{"id":90,"date":"2025-01-11T23:22:53","date_gmt":"2025-01-11T15:22:53","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=90"},"modified":"2025-01-11T23:22:53","modified_gmt":"2025-01-11T15:22:53","slug":"e-xenia-and-tree-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81%e9%87%8d%e5%bf%83%e5%89%96%e5%88%86","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=90","title":{"rendered":"E. Xenia and Tree \u89e3\u6790(\u601d\u7dad\u3001\u91cd\u5fc3\u5256\u5206)"},"content":{"rendered":"\n

Codeforce 342 E. Xenia and Tree \u89e3\u6790(\u601d\u7dad\u3001\u91cd\u5fc3\u5256\u5206)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF342E\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>\n\u7d66\u4f60\u4e00\u68f5\u6a39\uff0c\u6709\u5169\u7a2e\u64cd\u4f5c\uff0c\u628a\u67d0\u9ede\u6a19\u6210\u7d05\u8272\u6216\u8005\u67e5\u8a62\u96e2\u67d0\u9ede\u6700\u8fd1\u7684\u7d05\u9ede\u6709\u591a\u9060\u3002<\/p>\n<\/blockquote>\n

\u524d\u8a00<\/h3>\n

\u9019\u984c\u6211\u662f\u7576\u4f5c\u5b78\u7fd2\u91cd\u5fc3\u5256\u5206\u7684\u7fd2\u984c\u770b\u5f85\u7684\uff0c\u6700\u8a73\u7d30\u7684\u7248\u672c\u8acb\u770b\u6559\u5b78\u6587<\/a><\/p>\n

\u60f3\u6cd5<\/h3>\n

\u6bcf\u5169\u500b\u6a39\u4e0a\u7684\u9ede\uff0c\u5176\u91cd\u5fc3\u5256\u5206\u6a39(CD\u6a39)\u4e0a\u7684$LCA$\u4e00\u5b9a\u5728\u5176\u6700\u77ed\u8def\u5f91\u4e0a\u3002\u56e0\u6b64\u7576\u6211\u5011\u628a\u9ede$v$\u5857\u6210\u7d05\u8272\u6642\uff0c\u6211\u5011\u53ea\u9700\u8981\u66f4\u6539CD\u6a39\u4e0a$v$\u7684\u7956\u5148\u5230\u6700\u8fd1\u7684\u7d05\u9ede\u7684\u8ddd\u96e2\u5c31\u597d\u3002\n\u4ee4$ans[v]$\u4ee3\u8868$v$\u5b50\u6a39(CD\u6a39\u4e0a\u7684\u5b50\u6a39)\u4e0a\u5230\u96e2$v$\u6700\u8fd1\u7684\u7d05\u9ede\u7684\u8ddd\u96e2\u3002\u5047\u8a2d\u628a$v$\u5857\u8272\uff0c$j$\u70ba$v$\u5728CD\u6a39\u4e0a\u7684\u67d0\u500b\u7956\u5148\uff0c$ans[j]=min(ans[j],dist(v,j))$\uff0c$dist(v,j)$\u4ee3\u8868\u5728\u539f\u5716\u4e0a$v,j$\u9593\u7684\u6700\u77ed\u8ddd\u96e2\uff0c\u6211\u5011\u53ef\u4ee5\u7528\u8001\u65b9\u6cd5:$dist(v,j)=dep[v]+dep[j]-2\\times dep[lca(v,j)]$\uff0c$dep[v]$\u662f$v$\u5728\u539f\u5716\u7684\u6df1\u5ea6\u3002<\/p>\n

\u800c\u8981\u641c\u5c0b\u96e2$v$\u6700\u8fd1\u7684\u7d05\u9ede\u8ddd\u96e2\u6642\uff0c\u7531\u65bc\u5169\u9ede\u9593\u7684\u6700\u77ed\u8ddd\u96e2\u4e0a\u4e00\u5b9a\u6709CD\u6a39\u4e0a$v$\u7684\u7956\u5148\uff0c\u56e0\u6b64\u6211\u5011\u904d\u6b77\u90a3\u4e9b\u7956\u5148(\u9ede$j$)\uff0c\u627e$dist(v,j)+ans[j]$\u7684\u6700\u5c0f\u503c\u3002<\/p>\n

\u7a0b\u5f0f\u78bc:<\/h3>\n
const int _n=1e5+10;\nint t,n,m,aa,bb,vv,ans[_n];\nVI G[_n];\nint sz[_n],cd_fa[_n];\nbool del[_n];\nvoid dfsSz(int v,int faa){\n  sz[v]=1;\n  rep(i,0,SZ(G[v]))if(G[v][i]!=faa and !del[G[v][i]])dfsSz(G[v][i],v),sz[v]+=sz[G[v][i]];\n}\nint get_centroid(int v,int faa,int cnt){\n  rep(i,0,SZ(G[v]))if(G[v][i]!=faa and !del[G[v][i]] and sz[G[v][i]]>cnt\/2)\n    return get_centroid(G[v][i],v,cnt);\n  return v;\n}\nvoid centroid_decomposition(int v,int faa){\n  dfsSz(v,faa);int centroid=get_centroid(v,faa,sz[v]);\n  cd_fa[centroid]=faa,del[centroid]=1;\n  rep(i,0,SZ(G[centroid]))if(G[centroid][i]!=faa and !del[G[centroid][i]])\n    centroid_decomposition(G[centroid][i],centroid);\n}\nconst int MAXB=18;\nint dep[_n],fa[_n][MAXB];\nvoid dfs(int v,int faa,int d){\n  dep[v]=d;fa[v][0]=faa;\n  rep(i,0,SZ(G[v]))if(faa!=G[v][i])dfs(G[v][i],v,d+1);\n}\nvoid bfa(){\n  rep(j,1,MAXB)rep(i,1,n+1)if(~fa[i][j-1])\n    fa[i][j]=fa[fa[i][j-1]][j-1];\n}\nint lca(int a,int b){\n  if(dep[a]<dep[b])swap(a,b);\n  per(j,0,MAXB)if(~fa[a][j] and dep[fa[a][j]]>=dep[b])a=fa[a][j];\n  if(a==b)return a;\n  per(j,0,MAXB)if(~fa[a][j] and fa[a][j]!=fa[b][j])a=fa[a][j],b=fa[b][j];\n  return fa[a][0];\n}\nvoid update(int vv){\n  int b=vv;\n  while(b!=-1){\n    int l=lca(vv,b);\n    ans[b]=min(ans[b],dep[vv]+dep[b]-2*dep[l]);\n    b=cd_fa[b];\n  }\n}\nmain(void) {ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);\n  cin>>n>>m;rep(i,0,n-1){cin>>aa>>bb;G[aa].pb(bb),G[bb].pb(aa);}\n  dfs(1,-1,0);rep(i,1,n+1)rep(j,1,MAXB)fa[i][j]=-1; bfa();\n  centroid_decomposition(1,-1);rep(i,1,n+1)ans[i]=1e5;\n  update(1);\n  while(m--){\n    cin>>t>>vv;\n    if(t==1)update(vv);\n    else{\n      int minn=1e9,b=vv;\n      while(b!=-1){\n        int l=lca(vv,b);\n        minn=min(minn,ans[b]+dep[b]+dep[vv]-2*dep[l]);\n        b=cd_fa[b];\n      }cout<<minn<<'\\n';\n    }\n  }\n  return 0;\n}\n<\/code><\/pre>\n
\u6a19\u982d\u3001\u6a21\u677f\u8acb\u9edeSubmission\u770b\nSubmission<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[3],"tags":[10,9,8,32],"class_list":["post-90","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-ojcode","tag-8","tag-32"],"jetpack_publicize_connections":[],"yoast_head":"\nE. 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