{"id":164,"date":"2025-01-12T13:01:49","date_gmt":"2025-01-12T05:01:49","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=164"},"modified":"2025-01-12T13:01:49","modified_gmt":"2025-01-12T05:01:49","slug":"e-xor-on-segment-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81%e7%b7%9a%e6%ae%b5%e6%a8%b9","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=164","title":{"rendered":"E. XOR on Segment \u89e3\u6790(\u601d\u7dad\u3001\u7dda\u6bb5\u6a39)"},"content":{"rendered":"\n

Codeforce 242 E. XOR on Segment \u89e3\u6790(\u601d\u7dad\u3001\u7dda\u6bb5\u6a39)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF242E
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>
\n\u7d66\u4e00\u500b\u6578\u5217\uff0c\u6709\u5169\u7a2e\u64cd\u4f5c\uff0c\u5340\u9593\u548c\u67e5\u8a62\u6216\u8005\u662f\u5340\u9593\u5c0d\u67d0\u500b\u6578\u5b57$x$\u4f5cXOR\u3002<\/p>\n<\/blockquote>\n

\u524d\u8a00<\/h3>\n

\u9019\u984c\u883b\u9177\u7684
\n\"\"<\/p>\n

\u60f3\u6cd5<\/h3>\n

\u9996\u5148\u4e00\u958b\u59cb\u6703\u89ba\u5f97\u5c31\u662f\u7dda\u6bb5\u6a39\u6a21\u677f\u5957\u9032\u53bb\u5c31\u597d\uff0c\u4f46\u662f\u601d\u8003\u4e00\u4e0b\u5f8c\u6703\u767c\u73fe\u5340\u6bb5\u548c\u505aXOR\u548c\u500b\u5225\u6578\u5b57\u505aXOR\u518d\u52a0\u8d77\u4f86\u7684\u7d50\u679c\u4e0d\u4e00\u6a23\u3002
\n\u56e0\u6b64\u6211\u5011\u9700\u8981\u5c0d\u65bc\u6578\u5217\u4e2d\u6578\u5b57\u7684\u6bcf\u4e00\u500bbit\u90fd\u5efa\u4e00\u68f5\u7dda\u6bb5\u6a39\u3002\u5047\u8a2d\u73fe\u5728$a[i]$\u53ea\u6709\u4e00\u500bbit\uff0c\u90a3\u9ebc\u5c0d$1$\u53d6XOR\u548c\u53d6NOT\u662f\u4e00\u6a23\u7684\u3002\u800c\u6211\u5011\u5c0d$[l,r]$\u53d6XOR\u6642\uff0c$[l,r]$\u7684\u548c\u539f\u672c\u5982\u679c\u662f$k$\uff0c\u5c31\u6703\u8b8a\u6210$length-k$\uff0c\u4e5f\u5c31\u662f$r-l-k$\u3002\u5982\u6b64\u6211\u5011\u5c31\u6709\u8fa6\u6cd5\u5efa\u7dda\u6bb5\u6a39\u4e86(\u7dad\u8b77\u67d0\u500bbit\uff0c\u5728\u5340\u9593\u6709\u5e7e\u500b$1$)\u3002<\/p>\n

\u7a0b\u5f0f\u78bc:<\/h3>\n
const int _n=2e5+10;  \nint t,l,r,x,n,m,a[_n];  \nclass Seg{  \n  public:  \n  int nn;  \n  int t[_n<<2],laz[_n<<2];  \n  void pull(int v){t[v]=t[2*v+1]+t[2*v+2];}  \n  void apply(int v,int len){t[v]=len-t[v],laz[v]=(laz[v]?0:len);}  \n  void push(int v){  \n    if(laz[v])apply(2*v+1,laz[v]\/2),apply(2*v+2,laz[v]\/2+laz[v]%2),laz[v]=0;  \n  }  \n  void build(int v,int l,int r,int b){  \n    if(l+1==r)t[v]=((a[l]&(1<<b))>0);  \n    else{int m=(l+r)>>1;build(2*v+1,l,m,b),build(2*v+2,m,r,b);pull(v);}  \n  }  \n  void add(int v,int l,int r,int ql,int qr){  \n    if(r<=ql or qr<=l)return;  \n    else if(ql<=l and r<=qr)apply(v,r-l);  \n    else{  \n      push(v);int m=(l+r)>>1;  \n      add(2*v+1,l,m,ql,qr),add(2*v+2,m,r,ql,qr);  \n      pull(v);  \n    }  \n  }  \n  void add(int l,int r){add(0,0,nn,l,r);}  \n  void init(int n_,int b){nn=n_;build(0,0,nn,b);}  \n  int query(int v,int l,int r,int ql,int qr){  \n    if(r<=ql or l>=qr)return 0;  \n    if(ql<=l and qr>=r)return t[v];  \n    int m=(l+r)>>1,res;push(v);  \n    res=query(2*v+1,l,m,ql,qr)+query(2*v+2,m,r,ql,qr);  \n    pull(v);return res;  \n  }  \n};  \nSeg STs[21];  \nmain(void) {cin.tie(0);ios_base::sync_with_stdio(0);  \n  cin>>n;rep(i,0,n)cin>>a[i];  \n  rep(i,0,21)STs[i].init(n,i);  \n  cin>>m;while(m--){  \n    cin>>t;  \n    if(t==1){  \n      cin>>l>>r;l--;  \n      ll res=0;rep(i,0,21)res+=1ll*(STs[i].query(0,0,n,l,r))*(1<<i);  \n      cout<<res<<'\\n';  \n    }else{  \n      cin>>l>>r>>x;l--;  \n      rep(i,0,21)if(x&(1<<i))STs[i].add(l,r);  \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":[10,9,8,20],"class_list":["post-164","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-ojcode","tag-8","tag-20"],"jetpack_publicize_connections":[],"yoast_head":"\nE. 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