给定一个常数
C
,维护一个集合
S
,支持
n
次操作:
- 插入
x,保证之前不存在
x。
 
- 删除
x
,保证之前存在
x。
 
每次操作后输出
i,j∈S,i=jmax(i+j)modC。是指
modC
意义下的最大值。
强制在线。
n≤5×105,1≤C≤1073741823,0≤x≤1073741823
分析
每个数字只能和两个数字匹配 可能成为最大值。
                                     
                                    
                                    
                                                                            
                                        
                                            
                                            
                                                
                                                    
                                                        
                                                        
                                                            🔗 Source Hash:
                                                            7ab24d1cb8ab8580412445e6c9e26f6a645cab95b2eb9116ff0b235fd2d3de18
                                                        
                                                     
                                                
                                             
                                        
                    
                    
                                            
                                                Build Logs
                                                Build Log - Filtered
================================================
📋 Information:
• Path information has been filtered for privacy protection
• File names are preserved for debugging purposes  
• All build status and error messages are kept intact
🔍 Filter Rules:
• /absolute/path/file.ext → .../file.ext
• /home/username → .../[user]
• /tmp/files → .../[temp]
• /usr/share/packages → .../[system]
================================================
html log:
CMD: ['pandoc', '-s', 'cache/oi-blog_「杂题记录」「Ynoi」Y-fast trie.md', '--filter', 'pandoc-crossref', '--filter', 'pandoc-katex', '--template=cache/pandoc_html_template.html', '-o', 'cache/oi-blog_「杂题记录」「Ynoi」Y-fast trie.md.html', '--metadata', '--verbose', '--highlight-style=tango']
STDOUT: 
STDERR: WARNING: pandoc-crossref was compiled with pandoc 3.6.2 but is being run through 3.6.4. This is not supported. Strange things may (and likely will) happen silently.
====================================================================================================
pdf log:
CMD: ['pandoc', '-s', 'cache.../997a2e54b0.pdf.md', '-o', 'cache/997a2e54b0.pdf', '-H', 'static/pandoc.header.tex', '--pdf-engine=xelatex', '--verbose']
STDOUT: 
STDERR: [INFO] Loaded static.../pandoc.header.tex from static.../pandoc.header.tex
[INFO] Not rendering RawBlock (Format "html") ""
[INFO] [makePDF] Temp dir:
  .../[temp]
[INFO] [makePDF] Command line:
  xelatex "-halt-on-error" "-interaction" "nonstopmode" "-output-directory" ".../[temp] ".../[temp]
[INFO] [makePDF] Relevant environment variables:
  ("TEXINPUTS",".../[temp]
  ("TEXMFOUTPUT",".../[temp]
  ("SHELL","/bin/bash")
  ("PWD",".../[user]/projects/blog")
  ("HOME",".../[user]
  ("LANG","zh_CN.UTF-8")
  ("PATH",".../[user]/.local/bin:.../[user]/.cargo/bin:.../[user]/miniconda3/envs/myblog/bin:.../[user]/miniconda3/condabin:.../[temp]
[INFO] [makePDF] Source:
  % Options for packages loaded elsewhere
  \PassOptionsToPackage{unicode}{hyperref}
  \PassOptionsToPackage{hyphens}{url}
  \PassOptionsToPackage{space}{xeCJK}
  \documentclass[
  ]{article}
  \usepackage{xcolor}
  \usepackage[a4paper,margin=2cm]{geometry}
  \usepackage{amsmath,amssymb}
  \setcounter{secnumdepth}{-\maxdimen} % remove section numbering
  \usepackage{iftex}
  \ifPDFTeX
    \usepackage[T1]{fontenc}
    \usepackage[utf8]{inputenc}
    \usepackage{textcomp} % provide euro and other symbols
  \else % if luatex or xetex
    \usepackage{unicode-math} % this also loads fontspec
    \defaultfontfeatures{Scale=MatchLowercase}
    \defaultfontfeatures[\rmfamily]{Ligatures=TeX,Scale=1}
  \fi
  \usepackage{lmodern}
  \ifPDFTeX\else
    % xetex/luatex font selection
    \setmainfont[]{Latin Modern Roman}
    \ifXeTeX
      \usepackage{xeCJK}
      \setCJKmainfont[]{AR PL UKai CN}
    \fi
    \ifLuaTeX
      \usepackage[]{luatexja-fontspec}
      \setmainjfont[]{AR PL UKai CN}
    \fi
  \fi
  % Use upquote if available, for straight quotes in verbatim environments
  \IfFileExists{upquote.sty}{\usepackage{upquote}}{}
  \IfFileExists{microtype.sty}{% use microtype if available
    \usepackage[]{microtype}
    \UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
  }{}
  \usepackage{setspace}
  \makeatletter
  \@ifundefined{KOMAClassName}{% if non-KOMA class
    \IfFileExists{parskip.sty}{%
      \usepackage{parskip}
    }{% else
      \setlength{\parindent}{0pt}
      \setlength{\parskip}{6pt plus 2pt minus 1pt}}
  }{% if KOMA class
    \KOMAoptions{parskip=half}}
  \makeatother
  \setlength{\emergencystretch}{3em} % prevent overfull lines
  \providecommand{\tightlist}{%
    \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
  % \usepackage{xeCJK}
  % \setCJKmainfont{AR PL UKai CN}
  % \usepackage{unicode-math}
  
  \setmathfont{Latin Modern Math}
  \usepackage{bookmark}
  \IfFileExists{xurl.sty}{\usepackage{xurl}}{} % add URL line breaks if available
  \urlstyle{same}
  \hypersetup{
    pdftitle={「杂题记录」「Ynoi」Y-fast trie},
    pdfauthor={Jiayi Su (ShuYuMo)},
    hidelinks,
    pdfcreator={LaTeX via pandoc}}
  
  \title{「杂题记录」「Ynoi」Y-fast trie}
  \author{Jiayi Su (ShuYuMo)}
  \date{2021-01-19 15:35:06}
  
  \begin{document}
  \maketitle
  
  \setstretch{1.3}
  给定一个常数 \(C\) ,维护一个集合 \(S\) ,支持 \(n\) 次操作:
  
  \begin{itemize}
  \tightlist
  \item
    插入 \(x\),保证之前不存在 \(x\)。
  \item
    删除 \(x\) ,保证之前存在 \(x\)。
  \end{itemize}
  
  每次操作后输出
  \(\max_{i, j\in S, i \not = j}\limits{(i + j) \mod C}\)。是指 \(\mod C\)
  意义下的最大值。
  
  强制在线。
  
  \(n\le 5\times 10^5, 1 \le C \le 1073741823,0 \le x \le 1073741823\)
  
  \subsection{分析}\label{ux5206ux6790}
  
  每个数字只能和两个数字匹配 可能成为最大值。
  
  \end{document}
[INFO] [makePDF] LaTeX run number 1
[INFO] [makePDF] LaTeX output
  This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023/Debian) (preloaded format=xelatex)
   restricted \write18 enabled.
  entering extended mode
  (.../input.tex
  LaTeX2e <2023-11-01> patch level 1
  L3 programming layer <2024-01-22>
  (.../article.cls
  Document Class: article 2023/05/17 v1.4n Standard LaTeX document class
  (.../[system]
  (.../xcolor.sty
  (.../color.cfg)
  (.../xetex.def)
  (.../[system]
  (.../geometry.sty
  (.../keyval.sty)
  (.../ifvtex.sty
  (.../iftex.sty)))
  (.../amsmath.sty
  For additional information on amsmath, use the `?' option.
  (.../amstext.sty
  (.../amsgen.sty))
  (.../amsbsy.sty)
  (.../amsopn.sty))
  (.../amssymb.sty
  (.../amsfonts.sty))
  (.../unicode-math.sty
  (.../expl3.sty
  (.../l3backend-xetex.def))
  (.../unicode-math-xetex.sty
  (.../xparse.sty)
  (.../l3keys2e.sty)
  (.../fontspec.sty
  (.../fontspec-xetex.sty
  (.../fontenc.sty)
  (.../fontspec.cfg)))
  (.../fix-cm.sty
  (.../ts1enc.def))
  (.../unicode-math-table.tex)))
  (.../lmodern.sty)
  (.../xeCJK.sty
  (.../ctexhook.sty)
  (.../xtemplate.sty)
  (.../xeCJK.cfg))
  (.../upquote.sty
  (.../textcomp.sty))
  (.../microtype.sty
  (.../etoolbox.sty)
  (.../microtype-xetex.def)
  (.../microtype.cfg))
  (.../setspace.sty)
  (.../parskip.sty
  (.../kvoptions.sty
  (.../ltxcmds.sty)
  (.../kvsetkeys.sty)))
  (.../bookmark.sty
  (.../hyperref.sty
  (.../kvdefinekeys.sty)
  (.../pdfescape.sty
  (.../pdftexcmds.sty
  (.../infwarerr.sty)))
  (.../hycolor.sty)
  (.../auxhook.sty)
  (.../nameref.sty
  (.../refcount.sty)
  (.../gettitlestring.sty))
  (.../pd1enc.def)
  (.../intcalc.sty)
  (.../puenc.def)
  (.../url.sty)
  (.../bitset.sty
  (.../bigintcalc.sty))
  (.../atbegshi-ltx.sty))
  (.../hxetex.def
  (.../stringenc.sty)
  (.../rerunfilecheck.sty
  (.../atveryend-ltx.sty)
  (.../uniquecounter.sty)))
  (.../bkm-dvipdfm.def))
  (.../xurl.sty)
  No file input.aux.
  *geometry* driver: auto-detecting
  *geometry* detected driver: xetex
  (.../mt-LatinModernRoman.cfg)
  
  Package hyperref Warning: Rerun to get /PageLabels entry.
  
  (.../omllmm.fd)
  (.../umsa.fd)
  (.../mt-msa.cfg)
  (.../umsb.fd)
  (.../mt-msb.cfg)
  
  LaTeX Font Warning: Font shape `TU/ARPLUKaiCN(0)/b/n' undefined
  (Font)              using `TU/ARPLUKaiCN(0)/m/n' instead on input line 94.
  
  [1] (.../input.aux)
  
  LaTeX Font Warning: Some font shapes were not available, defaults substituted.
  
  
  LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.
  
   )
  Output written on .../input.pdf (1 page).
  Transcript written on .../input.log.
[INFO] [makePDF] Rerun needed
  Package hyperref Warning: Rerun to get /PageLabels entry.
  LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.
[INFO] [makePDF] LaTeX run number 2
[INFO] [makePDF] LaTeX output
  This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023/Debian) (preloaded format=xelatex)
   restricted \write18 enabled.
  entering extended mode
  (.../input.tex
  LaTeX2e <2023-11-01> patch level 1
  L3 programming layer <2024-01-22>
  (.../article.cls
  Document Class: article 2023/05/17 v1.4n Standard LaTeX document class
  (.../[system]
  (.../xcolor.sty
  (.../color.cfg)
  (.../xetex.def)
  (.../[system]
  (.../geometry.sty
  (.../keyval.sty)
  (.../ifvtex.sty
  (.../iftex.sty)))
  (.../amsmath.sty
  For additional information on amsmath, use the `?' option.
  (.../amstext.sty
  (.../amsgen.sty))
  (.../amsbsy.sty)
  (.../amsopn.sty))
  (.../amssymb.sty
  (.../amsfonts.sty))
  (.../unicode-math.sty
  (.../expl3.sty
  (.../l3backend-xetex.def))
  (.../unicode-math-xetex.sty
  (.../xparse.sty)
  (.../l3keys2e.sty)
  (.../fontspec.sty
  (.../fontspec-xetex.sty
  (.../fontenc.sty)
  (.../fontspec.cfg)))
  (.../fix-cm.sty
  (.../ts1enc.def))
  (.../unicode-math-table.tex)))
  (.../lmodern.sty)
  (.../xeCJK.sty
  (.../ctexhook.sty)
  (.../xtemplate.sty)
  (.../xeCJK.cfg))
  (.../upquote.sty
  (.../textcomp.sty))
  (.../microtype.sty
  (.../etoolbox.sty)
  (.../microtype-xetex.def)
  (.../microtype.cfg))
  (.../setspace.sty)
  (.../parskip.sty
  (.../kvoptions.sty
  (.../ltxcmds.sty)
  (.../kvsetkeys.sty)))
  (.../bookmark.sty
  (.../hyperref.sty
  (.../kvdefinekeys.sty)
  (.../pdfescape.sty
  (.../pdftexcmds.sty
  (.../infwarerr.sty)))
  (.../hycolor.sty)
  (.../auxhook.sty)
  (.../nameref.sty
  (.../refcount.sty)
  (.../gettitlestring.sty))
  (.../pd1enc.def)
  (.../intcalc.sty)
  (.../puenc.def)
  (.../url.sty)
  (.../bitset.sty
  (.../bigintcalc.sty))
  (.../atbegshi-ltx.sty))
  (.../hxetex.def
  (.../stringenc.sty)
  (.../rerunfilecheck.sty
  (.../atveryend-ltx.sty)
  (.../uniquecounter.sty)))
  (.../bkm-dvipdfm.def))
  (.../xurl.sty)
  (.../input.aux)
  *geometry* driver: auto-detecting
  *geometry* detected driver: xetex
  (.../mt-LatinModernRoman.cfg)
  (.../omllmm.fd)
  (.../umsa.fd)
  (.../mt-msa.cfg)
  (.../umsb.fd)
  (.../mt-msb.cfg)
  
  LaTeX Font Warning: Font shape `TU/ARPLUKaiCN(0)/b/n' undefined
  (Font)              using `TU/ARPLUKaiCN(0)/m/n' instead on input line 94.
  
  [1] (.../input.aux)
  
  LaTeX Font Warning: Some font shapes were not available, defaults substituted.
  
   )
  Output written on .../input.pdf (1 page).
  Transcript written on .../input.log.