Go1.19で採用された Pattern-defeating Quicksort の紹介

今回はPattern-defeating Quicksortの論文を読んでいき、Goでどのように実装されているか簡単に見ていく

Transcript

1. (PͰ࠾༻͞Εͨ
   1BUUFSOEFGFBUJOH2VJDLTPSUͷ঺հ
   )JSPNV/BLBNVSB !QPSJO
   
   1BUUFSOEFGFBUJOH2VJDLTPSUJO(P
   

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2. தଜ߂෢
   ΤϜεϦʔͷ"*ɾػցֶशνʔϜͷιϑτ΢ΣΞ
   ΤϯδχΞͰओʹݕࡧج൫पΓΛ୲౰͍ͯ͠Δɻ
   ֤छΞΧ΢ϯτQPSJOͰ΍ͬͯ·͢ɻ
   )*SPNV/BLBNVSB
   The Gopher was designed by Renée French
   

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3. *OUSPEVDUJPO
   

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4. ϦϦʔεϊʔυݟΔͱTPSUύοέʔδͷ಺෦ΞϧΰϦζϜ͕Կ΍Βมߋ͞ΕͨͬΆ͍
   (PͷTPSUύοέʔδͷมߋ
   
   

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5. ࣮ࡍʹTPSU[TPSUGVODHPͱTPSU[TPSUJOUFSGBDFHPʹͦΕͧΕQERTPSU@GVODɺQERTPSUͱ͍͏
   ؔ਺͕௥Ճ͞Ε͍ͯΔɻݺͼग़͍ͯ͠Δͷ͸TPSU4PSUͱTPSU4MJDF
   (PͷTPSUύοέʔδͷมߋ
   
   

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6. ࠓճ͸1BUUFSOEFGFBUJOH2VJDLTPSU<>
   ͷ࿦จΛಡΜͰ͍͖ɺ(PͰͲͷΑ͏ʹ࣮
   ૷͞Ε͍ͯΔ͔؆୯ʹݟ͍ͯ͘
   1BUUFSOEFGFBUJOH2VJDLTPSU
   [1] https://arxiv.org/abs/2106.05123
   

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7. 1BUUFSOEFGFBUJOH2VJDLTPSUͷͬ͘͟Γͱͨ͠ཧղ
   ূ໌ͳͲࡉ͔͍࿩͸εΩοϓͯ͠ͳΜͱͳ͘ԿΛ΍ͬͯΔͷ͔ͷཧղΛ໨ࢦ͢
   
   ͜ͷൃදͰಘΕΔ΋ͷ
   

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8. 1BUUFSOEFGFBUJOH2VJDLTPSU
   

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9. *OUSPTPSUͷ෮श
   1BUUFSOEFGFBUJOH2VJDLTPSU͸Πϯτϩιʔτͷվྑ൛ͳͷͰɺ؆୯ʹΠϯτϩιʔτΛ෮
   श͓͖ͯ͠·͢ɻ
   Πϯτϩιʔτ͸ۙ೥࠷΋࢖༻͞Ε͍ͯΔϋΠϒϦουιʔτΞϧΰϦζϜͰ͋Γɺૠೖιʔ
   τɺώʔϓιʔτɺΫΠοΫιʔτΛ૊Έ߹ΘͤͨϋΠϒϦουΞϧΰϦζϜͰ͢ɻ
   ώϡʔϦεςΟοΫͳํ๏Ͱɺ͍ͭͲͷઓུΛ࠾༻͢Δ͔Λܾఆ͠·͢ɻྫ͑͹ɺ࠶ؼͷਂ͞
   ͕ਂ͘ͳΓ͗͢Δͱώʔϓιʔτʹ੾Γସ͑ͨΓɺύʔςΟγϣϯͷαΠζ͕খ͘͞ͳΓ͗͢
   Δͱૠೖιʔτʹ੾Γସ͑ͨΓ͠·͢ɻ
   

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10. 1BUUFSOEFGFBUJOH2VJDLTPSU͸ΠϯτϩιʔτΛ֦ு͓Αͼվྑͨ͠΋ͷͰ͢ɻ
    ޙͰৄ͘͠આ໌͍͖ͯ͠·͕͢ɺ1BUUFSOEFGFBUJOH2VJDLTPSUͷ؊͸؆୯ʹݴ͏ͱ
    ύʔςΟγϣϯॲཧΛ͍͍ײ͡ʹͨ͠
    ࠷ѱέʔεΛ্ख͘ݕ஌ͯ͠ϑΥʔϧόοΫ͢ΔΑ͏ʹͨ͠
    ͷͭͰ͢ɻ
    1BUUFSOEFGFBUJOH2VJDLTPSU֓ཁ
    
    

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11. ॏෳΛؚΉ໿ཁૉͷγʔέϯεΛιʔτ͢Δ1BUUFSOEFGFBUJOH2VJDLTPSUͷࢹ֮Խɻ
    1BUUFSOEFGFBUJOH2VJDLTPSU֓ཁ
    
    

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12. 1BSUJUJPOJOH
    

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13. 1BUUFSOEFGFBUJOH2VJDLTPSU͸Φϥϯμࠃض໰୊ͷߟ͑ํ͕ϕʔεʹͳ͍ͬͯΔͷͰɺ·ͣ͸Φϥϯμ
    ࠃض໰୊Λ෮श͠·͢ɻ
    Φϥϯμࠃض໰୊͸ɺɺͷΈΛؚΉγʔέϯεΛಉ͡ཁૉͰύʔςΟγϣϯ͢Δ໰୊Ͱ͢ɻྫ͑͹Լ
    هͷJOΛPVUʹม׵͢Δ໰୊Ͱ͢ɻ
    
    
    JO
    PVU
    1BSUJUJPOJOH
    
    

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14. 1BSUJUJPOJOH
    
    ΞϧΰϦζϜ͸୯७Ͱઢܗ࣌ؒͰղ͚·͢ɻNJEͱMPXΛ഑ྻͷ࠷ॳͷཁૉͷJOEFYʹηοτ͠ɺIJHIΛ࠷
    ޙͷཁૉͷJOEFYʹηοτ͠·͢ɻ
    w ΋͠NJEͳΒMPXͱNJEͷཁૉΛSFQMBDFͯ͠IJHIͰσΫϦϝϯτ
    w ΋͠NJEͳΒNJEΛΠϯΫϦϝϯτ
    w ΋͠NJEͳΒIJHIͱNJEͷཁૉΛSFQMBDFͯ͠IJHIΛσΫϦϝϯτ
    

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15. 
    MPX
    NJE
    IJHI
    

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16. 
    MPX
    NJE
    IJHI
    
    MPX
    NJE
    IJHI
    NJEͳͷͰɺIJHIͱSFQMBDFͯ͠IJHI
    

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17. 
    MPX
    NJE
    IJHI
    
    MPX
    NJE
    IJHI
    
    MPX NJE IJHI
    NJEͳͷͰɺIJHIͱSFQMBDFͯ͠IJHI
    NJEͳͷͰɺNJE
    

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18. 
    MPX
    NJE
    IJHI
    
    MPX
    NJE
    IJHI
    
    MPX NJE IJHI
    
    MPX NJE IJHI
    NJEͳͷͰɺIJHIͱSFQMBDFͯ͠IJHI
    NJEͳͷͰɺNJE
    NJEͳͷͰɺMPXͱSFQMBDFͯ͠NJE MPX
    

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19. 
    MPX
    NJE
    IJHI
    
    MPX
    NJE
    IJHI
    
    MPX NJE IJHI
    
    MPX NJE IJHI
    
    MPX NJE IJHI
    NJEͳͷͰɺIJHIͱSFQMBDFͯ͠IJHI
    NJEͳͷͰɺNJE
    NJEͳͷͰɺMPXͱSFQMBDFͯ͠NJE MPX
    NJEͳͷͰɺMPXͱSFQMBDFͯ͠NJE MPX
    

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20. 
    MPX
    NJE
    IJHI
    
    MPX
    NJE
    IJHI
    
    MPX NJE IJHI
    
    MPX NJE IJHI
    
    MPX NJE IJHI
    
    MPX NJE
    IJHI
    NJEͳͷͰɺIJHIͱSFQMBDFͯ͠IJHI
    NJEͳͷͰɺNJE
    NJEͳͷͰɺMPXͱSFQMBDFͯ͠NJE MPX
    NJEͳͷͰɺMPXͱSFQMBDFͯ͠NJE MPX
    NJEͳͷͰɺNJE
    

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21. 
    MPX
    NJE
    IJHI
    
    MPX
    NJE
    IJHI
    
    MPX NJE IJHI
    
    MPX NJE IJHI
    
    MPX NJE IJHI
    
    MPX NJE
    IJHI
    MPX NJE
    IJHI
    
    NJEͳͷͰɺIJHIͱSFQMBDFͯ͠IJHI
    NJEͳͷͰɺNJE
    NJEͳͷͰɺMPXͱSFQMBDFͯ͠NJE MPX
    NJEͳͷͰɺMPXͱSFQMBDFͯ͠NJE MPX
    NJEͳͷͰɺNJE
    NJEͳͷͰɺIJHIͱSFQMBDFͯ͠IJHI
    NJE͕IJHIΛ௒͑ͨͷͰऴྃ
    

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22. 1BSUJUJPOJOHJO1BUUFSOEFGFBUJOH2VJDLTPSU
    
    
    
    
    ୯७ͳΫΠοΫιʔτͷ࣮૷Ͱ͸ɺ౳͍͠ൺֱཁૉΛಉ͡ύʔςΟγϣϯʹ഑ஔ͢Δ͜ͱʹ
    ΑΓϺ O?
    ͷ࠷ѱͷέʔε͕Ҿ͖ى͜͞Ε·͢ɻ
    ౳͍͠ཁૉΛޮ཰తʹॲཧ͢Δʹ͸ɺ౳͍͠ཁૉΛूΊͯɺͦΕΑΓେ͖͍ཁૉɺখ͍͞ཁ
    ૉͷ෼ׂʹͰ͖Ε͹ɺͦͷޙͷιʔτͰ౳͍͠ཁૉΛؚΉύʔςΟγϣϯͷιʔτΛε
    ΩοϓͰ͖·͢ɻ·͞ʹΦϥϯμࠃض໰୊ͱಉ౳ͷࡾ෼ׂͷߟ͑ํ͕࢖͑ͦ͏Ͱ͢ɻ
    ͜ͷΑ͏ʹύʔςΟγϣϯΛ෼ׂͰ͖Δͱخ͍͠
    
    

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23. 1BSUJUJPOJOHJO1BUUFSOEFGFBUJOH2VJDLTPSU
    
    ͜Ε·Ͱʹઆ໌ͨ͠Φϥϯμͷࠃض໰୊ͷղ๏Λ୯७ʹద༻͢Δͱɺ͢΂ͯͷཁૉΛεϫο
    ϓ͢ΔલʹϐϘοτͱ౳͍͔͠Ͳ͏͔Λ໌ࣔతʹνΣοΫ͢Δඞཁ͕͋Γ·͢ɻ͜Ε͸ɺ౳
    ͍͠ཁૉ͕ଟ਺ଘࡏ͢Δ͔Ͳ͏͔ʹؔ܎ͳ͘ൃੜ͠ɺฏۉతͳέʔεͰ͸ύϑΥʔϚϯε͕
    ௿Լ͠·͢ɻ
    ͜ͷ࿦จͰ͸͜ͷ໰୊ʹରॲ͢Δ৽͍͠ղܾࡦΛٞ࿦͓ͯ͠ΓɺLݸͷҟͳΔཁૉΛ࣋ͭೖ
    ྗʹରͯ͠0 OL
    ͷ࠷ѱέʔεʹऩ·Δख๏ΛఏҊ͍ͯ͠·͢ɻ1BUUFSOEFGFBUJOH
    2VJDLTPSUͰ͸͜ͷख๏ΛϕʔεʹΠϯτϩιʔτΛվྑ͍ͯ͠·͢ɻ
    

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24. 1BSUJUJPO-FGU3JHIU
    1
    1
    QBSUJUJPO@SJHIU
    QBSUJUJPO@MFGU
    1BUUFSOEFGFBUJOH2VJDLTPSU͸ͭͷύʔςΟγϣϯ༻ؔ਺Λ૊Έ߹ΘͤͯઌఔͷύʔςΟγϣϯ
    Λୡ੒͠·͢ɻͭ͸ϐϘοτQʹ౳͍͠ཁૉΛࠨͷύʔςΟγϣϯʹάϧʔϓԽ QBSUJUJPOMFGU
    
    
    ͠ɺ΋͏ͭ͸ϐϘοτʹ౳͍͠ཁૉΛӈͷύʔςΟγϣϯ QBSUJUJPOSJHIU
    
    ʹάϧʔϓԽ͠·͢ɻ
    ͜ͷύʔςΟγϣϯͷ૊Έํͷར఺͸ʮཁૉ͕ϐϘοτͷ஋Ҏ্͔Ͳ͏͔ʯͱ͍͏৚݅ҰݸͰ൑ఆͰ
    ͖Δ͜ͱͰ͢ɻ
    

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25. 1BUJUJPOJO(P
    (PͰ͸TPSUύοέʔδ಺ͷQBUJUJPOؔ਺͕ύʔςΟγϣϯΛ୲͏ɻ࣮ࡍʹؔ਺ΛFYQPSUͯ͠Ұճͩ
    ͚ಈ͔ͯ͠ΈΔͱ͔֬ʹQBUJUJPO@MFGUͷ݁ՌΛಘΒΕ͍ͯΔɻ
    

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26. 1BSUJUJPO-FGU3JHIU
    QBSUJUJPOؔ਺Λར༻ͯ͠࠶ؼతʹγʔέϯεΛύʔςΟγϣϯ͍͖ͯ͠·͢ɻ
    ྫ͑͹ԼهਤͷΑ͏ʹɺϐϘοτQͰЋΛύʔςΟγϣϯ͠ɺ࠶ؼతʹӈଆͷύʔςΟγϣϯΛϐ
    ϘοτRͱͯ͠ЌΛύʔςΟγϣϯ͍͖ͯ͠·͢ɻ
    Q͕Rʹ౳͘͠ͳ͍৔߹͸ɺ্هͷεςοϓΛ࠶ؼతʹద༻͠·͢ɻ࠷ऴతʹQRͱͳͬͨ࣌͸ɺಉ
    ͡஋ΛਅΜதʹूΊͨߏ੒ʹͰ͖͍ͯ·͢Լਤɻ
    ͪͳΈʹɺ͋Δ఺RͰЌ͕ۭʹͳͬͨ৔߹ɺQʹ౳͍͠ཁૉ͸ͳ͘ɺЋΛ࠷ॳʹ෼ׂͨ͠ͱ͖ʹ
    ෼ׂ͕ߦΘΕͨͱ݁࿦෇͚Δ͜ͱ͕Ͱ͖·͢ɻ
    

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27. https://www.youtube.com/watch?v=jz-PBiWwNjc ͔ΒҾ༻
    

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28. 1JWPU4FMFDUJPO
    

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29. +PIO5VLFZ`TOJOUIFS
    ϐϘοτͷબ୒ʹ͓͍ͯɺෆۉߧύʔςΟγϣϯॲཧΛආ͚ΔͨΊʹɺͳΔ΂͘தԝ஋Λબ୒͢Δ͜
    ͱ͕ཧ૝Ͱ͢ɻҰํͰେ͖ͳೖྗͷ৔߹͸ద੾ͳϐϘοτΛબ୒͢Δͷ͸ύϑΥʔϚϯεͷ໰୊͕ൃ
    ੜ͠·͢ɻͦ͜Ͱ͜ͷ࿦จͰ͸༗໊ͳ+PIO5VLFZ`TOJOUIFSͱ͍͏ख๏ͰϐϘοτΛબ୒͠·͢ɻ
    ݫີͳதԝ஋Λܭࢉ͢Δʹ͸͢΂ͯͷσʔλϙΠϯτΛอଘ͠ɺͦΕΒΛฒ΂ସ͑ͯதؒ஋Λબ୒͢
    Δඞཁ͕͋Γ·͕͢ɺ͜ͷํ๏Ͱ͋Ε͹ૉૣ͘େࡶ೺ͳதԝ஋ͷۙࣅ͕ಘΒΕ·͢ɻ
    

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30. +PIO5VLFZ`TOJOUIFSJO(P
    ࣮ࡍͷ(Pͷ࣮૷Ͱ͸ϐϘοτΛબ୒͢Δαϒγʔέϯεͷ௕͞ʹΑͬͯϐϘοτબ୒ํ๏Λ੾Γସ
    ͑·͢ɻ௕͕͞ҎԼͳΒ୯७ʹதԝ஋ΛͱΓɺҎԼͳΒ୯७ʹ࠷ॳɺதԝɺ࠷ޙͷͭͷ஋ͷத
    ԝ஋ΛͱΓɺҎ্ͳΒ+PIO5VLFZ`TOJOUIFSΛར༻͠·͢ɻ
    

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31. #BE1BUJUJPO
    

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32. #BE1BUJUJPO
    
    1BUUFSOEFGFBUJOH2VJDLTPSU͸ɺࢦఆͨ͠ϐϘοτύʔηϯλΠϧQ ೚ҙͷ஋
    ΑΓ΋ෆۉߧͳ෼ׂ
    ૢ࡞ΛෆྑύʔςΟγϣϯͱݺͼ·͢ ͪͳΈʹϐϘοτύʔηϯλΠϧQ͕ͩͱཧ૝త͸ύʔ
    ςΟγϣϯʹͳΓ·͢
    ɻྫ͑͹ԼهͷΑ͏ͳγʔέϯεͰϐϘοτύʔηϯλΠϧͷϙΠϯτ
    ࠓճ͸
    Λ࠾༻ͯ͠͠·͏ͱ΄ͱΜͲύʔςΟγϣϯ͕ػೳ͠·ͤΜɻ
    

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33. #BE1BUJUJPO
    
    :VWBM'JMNVT<>͸Qͷ࠷దͳέʔεͱൺֱͯ͠ΫΠοΫιʔτͷ଎౓௿ԼΛௐ΂·ͨ͠ɻ
    γϟϊϯͷ஋ΤϯτϩϐʔΛར༻ͯ͠ɺԼهͷΑ͏ͳάϥϑ͕ॻ͚·͢ɻ
    ͜ͷάϥϑ͔Βɺྫ͑͹Qͷ৔߹͚ͩͷ৔߹͸ɺཧ૝తͳ৔߹ͱൺ΂͚ͯͩ஗͘ͳΔ͜ͱ
    ͕Θ͔Γ·͢ɻQΛԼճΔͱύϑΥʔϚϯεͷ௿Լ͕ܹ͘͠ͳΔ͜ͱ΋Θ͔Γ·͢ɻ͜ͷͨΊɺ
    Qͷᮢ஋Λઃఆ͠ɺͦΕΑΓԼճΔෆྑύʔςΟγϣϯͷέʔε͕ଟ͚Ε͹ϑΥʔϧόοΫ͢Δઓུ
    ΛऔΓ·͢ɻ
    [3] https://cs.stackexchange.com/questions/31928/solving-recurrence-relation-with-two-recursive-calls/31930#31930
    

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34. #BE1BUJUJPO
    
    ෆྑύʔςΟγϣϯΛෳ਺ճૺ۰͢ΔͷΛճආ͢ΔͨΊʹԼهεςοϓΛߦ͍·͢ɻ
    w ࠷ॳʹɺΧ΢ϯλʔͱͯ͠MPH αϒγʔέϯε௕
    ʹઃఆ͠·͢
    w ෆྑύʔςΟγϣϯʹૺ۰͢ΔͨͼʹɺΧ΢ϯλʔΛσΫϦϝϯτ͠·͢
    w ࠶ؼݺͼग़͠ͷ։࢝࣌ʹΧ΢ϯλʔ͕ͷ৔߹ɺΫΠοΫιʔτͰ͸ͳ͘ɺώʔϓιʔτΛ࢖༻
    ࿦จͰ͸͜ͷϐϘοτύʔηϯλΠϧQͷᮢ஋Λͱ͓ͯ͠Γ(P΋ʹͳ͍ͬͯ·͢ɻ
    ͜ͷεΩʔϜͷར఺͸ɺΞʔΩςΫνϟ͕มߋ͞Εͨ৔߹ ώʔϓιʔτͷ୅ΘΓʹผͷ࠷ѱͷέʔε
    ͷιʔτΞϧΰϦζϜΛ࢖༻͍ͯ͠Δ৔߹ͳͲ
    ʹɺͦΕʹ߹ΘͤͯQΛௐ੔Ͱ͖Δ͜ͱͰ͢ (Pͷ৔
    ߹͸͕ϋʔυίʔυ͞Ε͍ͯͯมߋ͸Ͱ͖ͳ͍
    ɻ
    

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35. #BE1BUJUJPO
    
    (PͰ͸QERTPSUؔ਺ͷMJNJUҾ਺͕Χ΢ϯλʔ
    ʹ͋ͨΓɺ͜Ε͕ʹͳΔͱώʔϓιʔτʹ੾
    ΓସΘΓ·͢ɻ
    

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36. #BE1BUJUJPO
    
    ͪͳΈʹͪΐͬͱͨ͠޻෉ͱͯ͠Χ΢ϯλʔ͸γʔέϯεͷ௕͞ͷॴཁϏοτ਺ͱͯؒ͠
    ઀తʹMPH@ O
    Λܭࢉ͍ͯ͠Δɻ
    

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37. 1BUUFSOEFGFBUJOH2VJDLTPSUJO(P
    

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38. 1BUUFSOEFGFBUJOH2VJDLTPSUJO(P
    (Pʹ࣮૷͞Εͨ1BUUFSOEFGFBUJOH2VJDLTPSU͸࿦จͱൺ΂ͯԼهͷΑ͏ͳมߋ͕Ճ͑ΒΕͯ
    ͍·͢ɻ
    w #MPDL2VJDLTPSUΛ࢖ͬͨ࠷దԽΛແޮ কདྷ௥Ճ͞ΕΔՄೳੑ͸͋Γͦ͏
    
    w ϕϯνϚʔΫ݁Ռʹैͬͯɺ͍͔ͭ͘ͷύϥϝʔλʔΛมߋ
    

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39. (Pʹ͓͚ΔϕϯνϚʔΫ͸
    JTTVFͰఏग़͞Ε͍ͯ·͢ɻ΄ͱ
    ΜͲͷέʔεͰύϑΥʔϚϯε͕վળ͠
    ͍ͯ·͢ɻ
    

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40. $PODMVTJPO
    

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41. $PODMVTJPO
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42. ΤϜεϦʔͰ͸ࢸΔॴͰ(PΛ࠾༻ͯ͠։ൃΛ͍ͯ͠Δɻ΋ͪΖΜ(PΛ࣮຿Ͱ΍ͬͨ
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    1VTI௨஌ج൫
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    ͖͍ͨΞυόΠεʯ<>ͷྠಡձ΋։͔Ε͍ͯΔɻιϑτ΢ΣΞΤϯδχΞ͚ͩͰͳ
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    ΤϜεϦʔ͸(PͰ։ൃ͍ͨ͠ϝϯόʔΛืूத
    [3] https://www.amazon.co.jp/dp/4873119693/ref=cm_sw_em_r_mt_dp_G4Z5RYS2FDVTVWXVJEYS?_encoding=UTF8&psc=1
    

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43. (PͰ࠾༻͞Εͨ
    1BUUFSOEFGFBUJOH2VJDLTPSUͷ঺հ
    )JSPNV/BLBNVSB !QPSJO
    
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