{"id":100,"date":"2025-01-11T23:28:12","date_gmt":"2025-01-11T15:28:12","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=100"},"modified":"2025-01-11T23:28:12","modified_gmt":"2025-01-11T15:28:12","slug":"d-alyona-and-strings-%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=100","title":{"rendered":"D. Alyona and Strings \u89e3\u6790(\u601d\u7dad\u3001DP)"},"content":{"rendered":"\n

Codeforce 682 D. Alyona and Strings \u89e3\u6790(\u601d\u7dad\u3001DP)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF682D
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>
\n\u7565\uff0c\u8acb\u76f4\u63a5\u770b\u539f\u984c\u3002<\/p>\n<\/blockquote>\n

\u524d\u8a00<\/h3>\n

a<\/p>\n

\u60f3\u6cd5<\/h3>\n

\u9996\u5148\u6703\u611f\u89ba\u61c9\u8a72\u662f\u985e\u4f3c$LCS$\u7684\u554f\u984c\uff0c\u4f46\u662f\u6709\u4e00\u9ede\u8b8a\u5f62\u3002\u56e0\u6b64\u6211\u5011\u6703\u5148\u60f3\u5230\u61c9\u8a72\u662f$DP$\uff0c\u800c\u53ef\u80fd\u6703\u60f3\u5230\u53e6\u5916\u5169\u500b\u72c0\u614b\u662f:<\/p>\n

    \n
  1. \u5171\u540c\u90e8\u5206\u662f\u4e0d\u662f\u76ee\u524d\u5169\u500b\u5b57\u4e32\u524d\u7db4\u7684\u7d50\u5c3e<\/li>\n
  2. \u6700\u5c0f\u7684\u5206\u6bb5\u662f\u5e7e\u6bb5<\/li>\n<\/ol>\n

    \u4e5f\u5c31\u662f$:dp[i][j][end][k]=$\u6700\u9577\u9577\u5ea6\uff0c$end=0:$\u975e\u7d50\u5c3e\uff0c$end=1:$\u662f\u7d50\u5c3e
    \n\u90a3\u9ebc\u6211\u5011\u5c31\u6703\u767c\u73fe\u8f49\u79fb\u5f0f$:dp[i][j][0][c]=$
    \n$\\max$$\\begin{cases}
    \ndp[i-1][j][1][c],\\ dp[i-1][j][0][c]\\
    \ndp[i][j-1][1][c],\\ dp[i][j-1][0][c]\\
    \ndp[i-1][j-1][1][c],\\ dp[i-1][j-1][0][c]\\
    \n\\end{cases}$
    \n\u4e14\u5982\u679c$s[i]\\neq t[j]:dp[i][j][1][c]=0$
    \n\u5982\u679c$s[i]=t[j]:dp[i][j][1][c]=$
    \n$\\max{dp[i-1][j-1][1][c]+1,\\ dp[i-1][j-1][0][c-1]+1}$<\/p>\n

    \u7a0b\u5f0f\u78bc:<\/h3>\n
    const int _n=1010;  \nint n,m,k,dp[_n][_n][2][11];  \nchar s[_n],t[_n];  \nmain(void) {cin.tie(0);ios_base::sync_with_stdio(0);  \n  cin>>n>>m>>k>>(s+1)>>(t+1);  \n  rep(i,0,m+1)rep(c,1,k+1)dp[0][i][0][c]=dp[0][i][1][c]=-1e5;  \n  rep(i,0,n+1)rep(c,1,k+1)dp[i][0][0][c]=dp[i][0][1][c]=-1e5;  \n  rep(i,1,n+1)rep(j,1,m+1)rep(c,1,k+1){  \n    dp[i][j][0][c]=max(dp[i][j][0][c],dp[i-1][j][1][c]);  \n    dp[i][j][0][c]=max(dp[i][j][0][c],dp[i-1][j][0][c]);  \n    dp[i][j][0][c]=max(dp[i][j][0][c],dp[i][j-1][1][c]);  \n    dp[i][j][0][c]=max(dp[i][j][0][c],dp[i][j-1][0][c]);  \n    dp[i][j][0][c]=max(dp[i][j][0][c],dp[i-1][j-1][1][c]);  \n    dp[i][j][0][c]=max(dp[i][j][0][c],dp[i-1][j-1][0][c]);  \n    if(s[i]==t[j]){  \n      dp[i][j][1][c]=max(dp[i][j][1][c],dp[i-1][j-1][1][c]+1);  \n      dp[i][j][1][c]=max(dp[i][j][1][c],dp[i-1][j-1][0][c-1]+1);  \n    }else dp[i][j][1][c]=0;  \n  }ll maxx=0;rep(i,1,n+1)rep(j,1,m+1)rep(c,1,k+1){  \n    maxx=max(maxx,max(dp[i][j][0][c],dp[i][j][1][c]));  \n  }cout<<maxx<<'\\n';  \n  return 0;  \n}  \n<\/code><\/pre>\n
    \u6a19\u982d\u3001\u6a21\u677f\u8acb\u9edeSubmission\u770b
    \n    Submission<\/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-100","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-dp","tag-ojcode","tag-8"],"jetpack_publicize_connections":[],"yoast_head":"\nD. 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