{"id":84,"date":"2025-01-11T23:19:54","date_gmt":"2025-01-11T15:19:54","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=84"},"modified":"2025-01-11T23:19:54","modified_gmt":"2025-01-11T15:19:54","slug":"d-regular-bridge-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81%e5%9c%96%e8%ab%96","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=84","title":{"rendered":"D. Regular Bridge \u89e3\u6790(\u601d\u7dad\u3001\u5716\u8ad6)"},"content":{"rendered":"\n

Codeforce 550 D. Regular Bridge \u89e3\u6790(\u601d\u7dad\u3001\u5716\u8ad6)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF550D
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>
\n\u7d66\u4f60\u4e00\u500b$k\\le100$\uff0c\u8acb\u69cb\u9020\u51fa\u4e00\u500b\u81f3\u5c11\u6709\u4e00\u500bBridge\u7684\uff0c\u6bcf\u500b\u9ede\u7684degree\u90fd\u662f$k$\u7684\u7121\u5411\u5716\u3002<\/p>\n<\/blockquote>\n

\u524d\u8a00<\/h3>\n

\u5b78\u5230\u4e86Handshaking Lemma<\/p>\n

\u60f3\u6cd5<\/h3>\n

\u9996\u5148\u65e2\u7136\u8981\u6709\u4e00\u500bBridge\uff0c\u6211\u5011\u5c31\u5f9e\u5df2\u7d93\u6709\u4e00\u500bBridge\u7684\u5716\u958b\u59cb\u69cb\u9020\u3002
\n\u53ef\u80fd\u6703\u767c\u73fe\u5230$k=2$\u7121\u89e3\uff0c\u800c$k=3$($k$\u662f\u5947\u6578)\u6709\u4ee5\u4e0b\u9019\u500b\u89e3(\u6211\u4e00\u958b\u59cb\u6839\u672c\u6c92\u60f3\u5230):
\n\u9996\u5148\u53ea\u8003\u616eBridge\u7684\u4e00\u908a\uff0c\u7136\u5f8c\u5fc5\u7136\u6709$k-1=2$\u689d\u908a\u9023\u51fa\u53bb\uff0c\u63a5\u8457\u6211\u5011\u518d\u591a\u9023\u51fa\u53bb\u4e00\u500b\u9ede(2\u20144,3\u20145)\uff0c\u7136\u5f8c$leaf(\u9ede4,5)$\u9023\u5230\u53f3\u65b9\u6240\u6709\u9084\u6c92\u6eff\u7684\u9ede\uff0c\u63a5\u8457$leaf$\u518d\u5169\u5169\u9023\u8d77\u4f86\u3002
\n\"\"<\/p>\n

\u63a5\u8457\u8b49\u660e\u7576$k\\mod 2=0$\u6642\u7121\u89e3:\u9996\u5148\u53ea\u8003\u616eBridge\u7684\u4e00\u908a\uff0c\u63a5\u8457\u6211\u5011\u6703\u767c\u73fe\u9023\u63a5Bridge\u7684\u90a3\u500b\u9ede\u7684\u5ea6\u6578\u662f$k-1$\uff0c\u662f\u5947\u6578\uff0c\u800c\u5176\u4ed6\u9ede\u7684\u5ea6\u6578\u90fd\u662f$k$\uff0c\u662f\u5076\u6578\u3002\u6839\u64daHandshaking Lemma\uff0c\u7121\u89e3\u3002(\u5982\u679c\u4e0d\u77e5\u9053\u9019\u500bLemma\u4e5f\u53ef\u4ee5\u76f4\u63a5\u8b49\u660e\u4e0d\u5b58\u5728\uff0c\u53ea\u662f\u6bd4\u8f03\u7e41\u7463)<\/p>\n

\u7a0b\u5f0f\u78bc:<\/h3>\n
const int _n=1e6+10;  \nint t,n,k;   \nvector<PII> e;  \nmain(void) {ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);  \n  cin>>k;if(k%2==0){cout<<"NO\\n";return 0;}  \n  rep(i,2,k+1)e.pb({1,i});rep(i,k+1,2*k)rep(j,2,k+1)e.pb({i,j});  \n  for(int i=k+1;i<=2*k-2;i+=2)e.pb({i,i+1});  \n  cout<<"YES\\n"<<4*k-2<<' '<<2*SZ(e)+1<<'\\n';  \n  rep(i,0,SZ(e))cout<<e[i].fi<<' '<<e[i].se<<'\\n';  \n  rep(i,0,SZ(e))cout<<e[i].fi+2*k-1<<' '<<e[i].se+2*k-1<<'\\n';  \n  cout<<1<<' '<<2*k<<'\\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":[10,9,31,8],"class_list":["post-84","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-ojcode","tag-31","tag-8"],"jetpack_publicize_connections":[],"yoast_head":"\nD. 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