{"id":112,"date":"2025-01-11T23:40:41","date_gmt":"2025-01-11T15:40:41","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=112"},"modified":"2025-01-11T23:40:41","modified_gmt":"2025-01-11T15:40:41","slug":"b-kay-and-snowflake-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81dfs%e3%80%81dp%e3%80%81%e9%87%8d%e5%bf%83","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=112","title":{"rendered":"B. Kay and Snowflake \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001DP\u3001\u91cd\u5fc3)"},"content":{"rendered":"\n

Codeforce 685 B. Kay and Snowflake \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001DP\u3001\u91cd\u5fc3)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF685B
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>
\n\u7d66\u4f60\u4e00\u68f5\u6a39\uff0c\u8981\u6c42\u4f60\u6c42\u51fa\u6bcf\u68f5\u5b50\u6a39\u7684\u91cd\u5fc3\u3002<\/p>\n<\/blockquote>\n

\u524d\u8a00<\/h3>\n

\u5b8c\u5168\u4e0d\u77e5\u9053\u6211\u600e\u9ebc\u60f3\u5230\u7684<\/p>\n

\u60f3\u6cd5<\/h3>\n

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\n\u5728\u5efa\u91cd\u5fc3\u5256\u5206\u6a39\u7684\u6642\u5019\uff0c\u6211\u5011\u627e\u6839\u70ba$v$\u7684\u6a39\u7684\u91cd\u5fc3\u7684\u65b9\u6cd5\u662f\u770b\u770b\u76ee\u524d\u7bc0\u9ede\u6709\u6c92\u6709\u5927\u5c0f\u5927\u65bc\u76ee\u524d\u6a39\u7684\u4e00\u534a($size[v]\/2$)\u7684\u5b50\u6a39(\u4ee4\u6839\u70ba$u$)\uff0c\u4e26\u4e14\u7e7c\u7e8c\u770b\u770b\u9019\u68f5\u5b50\u6a39\u6709\u6c92\u6709\u5927\u5c0f\u5927\u65bc$size[v]\/2$\u7684\u5b50\u6a39(\u6ce8\u610f\uff0c\u4e0d\u662f$size[u]$)\uff0c\u5982\u679c\u6c92\u6709\u7684\u8a71\uff0c$u$\u5c31\u662f\u91cd\u5fc3\u3002
\n\u6ce8\u610f\u5230\uff0c\u7531\u65bc$u$\u7684\u91cd\u5fc3\u4ee3\u8868\u7684\u9ede\u662f\u5b50\u6a39\u5927\u5c0f\u90fd\u5c0f\u65bc$size[u]$\u7684\u9ede<\/strong>\uff0c\u53ea\u8981\u6211\u5011\u6162\u6162\u7531\u9019\u500b\u91cd\u5fc3\u5f80\u4e0a\u56de\u6714($u$\u7684\u91cd\u5fc3$\\rightarrow$$u$\u7684\u91cd\u5fc3\u7684\u7236\u7bc0\u9ede<\/strong>)\uff0c\u7e3d\u80fd\u627e\u5230\u6240\u6709\u5b50\u6a39\u5927\u5c0f\u90fd\u5c0f\u65bc\u4e14\u6700\u63a5\u8fd1$size[v]$\u7684\u9ede\uff0c\u800c\u90a3\u5c31\u662f\u7b54\u6848\u4e86\u3002
\n\u9700\u8981\u9806\u4fbf\u7dad\u8b77\u6bcf\u500b\u9ede\u6700\u5927\u7684\u5b50\u6a39\u7684\u5927\u5c0f\u5728$mx[]$\u88e1\uff0c\u52a0\u5feb\u904b\u7b97\u3002
\n\u7531\u65bc\u6211\u5011\u662f\u5f9e$u$\u7684\u91cd\u5fc3\u958b\u59cb\u627e\uff0c\u6240\u4ee5\u5373\u4f7f\u6574\u68f5\u6a39\u9000\u5316\u6210\u4e00\u500b\u934a<\/strong>\uff0c\u6211\u5011\u6bcf\u6b21\u4e5f\u53ea\u9700\u8981\u5f80\u4e0a\u79fb\u4e00\u683c\u5c31\u627e\u5230\u7b54\u6848\u4e86\u3002\u800c\u66f4\u4e00\u822c\u7684\u72c0\u6cc1\u6211\u731c\u60f3\u8907\u96dc\u5ea6\u63a5\u8fd1$O(n\\lg n)$\uff0c\u4f46\u66ab\u6642\u9084\u4e0d\u78ba\u5b9a\u600e\u9ebc\u8b49\u660eOrz<\/p>\n

\u7a0b\u5f0f\u78bc:<\/h3>\n
const int _n=3e5+10;  \nint t,n,q,v,p,dp[_n],sz[_n],mx[_n],fa[_n];  \nVI G[_n];  \nvoid dfsSz(int v,int faa){  \n  fa[v]=faa,sz[v]=1;  \n  for(int u:G[v])if(u!=faa)dfsSz(u,v),sz[v]+=sz[u],mx[v]=max(mx[v],sz[u]);  \n}  \nvoid dfs(int v,int faa){  \n  for(int u:G[v])if(u!=faa)dfs(u,v);  \n  for(int u:G[v])if(u!=faa and sz[u]>sz[v]\/2){  \n    u=dp[u];while(mx[u]<=sz[v]\/2)dp[v]=u,u=fa[u];  \n    return;  \n  }  \n  dp[v]=v;  \n}  \nmain(void) {ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);  \n  cin>>n>>q;rep(i,2,n+1){cin>>p;G[i].pb(p),G[p].pb(i);}  \n  dfsSz(1,0),mx[0]=sz[1],dfs(1,0);  \n  while(q--){  \n    cin>>v;cout<<dp[v]<<'\\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":[10,7,4,9,8],"class_list":["post-112","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-dfs","tag-dp","tag-ojcode","tag-8"],"jetpack_publicize_connections":[],"yoast_head":"\nB. 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