{"id":96,"date":"2025-01-11T23:25:54","date_gmt":"2025-01-11T15:25:54","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=96"},"modified":"2025-01-11T23:25:54","modified_gmt":"2025-01-11T15:25:54","slug":"e-tree-queries-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81lca","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=96","title":{"rendered":"E. Tree Queries \u89e3\u6790(\u601d\u7dad\u3001LCA)"},"content":{"rendered":"\n

Codeforce 1328 E. Tree Queries \u89e3\u6790(\u601d\u7dad\u3001LCA)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF1328E
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>
\n\u7d66\u4f60\u4e00\u68f5\u6a39\uff0c\u4e26\u4e14\u7d66\u4f60$m\\le2e5$\u500b\u8a62\u554f(\u5305\u542b$k$\u500b\u9ede)\uff0c\u6c42\u80fd\u4e0d\u80fd\u627e\u5230\u4e00\u500b\u5f9e\u9ede$1$\u958b\u59cb\u7684\u8def\u5f91\uff0c\u4f7f\u5f97\u9019$k$\u500b\u9ede\u96e2\u9019\u500b\u8def\u5f91\u7684\u8ddd\u96e2$\\le1$<\/p>\n<\/blockquote>\n

\u524d\u8a00<\/h3>\n

\u4e45\u9055\u7684\u6c92\u770b\u89e3\u7b54\u5beb\u7684\u984c\u76ee\uff0c\u6545\u5beb\u984c\u89e3<\/p>\n

\u60f3\u6cd5<\/h3>\n

\u53ef\u4ee5\u89c0\u5bdf\u5230\uff0c\u984c\u76ee\u7684\u6558\u8ff0\u8868\u793a\uff0c\u5c0d\u65bc\u4e00\u500b\u7bc0\u9ede$v$\uff0c\u4ed6\u7684\u5b50\u7bc0\u9ede\u662f\u53ef\u4ee5\u540c\u6642\u51fa\u73fe\u7684\u3002\u56e0\u6b64\u6211\u5011\u53ea\u9700\u8981\u95dc\u6ce8$k$\u500b\u9ede\u7684\u6bcf\u500b\u9ede\u7684\u7236\u7bc0\u9ede\u80fd\u4e0d\u80fd\u5f62\u6210\u4e00\u500b\u8def\u5f91\uff0c\u800c\u8981\u5224\u65b7\u4e00\u500b\u9ede\u96c6\u80fd\u4e0d\u80fd\u6210\u70ba\u4e00\u689d\u8def\u5f91\uff0c\u6211\u5011\u53ea\u9700\u8981\u5148\u628a\u9ede\u96c6\u4ee5\u9ede\u7684\u6df1\u5ea6\u6392\u5e8f\uff0c\u63a5\u8457\u5f9e\u6df1\u5ea6\u4f4e\u7684\u9ede\u5169\u500b\u5169\u500b\u770b\uff0c\u5c0d\u65bc\u9ede\u5c0d$(u,v)$\uff0c\u5982\u679c$lca(u,v)=u$($u$\u662f\u6df1\u5ea6\u4f4e\u7684\u9ede)\uff0c\u5c31\u4ee3\u8868\u6211\u5011\u80fd\u5920\u5f9e$u$\u9023\u5230$v$\u3002<\/p>\n

\u7a0b\u5f0f\u78bc:<\/h3>\n
const int _n=2e5+10,MAXB=19;  \nint n,m,u,v,k,a,b,dep[_n],fa[_n][MAXB];  \nVI G[_n];  \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}  \nbool cmp(const int& a,const int& b){return dep[a]<dep[b];}  \nmain(void) {cin.tie(0);ios_base::sync_with_stdio(0);  \n  cin>>n>>m;rep(i,0,n-1){cin>>u>>v;G[u].pb(v),G[v].pb(u);}  \n  dfs(1,-1,0);rep(i,1,n+1)rep(j,1,MAXB)fa[i][j]=-1; bfa();  \n  while(m--){  \n    cin>>k;VI ks;rep(i,0,k){cin>>v;ks.pb(v);}  \n    rep(i,0,k)ks[i]=(fa[ks[i]][0]==-1?1:fa[ks[i]][0]);  \n    sort(all(ks),cmp);  \n    rep(i,1,k)if(lca(ks[i-1],ks[i])!=ks[i-1]){cout<<"NO\\n";goto A;}  \n    cout<<"YES\\n";  \n    A:;  \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":[10,13,9,8],"class_list":["post-96","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-lca","tag-ojcode","tag-8"],"jetpack_publicize_connections":[],"yoast_head":"\nE. 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