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Fast Succinct Trie
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Shunsuke Kanda
August 06, 2019
Research
1
720
Fast Succinct Trie
第七回StringBeginnersでの発表資料です。
Shunsuke Kanda
August 06, 2019
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Transcript
'BTU4VDDJODU5SJF @kampersanda 7th StringBeginners հจɿ ;IBOH -JN -FJT "OEFSTFO ,BNJOTLZ
,FFUPOBOE1BWMP 4V3'1SBDUJDBM3BOHF2VFSZ'JMUFSJOHXJUI'BTU4VDDJODU5SJF *O4*(.0% QQ
'BTU4VDDJODU5SJF '45 w ͷ4*(.0%ͰఏҊ͞Εͨ؆ܿ5SJFදݱ ;IBOHFUBM4V3'1SBDUJDBMSBOHFRVFSZpMUFSJOHXJUI GBTUTVDDJODUUSJFT4*(.0% 4VDDJODU3BOHF'JMUFS
4V3' ͷͨΊʹఏҊ͞Εͨ Ұൠతͳ༻్ʹ͑Δ w ࠓճͷൃද4V3'Ͱͳ͘'45ʹযΛͯͨͷͰ͢ w ͪͳΈʹ ච಄ஶऀ͞ΜʹΑΔΘ͔Γ͍͢εϥΠυ͕͏͢Ͱʹ͋Γ·͢ ‣ IUUQXXXDTDNVFEVdIVBODIFTMJEFT'45QEG ࠓճͷ୯७ʹͦΕΛͳͧͬͨͷͰͳ͍Ͱ͢ 2
5SJFࣙॻ w 5SJFͱҰݴͰݴͬͯɺٻΊΒΕΔૢ࡞͍Ζ͍Ζ w ࠓճ؆୯ʹҎԼͷΑ͏ͳૢ࡞͕Ͱ͖ΕΑ͠ͱ͠·͢ .FNCFS 4 ɿจࣈྻ4͕Ωʔͱؚͯ͠·Ε͍ͯΔ͔ʁ
1SFpY 4 ɿจࣈྻ4ͷ಄ࣙͱ࠷Ұக͢ΔΩʔʁ 3 .FNCFS Θͨ͠ :FT .FNCFS Θͨ͘͠ /P 1SFpY Θͨ͘͠ Θͨ ͨ Θ ʹ ͠ Έ ͨ Θ ͠
ͦͦ؆ܿ5SJFͬͯԿʁ 'BTU4VDDJODU5SJF '45 ͱʁ 5SJFࣙॻͱͯ͠ͷ'45ͷੑೳʁ
ͦͦ؆ܿ5SJFͬͯԿʁ 'BTU4VDDJODU5SJF '45 ͱʁ 5SJFࣙॻͱͯ͠ͷ'45ͷੑೳʁ
؆ܿ5SJFͱʁ w ใཧతԼݶʹ͍ۙϝϞϦྔͰ5SJFΛදݱ͢Δσʔλߏ OMHМ 0 O Ϗοτ ‣ OઅɺМΞϧϑΝϕοταΠζ
w ʮॱংͷ؆ܿදݱʯ ʮϥϕϧͷྻʯͰΑ͘දݱ͞ΕΔ w ̏ͭͷදతͳॱংͷ؆ܿσʔλߏ #1 #BMBODFE1BSFOUIFTFT %'6%4 %FQUI'JSTU6OBSZ%FHSFF4FRVFODF -06%4 -FWFM0SEFSFE6OBSZ%FHSFF4FRVFODF w ͪͳΈʹɺ 9#8N#POTBJͳͲ؆ܿ5SJFͰ͕͢ࠓճѻΘͳ͍Ͱ͢ 6 O P O CJUT OMPHМCJUT
#1 #BMBODFE1BSFOUIFTFT w ֤અΛ։ׅހ(ͱดׅހ)ͷϖΞͰදݱ ਂ͞༏ઌॱͰΛࠪ ߦ͖ͷ๚Ͱ(Λஔ͖ɺؼΓͷ๚Ͱ)Λஔ͘ 7
'JSTU$IJME QPT QPT /FYU4JCMJOH QPT 'JOE$MPTF QPT ( ( ( ) ( ( ) ( ) ) ) ( ( ( ) ) ) ) 'JOE$MPTFɿରԠ͢ΔดׅހͷҐஔ
%'6%4 %FQUI'JSTU6OBSZ%FHSFF4FRVFODF w #1ΑΓଟػೳͳׅހྻදݱ ਂ͞༏ઌॱͰΛࠪ ֤અʹ͍ͭͯɺͦͷࢠͱಉ͡ͷ(ͱ̍ݸͷ)Λஔ͘ ࠷ޙʹઌ಄ʹ(Λஔ͘
8 ( ( ( ) ( ( ) ) ( ( ) ) ) ( ) ( ) ) $IJME QPT J 'JOE$MPTF 4FMFDU) 3BOL) QPT J 3BOLb QPT ɿQPT·Ͱͷbͷ 4FMFDUb L ɿL൪ͷb͕ݱΕΔҐஔ 'JOE$MPTF
-06%4 -FWFM0SEFSFE6OBSZ%FHSFF4FRVFODF w ͜ͷੈͰͬͱγϯϓϧͳදݱʢྑ͍ҙຯͰʣ ෯༏ઌॱʹΛࠪ ֤અʹ͍ͭͯɺͦͷࢠͱಉ͡ͷ1ͱ̍ݸͷ0Λஔ͘ ࠷ޙʹઌ಄ʹ10Λஔ͘
9 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 'JSTU$IJME QPT 4FMFDU0 3BOL1 1PT /FYU4JCMJOH QPT QPT 3BOLb QPT ɿQPT·Ͱͷbͷ 4FMFDUb L ɿL൪ͷb͕ݱΕΔҐஔ 'JSTU$IJME
؆ܿ5SJFͷϨϏϡʔ 10 ػೳੑ ݕࡧ ࣮ #1 ̋ ˚ %'6%4
˕ ̋ -06%4 ˚ ˕ қ w Ұൠతʹɺࣙॻͱͯ͠ͷ5SJF಄ࣙݕࡧ͕Ͱ͖Εे w #1ͱ%'6%4Ϧον͗͢ΔͷͰ-06%4͕࠾༻͞ΕΔέʔε͕ଟ͍ 59ɺ69ɺ."3*4"ɺ'45ɺͳͲ w ͦͷลΓͷൺֱ࣮ݧ "SSPZVFMPFUBM4VDDJODUUSFFTJOQSBDUJDF"-&/&9 ాΒॱংͷ؆ܿදݱΛ༻͍ͨτϥΠࣙॻͷධՁॲશࠃ ࠓͱͳͬͯ ͦ͜·Ͱ͡Όͳ͍
ͦͦ؆ܿ5SJFͬͯԿʁ 'BTU4VDDJODU5SJF '45 ͱʁ 5SJFࣙॻͱͯ͠ͷ'45ͷੑೳʁ
ઃܭͷϞνϕʔγϣϯ w ࠜͷۙͷઅͱ༿ͷۙͷઅͰੑׂ࣭͕ҧ͏ 12 w ͪͳΈʹɺͦͷΑ͏ͳϞνϕʔγϣϯ౷తʹ͋Γ·͢ "35ɿઅͷ࣍ʹΑΓదͳσʔλߏΛબ #VSTU5SJF)"5ɿࠜۙͷઅΛ୯७ͳྻͰදݱ
."3*4"ɿࠜͷۙͷ3BOL4FMFDUͷԋࢉ݁ՌΛΩϟογϡ ૄ සൟʹΞΫηε͞ΕΔ େଟͷઅ͕ଐ͢Δ ͕େࣄʂ ϝϞϦޮ͕େࣄʂ ͨ Θ ʹ ͠ Έ ͨ Θ ͠ ີ
-06%4%4ɿೋछྨͷ-06%4Ͱදݱ 13 ਤจΑΓҾ༻ w ࠜۙߴͳ-06%4%FOTF w ༿ۙϝϞϦޮͷྑ͍-06%44QBSTF
-06%4%FOTF 14 - )$ ͨ Θ ʹ ͠ Έ ͨ
Θ ͠ - )$ ͨ Θ Θ ͨ ʹ - )$ ͠ ͠ Έ ˞ଟগɺ؆ུԽͯ͠·͢ w -ɿͦͷࢬϥϕϧΛ࣋ͭࢠ͕ଘࡏ͢Δ͔ʁ w )$ɿͦͷࢠ෦અ͔ʁ МޒेԻ w ֤෦અΛ͞Мͷ ϏοτϚοϓͰදݱ
-06%4%FOTF 15 - )$ ͨ Θ ʹ ͠ Έ ͨ
Θ ͠ - )$ ͨ Θ Θ ͨ ʹ - )$ ͠ ͠ Έ ॳظঢ়ଶɿQPT ʮΘͨ͠ʯͰݕࡧ ߋ৽ɿQPTQPT จࣈ ֬ೝɿ-<QPT>ͳΒࢠ͕ଘࡏ͠ɺ)$<QPT>ͳΒͦͷࢠ෦અ ભҠɿ$IJME1PT QPT Мº3BOL )$ QPT QPT М ˞ଟগɺ؆ུԽͯ͠·͢
-06%4%FOTF 16 ͨ Θ ʹ ͠ Έ ͨ Θ ͠
ͨ Θ Θ ͨ ʹ ͠ ͠ Έ QPT $IJME1PT ʮΘͨ͠ʯͰݕࡧ М ˞ଟগɺ؆ུԽͯ͠·͢ - )$ - )$ - )$ QPT ߋ৽ɿQPTQPT จࣈ ֬ೝɿ-<QPT>ͳΒࢠ͕ଘࡏ͠ɺ)$<QPT>ͳΒͦͷࢠ෦અ ભҠɿ$IJME1PT QPT Мº3BOL )$ QPT 3BOL )$ QPT
-06%4%FOTF 17 ͨ Θ ʹ ͠ Έ ͨ Θ ͠
ͨ Θ Θ ͨ ʹ ͠ ͠ Έ QPT $IJME1PT ʮΘͨ͠ʯͰݕࡧ М ˞ଟগɺ؆ུԽͯ͠·͢ - )$ - )$ - )$ QPT ߋ৽ɿQPTQPT จࣈ ֬ೝɿ-<QPT>ͳΒࢠ͕ଘࡏ͠ɺ)$<QPT>ͳΒͦͷࢠ෦અ ભҠɿ$IJME1PT QPT Мº3BOL )$ QPT 3BOL )$ QPT
-06%4%FOTF 18 ͨ Θ ʹ ͠ Έ ͨ Θ ͠
ͨ Θ Θ ͨ ʹ ͠ ͠ Έ QPT )$<QPT>ͳͷͰ༿ ʮΘͨ͠ʯͰݕࡧ М ˞ଟগɺ؆ུԽͯ͠·͢ - )$ - )$ - )$ QPT ߋ৽ɿQPTQPT จࣈ ֬ೝɿ-<QPT>ͳΒࢠ͕ଘࡏ͠ɺ)$<QPT>ͳΒͦͷࢠ෦અ ભҠɿ$IJME1PT QPT Мº3BOL )$ QPT
-06%44QBSTF 19 ͨ Θ
ʹ ͠ Έ ͨ Θ ͠ - ͨ Θ Θ ͨ ʹ ͠ ͠ Έ )$ 4 ˞ଟগɺ؆ུԽͯ͠·͢ w ݪཧతʹී௨ͷ-06%4ͱҰॹ w-ɿϥϕϧͷྻ w)$ɿͦͷઅ෦અ͔ʁ w4ɿͦͷઅஉ͔ʁʢݪཧతʹී௨ͷ-06%4ʣ
-06%44QBSTF 20 ʮΘͨ͠ʯͰݕࡧ
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-06%44QBSTF 21 ʮΘͨ͠ʯͰݕࡧ
- ͨ Θ Θ ͨ ʹ ͠ ͠ Έ )$ 4 ˞ଟগɺ؆ུԽͯ͠·͢ QPT $IJME1PT QPT ୳ࡧɿQPT -<QPT>จࣈ ͳQPT ֬ೝɿ)$<QPT>ͳΒͦͷࢠ෦અ ભҠɿ$IJME1PT QPT 4FMFDU 4 3BOL )$ QPT ͨ Θ ʹ ͠ Έ ͨ Θ ͠ 3BOL )$ QPT 4FMFDU 4
ͨ Θ ʹ ͠
Έ ͨ Θ ͠ -06%44QBSTF 22 ʮΘͨ͠ʯͰݕࡧ - ͨ Θ Θ ͨ ʹ ͠ ͠ Έ )$ 4 ˞ଟগɺ؆ུԽͯ͠·͢ QPT $IJME1PT ୳ࡧɿQPT -<QPT>จࣈ ͳQPT ֬ೝɿ)$<QPT>ͳΒͦͷࢠ෦અ ભҠɿ$IJME1PT QPT 4FMFDU 4 3BOL )$ QPT 3BOL )$ QPT 4FMFDU 4
-06%44QBSTF 23 ʮΘͨ͠ʯͰݕࡧ
- ͨ Θ Θ ͨ ʹ ͠ ͠ Έ )$ 4 ˞ଟগɺ؆ུԽͯ͠·͢ QPT )$<QPT>ͳͷͰ༿ ୳ࡧɿQPT -<QPT>จࣈ ͳQPT ֬ೝɿ)$<QPT>ͳΒͦͷࢠ෦અ ભҠɿ$IJME1PT QPT 4FMFDU 4 3BOL )$ QPT ͨ Θ ʹ ͠ Έ ͨ Θ ͠
'45ͷͦͷଞͷ w -06%4%FOTF4QBSTFͦΕͧΕʹదͳ3BOLࣙॻͷઃܭ w 4*.%ʹΑΔϥϕϧ୳ࡧͷߴԽ w ϓϦϑΣον໋ྩͷ׆༻ 24 ਤจΑΓҾ༻
ͦͦ؆ܿ5SJFͬͯԿʁ 'BTU4VDDJODU5SJF '45 ͱʁ 5SJFࣙॻͱͯ͠ͷ'45ͷੑೳʁ
'45ͷԠ༻ɿ3BOHF2VFSZ'JMUFSJOH w '453BOHF2VFSZ'JMUFSJOHͷҝͷσʔλߏͱͯ͠ఏҊ͞Εͨ 26 * $ % . & .
- ɿ*$"-1͔Β*$%.ͷؒʹؚ·ΕΔσʔλ͋Δʁ ղɿ:&4ʢ*$%&ͱ*$%.ʣ ɿ*$"-1͔Β*$%.ͷؒʹؚ·ΕΔσʔλʁ ղɿͭʢ*$%&ͱ*$%.ʣ w 4V3' 4VDDJODU3BOHF'JMUFS Ͱ'45ͷར༻ʹՃ͑ɺϢχʔΫͳ ඌࣙΛΓޡݕग़Λڐ͢͜ͱͰɺ#MPPN'JMUFSʹඖఢ͢ΔϝϞϦ༻ྔ Ͱ3BOHF2VFSZ'JMUFSJOHΛ࣮ݱ͢Δ
'45ͷੑೳʢจΑΓҾ༻ʣ w طଘͷ؆ܿ5SJFࣙॻͱൺͯ 27 ϏοτΛόΠτจࣈྻͱͯ͠ ϗετ໊Λͻͬ͘Γฦͯ͠ FH DPNHPPMHF!LBOEB UYUSJFγϯϓϧͳ-06%4 1%5ܦ࿏ղ
%'6%4
'45ͷੑೳʢจΑΓҾ༻ʣ w CJUJOUͰ-06%4%FOTFͷߩݙ͕େ͖͍ Ұ༷Ͱੜ͞Εͨσʔλ ͳͷͰ֤અͷࢠͷ͕ͱͯେ͖͍ 28 CBTFMJOF-06%44QBSTFͷΈ w
5SJFࣙॻͱͯͪ͠ΐͬͱಛघͳσʔληοτʁ w ࣗવݴޠͳͲσʔληοτͰͷੑೳͲ͏ͳͷʁ
5SJFࣙॻɺ࣮͠·ͨ͠ 29 w IUUQTHJUIVCDPNLBNQFSTBOEBGBTU@TVDDJODU@USJF
.FNPSZ6TBHF .J# '45 %"354$ 9$%"5
59 ."3*4" 1%5 4FBSDI5JNF NJDSPTFDRVFSZ '45 %"354$ 9$%"5 59 ."3*4" 1%5 .FNPSZ6TBHF .J# '45 %"354$ 9$%"5 59 ."3*4" 1%5 4FBSDI5JNF NJDSPTFDRVFSZ '45 %"354$ 9$%"5 59 ."3*4" 1%5 30 ࣮ݧʢຊޠʣ ϝϞϦ ݕࡧ *1"ࣙॻ .TUSJOHT BWFMFOHUI 8JLJλΠτϧ .TUSJOHT BWFMFOHUI
31 ࣮ݧʢ"TLJUJT`TEBUBTFUʣ .FNPSZ6TBHF .J# '45
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·ͱΊ w '45γϯϓϧͳ-06%4ͳվྑ w σʔλ͔ΒΔΑ͏ͳઅͷࢠͷ͕ͱͯଟ͍5SJFʹ ରͯ͠ɺ-06%4%FOTFͷߩݙ͕ͱͯେ͖͍ 3BOHFRVFSZpMUFSJOHͷͨΊͷσʔλߏͱͯ͠Α͍ w ҰํͰɺࣗવݴޠσʔλͳͲͰطଘͷ5SJFࣙॻͷํ͕ޮ͕
ྑͦ͞͏ ͔͠͠ͳ͕Βɺ-06%4%FOTFͱଞͷ5SJFࣙॻʢྫ͑ 1%5ͱ͔ʣΛΈ߹ΘͤΔͳͲͷํࡦߟ͑ΒΕͦ͏ 32