t\tscanf(\"%d\",&amp;val[i]);\n\t\tsm[i]=val[i];\n\t}\n\tint op,x,y;\n\tfor(int i=1;i&lt;=q;++i){\n\t\tscanf(\"%d%d%d\",&amp;op,&amp;x,&amp;y);\n\t\tswitch(op){\n\t\t\tcase 0:{\n\t\t\t\tsplit(x,y);\n\t\t\t\tprintf(\"%d\\n\",sm[y]);\n\t\t\t\tbreak;\n\t\t\t}\n\t\t\tcase 1:{\n\t\t\t\tlink(x,y);\n\t\t\t\tbreak;\n\t\t\t}\n\t\t\tcase 2:{\n\t\t\t\tcut(x,y);\n\t\t\t\tbreak;\n\t\t\t}\n\t\t\tcase 3:{\n\t\t\t\tsplay(x);\n\t\t\t\tval[x]=y;\n\t\t\t\tupdt(x);\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\t}\n}\nint main(){\n\tinit();\n\treturn 0;\n}\n\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u6811\u94fe\u5256\u5206\u6709\u591a\u79cd\u65b9\u6cd5\u3002\u4f8b\u5982\u4ee5\u91cd\u91cf\u4e3a\u5173\u952e\u5b57\u7684\u91cd\u94fe\u5256\u5206\uff0c\u4ee5\u957f\u5ea6\u4e3a\u5173\u952e\u5b57\u7684\u957f\u94fe\u5256\u5206\u3002 \u800cLCT\uff08Link-Cut-Tr &hellip; <\/p>\n<p class=\"link-more\"><a href=\"http:\/\/SmokeyDays.top\/wordpress\/2019\/04\/02\/lp3690-%e3%80%90%e6%a8%a1%e6%9d%bf%e3%80%91link-cut-tree-%ef%bc%88%e5%8a%a8%e6%80%81%e6%a0%91%ef%bc%89\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u201clp3690 \u3010\u6a21\u677f\u3011Link Cut Tree \uff08\u52a8\u6001\u6811\uff09\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[30,106,56,70,8,6,5],"tags":[],"_links":{"self":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/843"}],"collection":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/comments?post=843"}],"version-history":[{"count":1,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/843\/revisions"}],"predecessor-version":[{"id":845,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/843\/revisions\/845"}],"wp:attachment":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/media?parent=843"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/categories?post=843"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/tags?post=843"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}