{"id":80,"date":"2025-01-11T23:15:57","date_gmt":"2025-01-11T15:15:57","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=80"},"modified":"2025-01-11T23:15:57","modified_gmt":"2025-01-11T15:15:57","slug":"c-vladik-and-memorable-trip-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81dp","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=80","title":{"rendered":"C. Vladik and Memorable Trip \u89e3\u6790(\u601d\u7dad\u3001DP)"},"content":{"rendered":"\n

Codeforce 811 C. Vladik and Memorable Trip \u89e3\u6790(\u601d\u7dad\u3001DP)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF811C
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>
\n\u7d66\u4f60\u4e00\u500b\u6578\u5217\uff0c\u4e00\u500b\u5340\u6bb5\u7684\u6578\u5217\u7684\u503c\u662f\u5340\u6bb5\u5167\u6240\u6709\u76f8\u7570<\/strong>\u6578\u7684$XOR$\u7e3d\u548c\u3002\u4f60\u53ef\u4ee5\u9078\u4efb\u610f\u591a\u7684\u5340\u6bb5\uff0c\u6c42\u6700\u5927\u7684\u6240\u6709\u5340\u6bb5\u7684\u503c\u7684\u7e3d\u548c\u3002\u7136\u800c\u6240\u6709\u540c\u6a23\u7684\u6578\u5b57\u4e0d\u662f\u5b8c\u5168\u6c92\u6709\u88ab\u5305\u542b\u5728\u5340\u6bb5\u88e1\uff0c\u4e0d\u7136\u5c31\u662f\u8981\u5168\u90e8\u5728\u540c\u500b\u5340\u6bb5\u88e1\u3002<\/p>\n<\/blockquote>\n

\u524d\u8a00<\/h3>\n

\u9019\u984c\u6211\u4e00\u76f4\u5230\u770b\u4e86\u89e3\u7b54\u624d\u77e5\u9053\u70ba\u4ec0\u9ebc\u4e0d\u662f$O(n)$\uff0c\u984c\u76ee\u4e00\u76f4\u6c92\u641e\u6e05\u695a<\/p>\n

\u60f3\u6cd5<\/h3>\n

\u9019\u984c\u7684\u96e3\u9ede\u5728\uff0c\u5f88\u96e3\u7528$O(n^2)$\u4ee5\u4e0b\u627e\u5230\u4e00\u500b\u771f\u6b63\u7684\u53ef\u884c\u7684\u5340\u6bb5\u3002
\n\u6b64\u984c\u7684\u505a\u6cd5\u662f\u7dda\u6027DP\uff0c$dp[i]$\u70ba\u8003\u616e\u5230\u6578\u5217\u7684\u7b2c$i$\u500b\u6642\u7684\u89e3\u7b54\uff0c\u800c\u8981\u8a08\u7b97$i+1$\uff0c\u6211\u5011\u53ea\u9700\u8981\u591a\u8003\u616e\u662f\u5426\u6709\u500b\u5340\u6bb5\u662f\u5728$i+1$\u7d50\u5c3e\u3002
\n\u9996\u5148\u53ef\u4ee5$O(n)$\u5f97\u5230\u6bcf\u500b\u6578\u5b57\u6700\u5de6\u548c\u6700\u53f3\u908a\u5728\u54ea\u88e1\uff0c\u6bcf\u7576\u8981\u8a08\u7b97$dp[i+1]$\u6642\uff0c\u5148\u770b\u770b$i+1$\u9019\u500b\u4f4d\u7f6e\u662f\u5426\u662f\u67d0\u500b\u6578\u5b57\u7684\u6700\u53f3\u7684\u4f4d\u7f6e\uff0c\u63a5\u8457\u5f9e$i+1$\u4f4d\u7f6e\u958b\u59cb\u5f80\u56de\u770b\uff0c\u5982\u679c\u76ee\u524d\u770b\u7684\u5143\u7d20\u7684\u6700\u53f3\u4f4d\u7f6e\u8d85\u51fa$i+1$\uff0c\u4ee3\u8868\u76ee\u524d$i+1$\u4e0d\u53ef\u80fd\u662f\u67d0\u500b\u5340\u6bb5\u7684\u7d50\u5c3e\uff0c\u90a3\u9ebc$dp[i+1]=dp[i]$\uff1b\u5982\u679c\u4e00\u5207\u6b63\u5e38\uff0c\u76f4\u5230\u76ee\u524d\u4f4d\u7f6e\u5df2\u7d93\u5230\u4e86\u76ee\u524d\u770b\u904e\u7684\u6240\u6709\u5143\u7d20\u7684\u6700\u5de6\u4f4d\u7f6e\uff0c\u5c31\u4ee3\u8868\u6211\u5011\u5df2\u7d93\u627e\u5230\u4e00\u500b\u7d50\u5c3e\u5728$i+1$\u7684\u5340\u6bb5\u4e86\uff0c\u6b64\u6642$dp[i+1]=\\max{dp[i],\u5340\u6bb5\u7684$XOR$+$dp[\u5340\u6bb5\u7684\u6700\u5de6-1]$}$<\/p>\n

\u5b98\u65b9\u89e3\u7b54\u6709\u500bChallenge\uff0c\u5229\u7528$a\\oplus b\\le a+b$\uff0c\u53ef\u4ee5\u61c9\u4ed8$n,a[i]\\le1e5$\u7684\u60c5\u6cc1\uff0c\u5f85\u4e4b\u5f8c\u60f3\u5230\u518d\u88dc\u5427!<\/p>\n

\u7a0b\u5f0f\u78bc:<\/h3>\n
const int _n=5010;  \nint t,n,a[_n],dp[_n];  \nbool vis[_n],has[_n];  \nPII alr[_n];  \nmain(void) {ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);  \n  cin>>n;rep(i,1,n+1){  \n    cin>>a[i];if(!alr[a[i]].fi)alr[a[i]].fi=i;  \n    alr[a[i]].se=i;  \n  }rep(i,1,n+1)if(alr[a[i]].se==i)has[i]=1;  \n  dp[0]=0,dp[1]=(has[1]?a[1]:0);rep(i,2,n+1){  \n    dp[i]=dp[i-1];  \n    if(has[i]){  \n      int val=0,L=alr[a[i]].fi;memset(vis,0,sizeof vis);  \n      int j=i;while(j>=L){  \n        if(alr[a[j]].se>i)goto A;  \n        L=min(L,alr[a[j]].fi);  \n        if(!vis[a[j]])val^=a[j],vis[a[j]]=1;j--;  \n      }  \n      dp[i]=max(dp[i],val+dp[L-1]);  \n    }  \n    A:;  \n  }cout<<dp[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":[10,4,9,8],"class_list":["post-80","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-dp","tag-ojcode","tag-8"],"jetpack_publicize_connections":[],"yoast_head":"\nC. 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