New Order in Cascade Sorting Order

by Hajime Mugishima

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/FX0SEFSJO$BTDBEF4PSUJOH0SEFS ϑϩϯτΤϯυΧϯϑΝϨϯε๺ւಓ )BKJNF.VHJTIJNB$ZCP[V*OD

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!NVHJ@VOP )BKJNF.VHJTIJNB $ZCP[V*OD 'SPOUFOE&YQFSU5FBN

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$BTDBEF4PSUJOH0SEFSͱ͸

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$BTDBEF4PSUJOH0SEFS w $BTDBEFʹؔ͢Δ࢓༷͸ɺ $44$BTDBEJOHBOE*OIFSJUBODFʹఆٛ͞Ε͍ͯΔ ݱࡏͷקࠂ͸-FWFM IUUQTXXXXPSH53DTTDBTDBEF w ͦͷதͰ΋ɺద༻͞ΕΔ༏ઌॱҐʹؔ͢Δ࢓༷͕ $BTDBEF4PSUJOH0SEFSͱͯ͠ఆٛ͞Ε͍ͯΔ

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͜Μͳײ͡ͷཧղͰ͸ʁͱ͍͏Πϝʔδ

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ৄࡉ౓ w $44ηϨΫλ͸ৄࡉ౓Ͱ༏ઌॱҐ͕ܾ·Δ w ηϨΫλ͸*%ˠΫϥεˠཁૉͷॱʹ༏ઌ͞ΕΔ w ৄࡉ౓͕ಉ͡৔߹ɺ࠷ޙʹએݴ͞Εͨ΋ͷ͕উͭ

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TUZMFଐੑ w TUZMFଐੑͰཁૉʹ௚઀ελΠϧΛࢦఆͰ͖Δ w ৄࡉ౓ͰͷελΠϧΑΓ΋༏ઌ͞ΕΔ

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JNQPSUBOU w JNQPSUBOUΛ࢖͑͹ࡉ͔͍͜ͱ͸ແࢹͯ͠࠷ڧʹͳΕΔ w ୭͠΋͕Ͳ͔͜Ͱʮؾܰʹ࢖͏ͳʯͱݴΘΕͨΑ͏ͳؾ͕͢Δ

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͜͜·Ͱ͸஌ͬͯΔʂ

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࢓༷Λ۷ΓԼ͛Δͱ ஌Βͳ͍෦෼͕͋ͬͨΓ͢Δ

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͞Βʹɺ$BTDBEF4PSUJOH0SEFSʹ ؔ࿈͢Δ࢓༷͸૿͍͑ͯΔ

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ͨͱ͑͹ʜ w JNQPSUBOUͰ΋্ॻ͖Ͱ͖ͳ͍ελΠϧ͸ଘࡏ͢Δʁ w $BTDBEF-BZFSTͱ4DPQFE4UZMF͸ͲͪΒ͕༏ઌ͞ΕΔʁ w 4UZMFଐੑͱ$BTDBEF-BZFSTɺͲͪΒ͕༏ઌ͞ΕΔʁ w $BTDBEF-BZFSTͷԼҐϨΠϠͰJNQPSUBOUΛ࢖͏ͱͲ͏ͳΔʁ w ৄࡉ౓͕ಉ͡৔߹ɺ4DPQFE4UZMF͸Ͳ͏ద༻͞ΕΔʁ

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$BTDBEF4PSUJOH0SEFSΛ࠶ֶश͠Α͏ʂ

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ैདྷͷ$BTDBEF4PSUJOH0SEFSͷ͓͞Β͍

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$BTDBEF4PSUJOH0SEFS $44$BTDBEJOHBOE*OIFSJUBODF-FWFM 0SJHJOBOE*NQPSUBODF $POUFYU 4QFDJ fi DJUZ 0SEFSPG"QQFBSBODF

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0SJHJOBOE*NQPSUBODF w 0SJHJOˠ$44ͷىݯఆٛݩ w 6TFS"HFOUϒϥ΢β͕࣋ͭ$44 w 6TFSϢʔβʔελΠϧγʔτ ˢΑΓ༏ઌʣ w "VUIPSϖʔδఏڙͷ$44 ˢΑΓ༏ઌʣ w *NQPSUBODFˠJNQPSUBOU෇༩ͷ༗ແ w JNQPSUBOU͕ڧ͍ͷ͸ɺ0SJHJOBOE*NQPSUBODF͕ $BTDBEF4PSUJOH0SEFSͷઌ಄ʹଘࡏ͍ͯ͠ΔͨΊ

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0SJHJOBOE*NQPSUBODF w JNQPSUBOU͸0SJHJOʹ΋ӨڹΛड͚Δ w *NQPSUBOU6TFS"HFOUϒϥ΢β͕࣋ͭ$44ʢˣΑΓ༏ઌʣ w *NQPSUBOU6TFSϢʔβʔελΠϧγʔτʢˣΑΓ༏ઌʣ w *NQPSUBOU"VUIPSϖʔδఏڙͷ$44 w ࣮͸ɺϒϥ΢β͕࣋ͭJNQPSUBOU෇༩ͷελΠϧ͸্ॻ͖Ͱ͖ͳ͍

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$POUFYU w 4IBEPX%0.ͷએݴ͸ৄࡉ౓ΑΓ༏ઌ͞ΕΔ

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$POUFYU w IPTU ٖࣅΫϥεͰ಺෦͔Β4IBEPX)PTUελΠϧʹׯবͰ͖Δ ˠ௨ৗ͸֎෦Ͱͷએݴ͕༏ઌ͞ΕΔ ௨ৗˠ֎෦ελΠϧ͕༏ઌ

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$POUFYU w IPTU ͱJNQPSUBOUΛ૊Έ߹ΘͤΔͱ༏ઌॱҐ͕ٯస ˠ4IBEPX%0.֎෦͔Β্ॻ͖ෆՄʹͳΔ JNQPSUBOUʹΑΓٯస͢Δ

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4QFDJGJDJUZ w $44ৄࡉ౓ ৄࡉ౓ࣗମͷઆ໌͸ׂѪ͠·͢ʣ w -FWFMͷ৔߹ɺTUZMFBUUSJCVUFʹ͍ͭͯ΋͜͜Ͱݴٴ͞Ε͍ͯΔ IUUQTXXXXPSH53DTTDBTDBEFDBTDBEFTQFDJ fi DJUZ %FFQ-຋༁ ͜ͷεςοϓͰ͸ɺελΠϧɾϧʔϧʹଐ͞ͳ͍એݴʢελΠϧଐੑͷ಺༰ͳͲʣ͸ɺ ͲͷηϨΫλΑΓ΋ߴ͍ಛҟੑΛ࣋ͭͱݟͳ͞Ε·͢ɻ

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4QFDJGJDJUZ w ༨ஊXIFSF ٖࣅΫϥε w ࢦఆ͞ΕͨηϨΫλͷৄࡉ౓͸ڧ੍తʹʹͳΔ w ༏ઌॱҐͷ੍ޚʹ͓͍ͯ͸ॏཁͳͷͰ཈͓͑ͯ͘ͱྑ͍ ৄࡉ౓

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0SEFSPG"QQFBSBODF w ͜͜·Ͱͷ͢΂ͯͰ֬ఆ͠ͳ͔ͬͨ৔߹ɺ ࠷ޙʹએݴ͞Εͨ΋ͷ͕উͭ

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$44$BTDBEJOHBOE*OIFSJUBODF -FWFMˠ-FWFM ˞&EJUPST%SBGU

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0SJHJOBOE*NQPSUBODF $POUFYU 5IF4UZMF"UUSJCVUF -BZFST 4QFDJ fi DJUZ 4DPQF1SPYJNJUZ 0SEFSPG"QQFBSBODF $BTDBEF4PSUJOH0SEFS $44$BTDBEJOHBOE*OIFSJUBODF-FWFM

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-BZFST5IF4UZMF"UUSJCVUF

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$BTDBEF-BZFST!MBZFS w 0SJHJO͓Αͼ$POUFYUͷதͰϨΠϠʔ ֊૚ Λ࡞ΕΔ w ΑΓޙͰએݴ͞ΕͨϨΠϠʔͷελΠϧ͕༏ઌ͞ΕΔ w Ϟμϯϒϥ΢βͷ࠷৽҆ఆ൛Ͱ͋Ε͹ར༻Մೳ #BTFMJOF

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҉໧ͷ-BZFS w ໌ࣔతʹ-BZFSʹؚΊ͍ͯͳ͍ελΠϧ ैདྷͷελΠϧ ͸ɺ҉໧తʹଘࡏ͢Δ࠷ऴϨΠϠʔʹ௥Ճ͞ΕΔ w -BZFSΛར༻͍ͯ͠ͳ͍ελΠϧ͸ɺར༻͍ͯ͠ΔελΠϧΑΓڧ͍

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4UZMF"UUSJCVUFͱ$BTDBEF-BZFST w TUZMFଐੑʹΑΔࢦఆ͸ϨΠϠʔͷελΠϧΑΓ༏ઌ͞ΕΔ w $BTDBEF4PSUJOH0SEFS্Ͱ͸TUZMFଐੑ͸ 5IF4UZMF"UUSJCVUFͱͯ͠ѻΘΕΔΑ͏ʹͳΓɺ 4UZMF"UUSJCVUFˠ$BTDBEF-BZFSTˠ4QFDJ fi DJUZͷॱং͕໌֬ʹ

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$BTDBEF-BZFSTͱJNQPSUBOU w JNQPSUBOU·͓ͨલ͔ w JNQPSUBOU͕෇༩͞Ε͍ͯΔએݴ͸-BZFSͷ༏ઌ౓͕ٯస͢Δ ઌʹએݴ͞Εͨ -BZFSͷελΠϧ͕༏ઌ

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$BTDBEF-BZFSTͱJNQPSUBOU w JNQPSUBOU·͓ͨલ͔ w JNQPSUBOU͕෇༩͞Ε͍ͯΔએݴ͸-BZFSͷ༏ઌ౓͕ٯస͢Δ ςετදࣔ༻λΠτϧ΋ ҉໧ϨΠϠʔͳͷͰ উͯͳ͘ͳͬͪΌͬͨʜ

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0SJHJOBOE*NQPSUBODF $POUFYU 5IF4UZMF"UUSJCVUF -BZFST 4QFDJ fi DJUZ 4DPQF1SPYJNJUZ 0SEFSPG"QQFBSBODF TUZMFଐੑ JNQPSUBOU એݴ͕ઌͷϨΠϠʔ JNQPSUBOU એݴ͕ޙͷϨΠϠʔ JNQPSUBOU ҉໧ϨΠϠʔ JNQPSUBOU TUZMFଐੑ ҉໧ϨΠϠʔ એݴ͕ޙͷϨΠϠʔ એݴ͕ઌͷϨΠϠʔ $BTDBEF4PSUJOH0SEFS۷ΓԼ͛ͨΠϝʔδ

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4DPQF1SPYJNJUZ

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4DPQFE4UZMF!TDPQF w !TDPQFͰ4DPQFE4UZMFείʔϓ෇͖ελΠϧΛએݴͰ͖Δ w %0.πϦʔ಺ͷҰ෦ൣғʹݶఆͯ͠ελΠϧΛద༻͢Δ w ࣌఺Ͱ͸'JSFGPYҎ֎ͷ ࠷৽ϝδϟʔϒϥ΢βͷ࠷৽όʔδϣϯͰར༻Մೳ QBSFOU഑ԼͷΈ ελΠϧ͕༗ޮ

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4DPQF1SPYJNJUZ!TDPQFͷۙ઀ੑ w ෳ਺ͷείʔϓ͕িಥͨ͠৔߹ɺ ΑΓείʔϓϧʔτʹ͍ۙελΠϧ͕༏ઌ͞ΕΔ w %0.πϦʔ্ͷϗοϓ਺ʢωετ਺ʣͰۙ઀ੑΛ൑ผ͢Δ

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4DPQF1SPYJNJUZ!TDPQFͷۙ઀ੑ ϗοϓ਺ ϗοϓ਺

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4DPQF1SPYJNJUZ!TDPQFͷۙ઀ੑ ϗοϓ਺

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ैདྷͷελΠϧͷ4DPQF1SPYJNJUZ w !TDPQFΛ࢖ΘͣείʔϓϧʔτΛ࣋ͨͳ͍એݴͷ৔߹ɺ ۙ઀ੑΛ൑அ͢ΔͨΊͷϗοϓ਺͸ʿͱΈͳ͞ΕΔ w ͭ·Γɺඞͣ!TDPQFΛ࢖͏ελΠϧ͕༏ઌ͞ΕΔʜʁ ϗοϓ਺ʿ ? ϗοϓ਺

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0SJHJOBOE*NQPSUBODF $POUFYU 5IF4UZMF"UUSJCVUF -BZFST 4QFDJ fi DJUZ 4DPQF1SPYJNJUZ 0SEFSPG"QQFBSBODF $BTDBEF4PSUJOH0SEFS $44$BTDBEJOHBOE*OIFSJUBODF-FWFM ༏ઌॱҐ͸ ৄࡉ౓ˠείʔϓ

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είʔϓͱৄࡉ౓ w $BTDBEF4PSUJOH0SEFSʹ͓͚Δ είʔϓͷڧ͞ʹ͍ͭͯ͸௕Βٞ͘࿦͞Ε͍ͯͨ 4USPOHWTXFBLTDPQJOHQSPYJNJUZ IUUQTHJUIVCDPNXDDTTXHESBGUTJTTVFT w ࠷ऴతʹɺείʔϓ͸ৄࡉ౓ΑΓऑ͍ʢXFBLTDPQJOHʣͰ߹ҙ͞Εͨ w ৄࡉ౓͕ಉ͡৔߹ͷΈείʔϓΛ༻͍ͨൺֱ͕ߦΘΕΔ

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είʔϓ͕ৄࡉ౓ΑΓڧ͍ͱԿ͕໰୊ʁ w طଘͷಈ࡞ͱͷޓ׵ੑ w είʔϓΛ࢖Θͳ͍ΦʔόϥΠυ͸׬શʹෆՄೳͱͳΔ w ৄࡉ౓ͷ๊͍͑ͯͨΦʔόϥΠυ࣌ͷ໰୊͕ѱԽ͔͠Ͷͳ͍ w ৄࡉ౓ͷ՝୊ͷҰͭ͸ɺڧ͍ࢦఆʹϩοΫ͞Εͯ͠·͏͜ͱ JEʹউͭʹ͸JE͕ඞཁʹͳΔ w είʔϓ͕ৄࡉ౓ΑΓ༏ઌ͞ΕΔ৔߹ɺείʔϓͰϩοΫ͞ΕΔ w ΦʔόϥΠυͷॊೈੑ͸ৄࡉ౓ΑΓ΋௿͍ %0.πϦʔ্Ͱ͍ۙࢦఆʹ͠ͳ͚Ε͹͍͚ͳ͍

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0SJHJOBOE*NQPSUBODF $POUFYU 5IF4UZMF"UUSJCVUF -BZFST 4QFDJ fi DJUZ 4DPQF1SPYJNJUZ 0SEFSPG"QQFBSBODF $BTDBEF4PSUJOH0SEFS $44$BTDBEJOHBOE*OIFSJUBODF-FWFM ΑΓڧ͍ৄࡉ౓ͷࢦఆ ʙҎԼɺৄࡉ౓͕ಉ͡৔߹ʙ ۙ઀ੑͷߴ͍είʔϓࢦఆ ۙ઀ੑͷ௿͍είʔϓࢦఆ είʔϓࢦఆͷͳ͍ελΠϧ

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·ͱΊ

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? 2 $ISPNJVNͰ ϓϨʔεϗϧμͷ MJOFIFJHIUͷ஋͸ʁ QY QY QY QY ͓͞Β͍

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!MBZFSͰͷJNQPSUBOUࢦఆ ˠ҉໧ϨΠϠʔΑΓ༏ઌ͞ΕΔ ? ͓͞Β͍

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ৄࡉ౓͕ಉ͡ ˠείʔϓۙ઀౓Ͱ΋൑ఆ͞ΕΔ ? ͓͞Β͍

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? ϗοϓ਺ʿ ϗοϓ਺ ໌ࣔతͳ!TDPQF͕ είʔϓͷۙ઀ੑͰ༏ઌ͞ΕΔ ˣ QY ͓͞Β͍

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͔͠͠ݱ࣮͸ඇ৘Ͱ͋Δ ϓϨʔεϗϧμͷMJOFIFJHIU͸ $ISPNJVNͷ6TFS"HFOU4UZMFͰ JNQPSUBOUࢦఆ͕ೖ͍ͬͯΔ ˣ "VUIPS4UZMFͰ͸ઈର্ॻ͖Ͱ͖ͳ͍ ͨ͑͜OPSNBM ϒϥ΢βґଘ ͓͞Β͍

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·ͱΊ w $BTDBEF4PSUJOH0SEFSʹؔ࿈͢Δ࢓༷͸૿͍͑ͯΔ w ௚઀ར༻͠ͳͯ͘΋ɺϥΠϒϥϦܦ༝Ͱ࢖͏͜ͱ΋͋ΓಘΔ FH1BOEB$44Ͱ͸$BTDBEF-BZFSΛར༻͍ͯ͠Δ w ࣍ੈ୅ͷ$44։ൃʹඋ͓͖͑ͯ·͠ΐ͏ʂ w ͳ͓ɺҾ͖ଓ͖JNQPSUBOU͸҆қʹ࢖͏ͱةݥͰ͢

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