{"id":82,"date":"2025-01-11T23:17:07","date_gmt":"2025-01-11T15:17:07","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=82"},"modified":"2025-01-11T23:17:07","modified_gmt":"2025-01-11T15:17:07","slug":"d-the-wu-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81%e4%ba%8c%e9%80%b2%e4%bd%8d%e9%81%8b%e7%ae%97","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=82","title":{"rendered":"D. The Wu \u89e3\u6790(\u601d\u7dad\u3001\u4e8c\u9032\u4f4d\u904b\u7b97)"},"content":{"rendered":"\n

Codeforce 1017 D. The Wu \u89e3\u6790(\u601d\u7dad\u3001\u4e8c\u9032\u4f4d\u904b\u7b97)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF1017D
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

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

\u524d\u8a00<\/h3>\n

\u5b98\u65b9\u89e3\u7b54\u5be6\u5728\u770b\u4e0d\u61c2\u2026\u4e4b\u5f8c\u9084\u8a18\u5f97\u7684\u8a71\u518d\u88dc\u90a3\u500b\u505a\u6cd5\u5427<\/p>\n

\u60f3\u6cd5<\/h3>\n

\u53ea\u8981\u6ce8\u610f\u5230$n\\le12$\u4ee3\u8868\u6240\u6709\u53ef\u80fd\u51fa\u73fe\u7684\u6578\u5b57$\\le\\sum\\limits_{i=0}^{11}2^i=2^{12}-1=4096-1$\uff0c\u90a3\u5c31\u6703\u6ce8\u610f\u5230\u9019\u984c\u7684$m,q\\le5\\cdot10^5$\u662f\u5047\u7684\uff0c\u56e0\u70ba\u7e3d\u5171\u4e5f\u624d$4096$\u7a2e\u5b57\u4e32\uff0c\u54ea\u4f86\u7684$5\\cdot10^5$\u9019\u9ebc\u591a\u6578\u5b57\u8b93\u4f60\u554f?
\n\u6240\u4ee5\u9019\u984c\u53ea\u9700\u8981\u628a\u6240\u6709\u7684\u8a62\u554f\u5b57\u4e32\u90fd\u7aae\u8209\u4e00\u904d\uff0c\u4e26\u4e14\u76f4\u63a5\u8a08\u7b97\u300c\u7576\u524d\u8a62\u554f\u5b57\u4e32\u8207$m$\u500b$multiset$\u88e1\u7684\u5b57\u4e32\u8a08\u7b97Wu\u503c\uff0c\u6bcf\u500b\u503c\u6709\u591a\u5c11\u500b\u300d\u5132\u5b58\u8d77\u4f86(\u53ea\u9700\u8981\u5132\u5b58Wu\u503c$\\le100$\uff0c\u56e0\u70ba$k\\le100$)\uff0c\u90a3\u9ebc\u4e4b\u5f8c\u6bcf\u6b21\u8a62\u554f\u53ea\u9700\u8981$O(100)$\u5c31\u53ef\u4ee5\u627e\u5230\u7b54\u6848\u4e86(\u8a08\u7b97\u524d\u7db4\u548c)\u3002<\/p>\n

\u5be6\u4f5c\u7d30\u7bc0:\u9996\u5148\u628a$multiset$\u88e1\u7684\u5143\u7d20\u90fd\u770b\u6210\u6578\u5b57\uff1b$cnt[i]=multiset$\u4e2d$i$\u7684\u500b\u6578\uff1b$(s,t)$\u7684Wu\u503c\u53ea\u548c$s,t$\u54ea\u4e9b$bit$\u76f8\u540c\u6709\u95dc\uff0c$wu[(s,t)\u5169\u500b\u6578\u5b57bit\u76f8\u540c\u7684\u4f4d\u7f6e\u6a19\u70ba1\u5176\u4ed6\u70ba0\u7684\u6578\u5b57]=Wu(s,t)$
\n\u800c\u8981\u8a08\u7b97(s,t)\u5169\u500b\u6578\u5b57bit\u76f8\u540c\u7684\u4f4d\u7f6e\u6a19\u70ba1\u5176\u4ed6\u70ba0\u7684\u6578\u5b57\u53ea\u9700\u8981:$(s\\widehat{}(\\sim t))&((1<<n)-1)=(s\\widehat{}(\\sim t))&\\sim-(1<<n)$\uff0c\u5176\u4e2d$(1<<n)-1\u662f\u7528\u4f86\u53ea\u4fdd\u7559\u5c0f\u65bc1<<n\u7684bit$\uff0c\u800c$(1<<n)-1=\\sim-(1<<n)$\u662f\u5229\u7528$-k=\\sim k+1$<\/p>\n

\u7a0b\u5f0f\u78bc:<\/h3>\n
const int _n=15;  \nint t,n,m,q,w[_n],k,cnt[4096],ans[4096][110],wu[4096];  \nchar s[_n];  \nmain(void) {ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);  \n  cin>>n>>m>>q;rep(i,1,n+1)cin>>w[i];  \n  rep(i,0,1<<n)rep(j,0,n)wu[i]+=w[n-j]*((i&(1<<j))>0);  \n  rep(i,0,m){  \n    int num=0;cin>>(s+1);  \n    rep(j,0,n)num+=(s[n-j]-'0')*(1<<j);  \n    cnt[num]++;  \n  }rep(qu,0,1<<n)rep(ts,0,1<<n){  \n    ans[qu][wu[(qu^~ts)&~-(1<<n)]>100?101:wu[(qu^~ts)&~-(1<<n)]]+=cnt[ts];  \n  }while(q--){  \n    cin>>(s+1)>>k;  \n    t=0;rep(j,0,n)t+=(s[n-j]-'0')*(1<<j);  \n    int res=0;rep(i,0,k+1)res+=ans[t][i];  \n    cout<<res<<'\\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":[30,8],"class_list":["post-82","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-30","tag-8"],"jetpack_publicize_connections":[],"yoast_head":"\nD. 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