Fast Succinct Trie

第七回StringBeginnersでの発表資料です。

Transcript

1. 'BTU4VDDJODU5SJF
   @kampersanda
   7th StringBeginners
   ঺հ࿦จɿ
   ;IBOH -JN -FJT "OEFSTFO ,BNJOTLZ ,FFUPOBOE1BWMP
   4V3'1SBDUJDBM3BOHF2VFSZ'JMUFSJOHXJUI'BTU4VDDJODU5SJF
   *O4*(.0% QQ
   

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2. 'BTU4VDDJODU5SJF '45
   
   w ೥ͷ4*(.0%ͰఏҊ͞Εͨ؆ܿ5SJFදݱ
   ;IBOHFUBM4V3'1SBDUJDBMSBOHFRVFSZpMUFSJOHXJUI
   GBTUTVDDJODUUSJFT4*(.0%
   4VDDJODU3BOHF'JMUFS 4V3'
   ͷͨΊʹఏҊ͞Εͨ
   Ұൠతͳ༻్ʹ΋࢖͑Δ
   w ࠓճͷൃද͸4V3'Ͱ͸ͳ͘'45ʹয఺Λ౰ͯͨ΋ͷͰ͢
   w ͪͳΈʹ
   ච಄ஶऀ͞ΜʹΑΔΘ͔Γ΍͍͢εϥΠυ͕΋͏͢Ͱʹ͋Γ·͢
   ‣ IUUQXXXDTDNVFEVdIVBODIFTMJEFT'45QEG
   ࠓճͷ͸୯७ʹͦΕΛͳͧͬͨ΋ͷͰ͸ͳ͍Ͱ͢
   2
   

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3. 5SJFࣙॻ
   w 5SJFͱҰݴͰݴͬͯ΋ɺٻΊΒΕΔૢ࡞͸͍Ζ͍Ζ
   w ࠓճ͸؆୯ʹҎԼͷΑ͏ͳૢ࡞͕Ͱ͖Ε͹Α͠ͱ͠·͢
   .FNCFS 4
   ɿจࣈྻ4͕Ωʔͱؚͯ͠·Ε͍ͯΔ͔ʁ
   1SFpY 4
   ɿจࣈྻ4ͷ઀಄ࣙͱ࠷௕Ұக͢ΔΩʔ͸ʁ
   3
   .FNCFS Θͨ͠
   :FT
   .FNCFS Θͨ͘͠
   /P
   1SFpY Θͨ͘͠
   Θͨ
   ͨ
   Θ ʹ
   ͠ Έ
   ͨ
   Θ
   ͠
   

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4. ͦ΋ͦ΋؆ܿ5SJFͬͯԿʁ
   'BTU4VDDJODU5SJF '45
   ͱ͸ʁ
   5SJFࣙॻͱͯ͠ͷ'45ͷੑೳ͸ʁ
   

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5. ͦ΋ͦ΋؆ܿ5SJFͬͯԿʁ
   'BTU4VDDJODU5SJF '45
   ͱ͸ʁ
   5SJFࣙॻͱͯ͠ͷ'45ͷੑೳ͸ʁ
   

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6. ؆ܿ5SJFͱ͸ʁ
   w ৘ใཧ࿦తԼݶʹ͍ۙϝϞϦྔͰ5SJFΛදݱ͢Δσʔλߏ଄
   OMHМ0 O
   Ϗοτ
   ‣ Oઅ਺ɺМΞϧϑΝϕοταΠζ
   w ʮॱং໦ͷ؆ܿදݱʯʮϥϕϧͷ഑ྻʯͰΑ͘දݱ͞ΕΔ
   w ̏ͭͷ୅දతͳॱং໦ͷ؆ܿσʔλߏ଄
   #1 #BMBODFE1BSFOUIFTFT
   
   %'6%4 %FQUI'JSTU6OBSZ%FHSFF4FRVFODF
   
   -06%4 -FWFM0SEFSFE6OBSZ%FHSFF4FRVFODF
   
   w ͪͳΈʹɺ
   9#8΍N#POTBJͳͲ΋؆ܿ5SJFͰ͕͢ࠓճ͸ѻΘͳ͍Ͱ͢
   6
   OP O
   CJUT OMPHМCJUT
   

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7. #1 #BMBODFE1BSFOUIFTFT
   
   w ֤અ఺Λ։ׅހ(ͱดׅހ)ͷϖΞͰදݱ
   ਂ͞༏ઌॱͰ໦Λ૸ࠪ
   ߦ͖ͷ๚໰Ͱ(Λஔ͖ɺؼΓͷ๚໰Ͱ)Λஔ͘
   7
   
   
   
   
   
   
   
   'JSTU$IJME QPT
   QPT
   /FYU4JCMJOH QPT
   'JOE$MPTF QPT
   
   ( ( ( ) ( ( ) ( ) ) ) ( ( ( ) ) ) )
   
   
   
   
   
   
   
   'JOE$MPTFɿରԠ͢ΔดׅހͷҐஔ
   

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8. %'6%4 %FQUI'JSTU6OBSZ%FHSFF4FRVFODF
   
   w #1ΑΓଟػೳͳׅހྻදݱ
   ਂ͞༏ઌॱͰ໦Λ૸ࠪ
   ֤અ఺ʹ͍ͭͯɺͦͷࢠͱಉ͡਺ͷ(ͱ̍ݸͷ)Λஔ͘
   ࠷ޙʹઌ಄ʹ(Λஔ͘
   8
   ( ( ( ) ( ( ) ) ( ( ) ) ) ( ) ( ) )
   
   
   
   
   
   
   
   
   
   
   
   
   $IJME QPT J
   'JOE$MPTF 4FMFDU)
   3BOL)
   QPT
   
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   QPT
   ɿQPT·Ͱͷbͷ਺
   4FMFDUb
   L
   ɿL൪໨ͷb͕ݱΕΔҐஔ
   'JOE$MPTF
   

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9. -06%4 -FWFM0SEFSFE6OBSZ%FHSFF4FRVFODF
   
   w ͜ͷੈͰ΋ͬͱ΋γϯϓϧͳ໦දݱʢྑ͍ҙຯͰʣ
   ෯༏ઌॱʹ໦Λ૸ࠪ
   ֤અ఺ʹ͍ͭͯɺͦͷࢠͱಉ͡਺ͷ1ͱ̍ݸͷ0Λஔ͘
   ࠷ޙʹઌ಄ʹ10Λஔ͘
   9
   1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0
   
   
   
   
   
   
   
   
   
   
   
   
   'JSTU$IJME QPT
   4FMFDU0
   3BOL1
   1PT
   
   
   /FYU4JCMJOH QPT
   QPT
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   QPT
   ɿQPT·Ͱͷbͷ਺
   4FMFDUb
   L
   ɿL൪໨ͷb͕ݱΕΔҐஔ
   'JSTU$IJME
   

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10. ؆ܿ5SJFͷϨϏϡʔ
    10
    ػೳੑ ݕࡧ଎౓ ࣮૷೉౓
    #1 ̋ ˚ ೉
    %'6%4 ˕ ̋ ೉
    -06%4 ˚ ˕ қ
    w Ұൠతʹɺࣙॻͱͯ͠ͷ5SJF͸઀಄ࣙݕࡧ͕Ͱ͖Ε͹े෼
    w #1ͱ%'6%4͸Ϧον͗͢ΔͷͰ-06%4͕࠾༻͞ΕΔέʔε͕ଟ͍
    59ɺ69ɺ."3*4"ɺ'45ɺͳͲ
    w ͦͷลΓͷൺֱ࣮ݧ
    "SSPZVFMPFUBM4VDDJODUUSFFTJOQSBDUJDF"-&/&9
    ໼ాΒॱং໦ͷ؆ܿදݱΛ༻͍ͨτϥΠࣙॻͷධՁ৘ॲશࠃ
    ࠓͱͳͬͯ͸
    ͦ͜·Ͱ໰୊͡Όͳ͍
    

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11. ͦ΋ͦ΋؆ܿ5SJFͬͯԿʁ
    'BTU4VDDJODU5SJF '45
    ͱ͸ʁ
    5SJFࣙॻͱͯ͠ͷ'45ͷੑೳ͸ʁ
    

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12. ઃܭͷϞνϕʔγϣϯ
    w ࠜͷ෇ۙͷઅ఺ͱ༿ͷ෇ۙͷઅ఺Ͱ͸ੑ࣭΍໾ׂ͕ҧ͏
    12
    w ͪͳΈʹɺͦͷΑ͏ͳϞνϕʔγϣϯ͸఻౷తʹ͋Γ·͢
    "35ɿઅ఺ͷ࣍਺ʹΑΓద੾ͳσʔλߏ଄Λબ୒
    #VSTU5SJF)"5ɿࠜ෇ۙͷઅ఺Λ୯७ͳ഑ྻͰදݱ
    ."3*4"ɿࠜͷ෇ۙͷ3BOL4FMFDUͷԋࢉ݁ՌΛΩϟογϡ
    ૄ
    සൟʹΞΫηε͞ΕΔ
    େଟ਺ͷઅ఺͕ଐ͢Δ
    ଎౓͕େࣄʂ
    ϝϞϦޮ཰͕େࣄʂ
    ͨ
    Θ ʹ
    ͠ Έ
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    ີ
    

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13. -06%4%4ɿೋछྨͷ-06%4Ͱදݱ
    13
    ਤ͸࿦จΑΓҾ༻
    w ࠜ෇ۙ͸ߴ଎ͳ-06%4%FOTF
    w ༿෇ۙ͸ϝϞϦޮ཰ͷྑ͍-06%44QBSTF
    

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14. -06%4%FOTF
    14
    -
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    ˞ଟগɺ؆ུԽͯ͠·͢
    w -ɿͦͷࢬϥϕϧΛ࣋ͭࢠ͕ଘࡏ͢Δ͔ʁ
    w )$ɿͦͷࢠ͸಺෦અ఺͔ʁ
    МޒेԻ
    w ֤಺෦અ఺Λ௕͞Мͷ
    ϏοτϚοϓͰදݱ
    
    
    
    

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15. -06%4%FOTF
    15
    -
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    ॳظঢ়ଶɿQPT
    ʮΘͨ͠ʯͰݕࡧ
    ߋ৽ɿQPTQPTจࣈ
    ֬ೝɿ-ͳΒࢠ͕ଘࡏ͠ɺ)$ͳΒͦͷࢠ͸಺෦અ఺
    ભҠɿ$IJME1PT QPT
    Мº3BOL )$ QPT
    
    QPT
    
    
    
    М
    ˞ଟগɺ؆ུԽͯ͠·͢
    
    
    
    

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16. -06%4%FOTF
    16
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    ߋ৽ɿQPTQPTจࣈ
    ֬ೝɿ-ͳΒࢠ͕ଘࡏ͠ɺ)$ͳΒͦͷࢠ͸಺෦અ఺
    ભҠɿ$IJME1PT QPT
    Мº3BOL )$ QPT
    
    
    
    
    3BOL )$ QPT
    
    

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17. -06%4%FOTF
    17
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    ߋ৽ɿQPTQPTจࣈ
    ֬ೝɿ-ͳΒࢠ͕ଘࡏ͠ɺ)$ͳΒͦͷࢠ͸಺෦અ఺
    ભҠɿ$IJME1PT QPT
    Мº3BOL )$ QPT
    
    
    
    
    3BOL )$ QPT
    
    

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18. -06%4%FOTF
    18
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    )$ͳͷͰ༿
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    ֬ೝɿ-ͳΒࢠ͕ଘࡏ͠ɺ)$ͳΒͦͷࢠ͸಺෦અ఺
    ભҠɿ$IJME1PT QPT
    Мº3BOL )$ QPT
    
    
    
    
    

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19. -06%44QBSTF
    19
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    ˞ଟগɺ؆ུԽͯ͠·͢
    w ݪཧతʹ͸ී௨ͷ-06%4ͱҰॹ
    w-ɿϥϕϧͷ഑ྻ
    w)$ɿͦͷઅ఺͸಺෦અ఺͔ʁ
    w4ɿͦͷઅ఺͸௕உ͔ʁʢݪཧతʹී௨ͷ-06%4ʣ
    

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20. -06%44QBSTF
    20
    ʮΘͨ͠ʯͰݕࡧ
    
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    ୳ࡧɿQPT -จࣈ
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    ભҠɿ$IJME1PT QPT
    4FMFDU 4 3BOL )$ QPT
    
    
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    ॳظঢ়ଶɿQPT QPT
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    ͠ Έ
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21. -06%44QBSTF
    21
    ʮΘͨ͠ʯͰݕࡧ
    
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    ˞ଟগɺ؆ུԽͯ͠·͢
    QPT $IJME1PT
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22. ͨ
    
    
    
    
    
    
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    22
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    ˞ଟগɺ؆ུԽͯ͠·͢
    QPT $IJME1PT
    ୳ࡧɿQPT -จࣈ
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    ભҠɿ$IJME1PT QPT
    4FMFDU 4 3BOL )$ QPT
    
    
    3BOL )$ QPT
    4FMFDU 4
    
    

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23. -06%44QBSTF
    23
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    ˞ଟগɺ؆ུԽͯ͠·͢
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24. '45ͷͦͷଞͷ޻෉
    w -06%4%FOTF4QBSTFͦΕͧΕʹద੾ͳ3BOLࣙॻͷઃܭ
    w 4*.%ʹΑΔϥϕϧ୳ࡧͷߴ଎Խ
    w ϓϦϑΣον໋ྩͷ׆༻
    24
    ਤ͸࿦จΑΓҾ༻
    

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25. ͦ΋ͦ΋؆ܿ5SJFͬͯԿʁ
    'BTU4VDDJODU5SJF '45
    ͱ͸ʁ
    5SJFࣙॻͱͯ͠ͷ'45ͷੑೳ͸ʁ
    

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26. '45ͷԠ༻ɿ3BOHF2VFSZ'JMUFSJOH
    w '45͸3BOHF2VFSZ'JMUFSJOHͷҝͷσʔλߏ଄ͱͯ͠ఏҊ͞Εͨ
    26
    *
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    w 4V3' 4VDDJODU3BOHF'JMUFS
    Ͱ͸'45ͷར༻ʹՃ͑ɺϢχʔΫͳ઀
    ඌࣙΛ࡟Γޡݕग़Λڐ͢͜ͱͰɺ#MPPN'JMUFSʹඖఢ͢ΔϝϞϦ࢖༻ྔ
    Ͱ3BOHF2VFSZ'JMUFSJOHΛ࣮ݱ͢Δ
    

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27. '45ͷੑೳʢ࿦จΑΓҾ༻ʣ
    w طଘͷ؆ܿ5SJFࣙॻͱൺ΂ͯ
    27
    Ϗοτ੔਺ΛόΠτจࣈྻͱͯ͠ ϗετ໊Λͻͬ͘Γฦͯ͠
    FH DPNHPPMHF!LBOEB
    UYUSJFγϯϓϧͳ-06%4
    1%5ܦ࿏෼ղ%'6%4
    

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28. '45ͷੑೳʢ࿦จΑΓҾ༻ʣ
    w CJUJOUͰ͸-06%4%FOTFͷߩݙ͕େ͖͍
    Ұ༷෼෍Ͱੜ੒͞Εͨ੔਺σʔλ
    ͳͷͰ֤અ఺ͷࢠͷ਺͕ͱͯ΋େ͖͍
    28
    CBTFMJOF-06%44QBSTFͷΈ
    w 5SJFࣙॻͱͯ͠͸ͪΐͬͱಛघͳσʔληοτʁ
    w ࣗવݴޠͳͲσʔληοτͰͷੑೳ͸Ͳ͏ͳͷʁ
    

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29. 5SJFࣙॻɺ࣮૷͠·ͨ͠
    29
    w IUUQTHJUIVCDPNLBNQFSTBOEBGBTU@TVDDJODU@USJF
    

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30. .FNPSZ6TBHF .J#
    
    
    
    
    
    
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    30
    ࣮ݧʢ೔ຊޠʣ
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    *1"ࣙॻ .TUSJOHT BWFMFOHUI
    
    8JLJλΠτϧ .TUSJOHT BWFMFOHUI
    
    

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31. 31
    ࣮ݧʢ"TLJUJT`TEBUBTFUʣ
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