{"id":47,"date":"2025-01-11T22:56:52","date_gmt":"2025-01-11T14:56:52","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=47"},"modified":"2025-01-11T22:56:52","modified_gmt":"2025-01-11T14:56:52","slug":"d-bash-and-a-tough-math-puzzle-%e8%a7%a3%e6%9e%90%e7%b7%9a%e6%ae%b5%e6%a8%b9%e3%80%81%e6%95%b8%e8%ab%96","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=47","title":{"rendered":"D. Bash and a Tough Math Puzzle \u89e3\u6790(\u7dda\u6bb5\u6a39\u3001\u6578\u8ad6)"},"content":{"rendered":"\n

Codeforce 914 D. Bash and a Tough Math Puzzle \u89e3\u6790(\u7dda\u6bb5\u6a39\u3001\u6578\u8ad6)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF914D
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>
\n\u7d66\u4f60\u4e00\u500b\u9577\u5ea6\u70ba$n$\u7684\u6578\u5217$a$\uff0c\u6bcf\u6b21\u73a9\u5bb6\u6703\u9078\u64c7\u4e00\u500b\u5340\u9593\u731c$g.c.d.$\u7684\u503c\uff0c\u6216\u8005\u6539\u8b8a\u6578\u5217\u4e2d\u7684\u67d0\u500b\u6578\u5b57\u3002\u800c\u731c\u4e2d\u4e0d\u4e00\u5b9a\u8981\u5b8c\u5168\u6e96\u78ba\uff0c\u5982\u679c\u73a9\u5bb6\u80fd\u5920\u6539\u52d5\u4e00\u500b\u5340\u9593\u4e2d\u7684\u6578\u5b57\u8b93$g.c.d.$\u5b8c\u5168\u731c\u4e2d\u4e5f\u662f\u53ef\u4ee5\u7684\u3002<\/p>\n<\/blockquote>\n

\u524d\u8a00<\/h3>\n

\u6211\u5c0d\u7dda\u6bb5\u6a39\u9084\u662f\u4e0d\u719f\u963f\uff0c\u4e00\u958b\u59cb\u4e00\u76f4\u611f\u89ba$g.c.d.$\u6c92\u8fa6\u6cd5\u7528\u7dda\u6bb5\u6a39\u7dad\u8b77\u2026<\/p>\n

\u60f3\u6cd5<\/h3>\n

\u4e0a\u6a21\u677f\uff0c\u5f9e\u7dad\u8b77\u5340\u9593\u548c\u7684\u6a21\u677f\u6539\u6210\u7dad\u8b77$g.c.d.$(\u9019\u5c31\u662f\u70ba\u4ec0\u9ebc\u6211code\u4e2d\u7684\u5143\u7d20\u4fee\u6539\u51fd\u5f0f\u53eb\u505a$add$)\u3002
\n\u63a5\u8457\u6ce8\u610f\u5230\u4e00\u4ef6\u4e8b\uff0c\u731c\u4e2d\u7684\u689d\u4ef6\u662f:\u5047\u8a2d\u5340\u9593\u4e2d\u6709$k$\u500b\u6578\u5b57\uff0c\u53ea\u8981\u5176\u4e2d$k-1$\u500b\u6578\u5b57\u53ef\u4ee5\u88ab$val$($val\\stackrel{def}{=}$\u73a9\u5bb6\u731c\u7684\u6578\u5b57)\u6574\u9664\u5c31\u53ef\u4ee5\u4e86(\u5982\u679c\u9019$k-1$\u500b\u6578\u5b57\u7684$g.c.d.\\ge val$\uff0c\u90a3\u9ebc\u53ea\u8981\u628a\u6700\u5f8c\u90a3\u500b\u6578\u5b57\u6539\u6210$val$\u5c31\u597d)\u3002
\n\u4e00\u958b\u59cb\u6211\u5c31\u76f4\u63a5\u9019\u6a23\u5be6\u4f5c\uff0c\u6bcf\u6b21\u5f9e$root$\u958b\u59cb\u5f80\u4e0b\u627e\u6709\u5e7e\u500b\u6578\u5b57\u53ef\u4ee5\u88ab\u6574\u9664\uff0c\u6574\u500b\u5340\u9593\u90fd\u770b\u904e\u4ee5\u5f8c\u518d\u4f86\u6aa2\u67e5\u662f\u5426$\\ge k-1$\uff0c\u4f46\u662f\u767c\u73fe\u9019\u6a23\u6703TLE\u3002
\n\u67e5\u7db2\u8def\u5f8c\u767c\u73fe\u6211\u5011\u5fc5\u9808\u7528\u4e00\u500b\u5168\u57df\u8b8a\u6578\u53bb\u8a08\u7b97:\u6709\u591a\u5c11\u5728\u5340\u9593\u4e2d\u6578\u5b57\u4e0d\u53ef\u88ab\u6574\u9664\uff0c\u5982\u679c\u767c\u73fe\u6578\u91cf$>1$\u5c31\u8981\u99ac\u4e0a\u8df3\u96e2\u641c\u5c0b\uff0c\u5982\u6b64\u4e00\u4f86\u5c31\u4e0d\u6703TLE\u4e86\u3002
\n($almost$\u51fd\u5f0f\u662f\u9019\u984c\u7684\u91cd\u9ede\uff0c\u5beb\u6cd5\u548c\u6a21\u677f\u6709\u9ede\u5dee\u7570\uff0c\u8981\u5c0f\u5fc3\u5be6\u4f5c\u3002)<\/p>\n

\u7a0b\u5f0f\u78bc:<\/h3>\n
const int _n=5e5+10;  \nint n,a[_n],q,tt,tot=0;  \nnamespace Seg{  \n  int nn;  \n  int t[_n<<2];  \n  void pull(int v){t[v]=__gcd(t[2*v+1],t[2*v+2]);}  \n  void apply(int v, int val){t[v]=val;}  \n  void build(int v, int l, int r){  \n    if(l+1==r)t[v]=a[l];  \n    else{int m=(l+r)>>1;build(2*v+1,l,m),build(2*v+2,m,r);pull(v);}  \n  }  \n  void add(int v,int l,int r,int ql,int qr,int val){  \n    if(r<=ql or qr<=l)return;  \n    else if(ql<=l and r<=qr)apply(v,val);  \n    else{  \n      int m=(l+r)>>1;  \n      add(2*v+1,l,m,ql,qr,val),add(2*v+2,m,r,ql,qr,val);  \n      pull(v);  \n    }  \n  }  \n  void add(int pos,ll val){add(0,0,nn,pos,pos+1,val);}  \n  void init(int n_){nn=n_;build(0,0,nn);}  \n  void almost(int v,int l,int r,int ql,int qr,int val){  \n    if(tot>1)return;  \n    if(r<=ql or qr<=l)return;  \n    else if(ql<=l and r<=qr and t[v]%val==0)return;  \n    else{  \n      if(l+1==r){tot++;return;}  \n      int m=(l+r)>>1;  \n      almost(2*v+1,l,m,ql,qr,val),almost(2*v+2,m,r,ql,qr,val);  \n    }  \n  }  \n}  \nmain(void) {cin.tie(0);ios_base::sync_with_stdio(0);  \n  cin>>n;rep(i,0,n)cin>>a[i]; cin>>q;  \n  Seg::init(n);  \n  while(q--){  \n    cin>>tt;  \n    if(tt==1){  \n      int l,r,x;cin>>l>>r>>x;l--,r--;  \n      tot=0;Seg::almost(0,0,n,l,r+1,x);  \n      if(tot<=1)cout<<"YES\\n";  \n      else cout<<"NO\\n";  \n    }else{  \n      int i,y;cin>>i>>y;i--;  \n      Seg::add(i,y);  \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":[10,9,21,20],"class_list":["post-47","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-ojcode","tag-21","tag-20"],"jetpack_publicize_connections":[],"yoast_head":"\nD. 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