{"id":53,"date":"2025-01-11T22:59:45","date_gmt":"2025-01-11T14:59:45","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=53"},"modified":"2025-01-11T22:59:45","modified_gmt":"2025-01-11T14:59:45","slug":"d-serval-and-rooted-tree-%e6%a8%b9%e7%8b%80dp","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=53","title":{"rendered":"D. Serval and Rooted Tree (\u6a39\u72c0DP)"},"content":{"rendered":"\n

Codeforce 1153D Serval and Rooted Tree (\u6a39\u72c0DP)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF1153D
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>
\n\u7d66\u4e00\u68f5\u6578\uff0c\u5047\u8a2d\u6709$k$\u500b\u8449\u7bc0\u9ede\uff0c\u6211\u5011\u53ef\u4ee5\u7d66\u8449\u7bc0\u9ede\u5206\u914d$1$~$k$\u9019\u4e9b\u6578\u5b57\uff0c\u7576\u505a\u9019\u4e9b\u7bc0\u9ede\u7684"\u503c"\u3002
\n\u6bcf\u500b\u975e\u8449\u7bc0\u9ede\u7684\u9ede(\u4e0d\u59a8\u4ee4\u70ba\u9ede$u$)\u7684\u503c\u6709\u53ef\u80fd\u662f\u6240\u6709$u$\u7684\u5b50\u7bc0\u9ede\u7684$\\min$\u6216$\\max$\u3002
\n\u4ee4\u6839\u7bc0\u9ede\u70ba\u7bc0\u9ede$1$\uff0c\u6c42\u6839\u7bc0\u9ede\u53ef\u80fd\u7684\u6700\u5927\u503c\u3002<\/p>\n<\/blockquote>\n

\u60f3\u6cd5<\/h3>\n

\u9996\u5148\u6709\u53ef\u80fd\u60f3\u5230\u8981\u505a\u6a39\u72c0dp\uff0c\u800c\u6bcf\u500b\u9ede\u7684\u72c0\u614b\u5c31\u662f:\u300c\u5047\u8a2d\u9ede$u$\u70ba\u6839\u7684\u5b50\u6a39\u6709$k_u$\u500b\u8449\u7bc0\u9ede\uff0c$dp[u]$\u70ba$1$~$k_u$\u4e2d\u7684\u6700\u5927\u53ef\u80fd(\u5982\u679c\u6211\u5011\u7d66\u9019$k_u$\u500b\u8449\u7bc0\u9ede\u5206\u914d$1$~$k_u$\u7684\u503c)\u300d\u3002
\n\u5982\u679c\u9ede$u$\u70ba$\\min$\uff0c\u90a3\u9ebc\u6211\u5011\u53ea\u8981\u627e\u51fa$u$\u7684\u5b50\u7bc0\u9ede\u4e2d$dp$\u503c\u6700\u5c0f\u7684\u5c31\u597d\u3002\u4f46\u662f\u5982\u679c\u9ede$u$\u70ba$\\max$\uff0c\u90a3\u9ebc\u8981\u5f97\u5230$dp[u]$\uff0c\u6211\u5011\u53ea\u9700\u8981\u5728\u300e\u300c$dp$\u503c\u6700\u5927\u7684$u$\u7684\u5b50\u7bc0\u9ede(\u4ee4\u70ba$v$)\u300d\u7684\u5b50\u6a39\u7684\u8449\u7bc0\u9ede\u300f\u4e2d\u5206\u914d$k_u$\u4e2d\u6700\u5927\u7684$k_v$\u500b\u5373\u53ef\u3002
\n\u4f46\u662f\u5982\u679c\u9019\u6a23\u505a\uff0c\u6211\u5011\u6703\u9700\u8981\u7dad\u8b77\u6bcf\u4e00\u500b\u7bc0\u9ede\u7684\u5b50\u6a39\u7e3d\u5171\u6709\u591a\u5c11\u500b\u8449\u7bc0\u9ede\u3002\u56e0\u6b64\u6211\u5011\u4e0d\u59a8\u628a$dp$\u9663\u5217\u5132\u5b58\u7684\u6771\u897f\u6539\u70ba:$dp[u]$\u70ba$k_u-$($1$~$k_u$\u4e2d\u7684\u6700\u5927\u53ef\u80fd)+1\uff0c\u4e5f\u5c31\u662f\u9019\u6b21\u662f\u5f9e$k_u$\u958b\u59cb\u5f80$1$\u6578\uff0c\u770b\u6700\u5927\u503c\u70ba\u7b2c\u5e7e\u500b\u6578\u5230\u7684\u3002
\n\u5982\u6b64\u4e00\u4f86\uff0c$dp$\u8f49\u79fb\u5f0f\u5373\u53ef\u6539\u70ba:
\n$\\begin{cases}
\ndp[u]=\\min{dp[v]}{v\\in son(u)}\\ \\text{if u is max}\\
\ndp[u]=\\sum<\/em>{v\\in son(u)} dp[v]\\ \\text{if u is min}
\n\\end{cases}$
\n\u800c\u6700\u7d42\u7684\u7b54\u6848\u5373\u70ba$k-dp[1]+1$<\/p>\n

\u7a0b\u5f0f\u78bc:<\/h3>\n
const int _n=3e5+10;  \nint t,n,s[_n],dpT[_n],k;  \nVI G[_n];  \nint dp(int v){  \n  if(dpT[v])return dpT[v];  \n  if(SZ(G[v])==0){k++;return dpT[v]=1;}  \n  if(s[v]==1){dpT[v]=dp(G[v][0]);rep(i,1,SZ(G[v]))dpT[v]=min(dpT[v],dp(G[v][i]));}  \n  if(s[v]==0)rep(i,0,SZ(G[v]))dpT[v]+=dp(G[v][i]);  \n  return dpT[v];  \n}  \nmain(void) {cin.tie(0);ios_base::sync_with_stdio(0);  \n  cin>>n;rep(i,1,n+1)cin>>s[i];  \n  rep(i,2,n+1){cin>>t;G[t].pb(i);}  \n  dp(1);cout<<k-dp(1)+1<<'\\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":[10,9,23],"class_list":["post-53","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-ojcode","tag-dp"],"jetpack_publicize_connections":[],"yoast_head":"\nD. 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