{"id":139,"date":"2025-01-12T12:45:31","date_gmt":"2025-01-12T04:45:31","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=139"},"modified":"2025-01-12T12:47:12","modified_gmt":"2025-01-12T04:47:12","slug":"f-moving-points-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81%e9%9b%a2%e6%95%a3%e5%8c%96%e3%80%81bit%e3%80%81%e5%89%8d%e7%b6%b4%e5%92%8c","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=139","title":{"rendered":"F. Moving Points \u89e3\u6790(\u601d\u7dad\u3001\u96e2\u6563\u5316\u3001BIT\u3001\u524d\u7db4\u548c)"},"content":{"rendered":"\n

Codeforce 1311 F. Moving Points \u89e3\u6790(\u601d\u7dad\u3001\u96e2\u6563\u5316\u3001BIT\u3001\u524d\u7db4\u548c)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF1311F
\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

\u6700\u8fd1\u5beb1900\u7684\u984c\u76ee\u66f4\u5bb9\u6613\u4e0d\u770b\u984c\u89e3\u4e86\uff0c\u4e0d\u77e5\u9053\u662f\u4e0d\u662f\u8f03\u5c11\u4eba$AC$\u7684\u540c\u96e3\u5ea6\u984c\u76ee\u6703\u6bd4\u8f03\u7c21\u55ae\u3002<\/p>\n

\u60f3\u6cd5<\/h3>\n

\u9996\u5148\u6ce8\u610f\u5230\uff0c\u5982\u679c$x$\u5ea7\u6a19\u4e0a\u7684\u524d\u5f8c\u5169\u9ede$x_i,x_j$\uff0c$x_i<x_j$\uff0c\u5982\u679c$v[x_i]>v[x_j]$\uff0c\u4e0d\u7ba1$v$\u662f\u6b63\u662f\u8ca0\uff0c\u5169\u9ede\u4e00\u5b9a\u67d0\u500b\u6642\u5019\u6703\u91cd\u758a\u3002\u53cd\u4e4b\uff0c\u5982\u679c$v[x_i]\\le v[x_j]$\uff0c\u90a3\u9ebc\u6211\u5011\u5c31\u9700\u8981\u628a\u7b54\u6848\u52a0\u4e0a$x_j-x_i$\u3002
\n\u800c\u6211\u5011\u53ef\u80fd\u6703\u60f3\u5230\u7528$BIT$\u4f86\u7dad\u8b77$:$\u5230\u67d0\u500b$x$\u5ea7\u6a19\u70ba\u6b62\uff0c\u5c0f\u65bc\u7b49\u65bc\u67d0\u500b\u901f\u5ea6\u7684\u9ede\u6709\u591a\u5c11\u500b\u3002\u4f46\u662f$-10^8\\le v_i\\le10^8$\u5be6\u5728\u592a\u5927\u4e86\uff0c\u56e0\u6b64\u6211\u5011\u9700\u8981\u96e2\u6563\u5316$v$\uff0c\u628a\u7bc4\u570d\u7e2e\u5230\u81f3\u5c11$[1,n]$\u3002
\n\u4f46\u662f\u6211\u5011\u53ef\u80fd\u6703\u767c\u73fe\uff0c\u6211\u5011\u4e0d\u53ea\u9700\u8981\u7dad\u8b77\u5c0f\u65bc\u7b49\u65bc\u67d0\u500b\u901f\u5ea6\u7684\u9ede\u6709\u591a\u5c11\u500b\uff0c\u9084\u9700\u8981\u77e5\u9053\u9019\u4e9b\u9ede\u548c\u76ee\u524d\u770b\u7684\u9ede$x_i$\u7684\u8ddd\u96e2\u7684\u548c\u3002
\n\u56e0\u6b64\u6211\u5011\u53ef\u4ee5\u9019\u6a23\u505a:\u9996\u5148\u628a\u6240\u6709$x_i$\u6e1b\u53bb\u6700\u5c0f\u7684$x$\u503c(\u4e5f\u5c31\u662f\u628a$x$\u9663\u5217\u5e73\u79fb\u5230\u975e\u8ca0\u5ea7\u6a19)\u3002\u9019\u6a23\u4e00\u4f86$BIT$\u7dad\u8b77\u76ee\u524d\u6709$r$\u500b\u9ede\u7684\u901f\u5ea6\u5c0f\u65bc\u7b49\u65bc$v$\uff0c\u4e14\u9019\u4e9b\u9ede\u7684$x$\u5ea7\u6a19\u548c\u70ba$p$\uff0c\u90a3\u9ebc\u7576\u6211\u5011\u8003\u616e$x_j$\u9019\u500b\u9ede\u7684\u6642\u5019(\u8981\u53bb\u627e\u6709\u591a\u5c11\u5728$x_j$\u4e4b\u524d\u7684\u9ede\u7684\u901f\u5ea6\u6bd4$x_j$\u7684\u901f\u5ea6\u5c0f)\uff0c\u53ea\u9700\u8981\u628a\u7b54\u6848\u52a0\u4e0a$r\\times x_j-p$\u5373\u53ef\u3002<\/p>\n

\u6ce8\u610f\uff0c\u672c\u984c$x$\u5ea7\u6a19\u6c92\u6709\u6392\u5e8f\uff0c\u8981\u81ea\u5df1\u5148\u6392\u5e8f\u904e\u3002
\n\u4e14\u9019\u984c\u6211\u7684\u7a0b\u5f0f\u78bc\u4e2d\u7684$PII$\u662f$pair<long\\ long,long\\ long>$<\/p>\n

\u7a0b\u5f0f\u78bc:<\/h3>\n
const int _n=2e5+10;  \nint t,n,minn=1e9;  \nVI vv;  \nPII s[_n];  \nnamespace BIT{  \n  int nn;PII t[_n];  \n  void update(int x,int val){while(x<=nn)t[x].fi+=val,t[x].se++,x+=(x&-x);}  \n  \/\/\u9019\u6a21\u677f\u662f1-base\uff0c\u800c\u4e14update\u662f\u628a\u4fee\u6539\u91cf\u52a0\u4e0a\u53bb  \n  PII query(int x){PII res={0,0};while(x>0){res.fi+=t[x].fi,res.se+=t[x].se,x-=(x&-x);}return res;}  \n  void init(int n_){nn=n_;}  \n}  \nmain(void) {cin.tie(0);ios_base::sync_with_stdio(0);  \n  cin>>n;rep(i,1,n+1){cin>>s[i].fi;minn=min(minn,s[i].fi);}rep(i,1,n+1){cin>>s[i].se;vv.pb(s[i].se);}  \n  sort(s+1,s+n+1);sort(all(vv));int nn=unique(all(vv))-vv.begin();  \n  rep(i,1,n+1)s[i].se=lower_bound(vv.begin(),vv.begin()+nn,s[i].se)-vv.begin()+1;  \n  rep(i,1,n+1)s[i].fi-=minn;  \n  BIT::init(nn); ll ans=0;  \n  rep(i,1,n+1){  \n    PII res=BIT::query(s[i].se);  \n    ans+=1ll*s[i].fi*res.se-res.fi;  \n    BIT::update(s[i].se,s[i].fi);  \n  }cout<<ans<<'\\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":[34,10,9,25,8,33],"class_list":["post-139","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-bit","tag-codeforce","tag-ojcode","tag-25","tag-8","tag-33"],"jetpack_publicize_connections":[],"yoast_head":"\nF. 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