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情報処理工学04資料 /infoeng04
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Kazuhisa Fujita
October 06, 2022
Technology
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情報処理工学04資料 /infoeng04
Kazuhisa Fujita
October 06, 2022
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Transcript
ใॲཧֶ ୈ̐ճ ౻ా Ұण ެཱখদେֶอ݈ҩྍֶ෦ྟচֶՊ
ը૾ ը૾ͷσʔλྔͷܭࢉϚελʔ͠Α͏ʂʂ
ը૾ʹؔ͢Δجૅࣝ
ը૾σʔλ • ը૾খ͞ͳਖ਼ํܗͷू·ΓͰදݱ͞ΕΔɽ • ͜ͷਖ਼ํܗ֨ࢠঢ়ʹฒΜͰ͍Δɽ • ͜ͷਖ਼ํܗͷ͜ͱΛըૉ͘͠ϐΫηϧͱݺͿɽ • ֤ըૉ৭ใΛ͍࣋ͬͯΔɽ •
৭ͦͷೱ୶ͷͰද͞ΕɼͦΕΛըૉͱݺͿɽ • ըૉࢄͰද͞ΕΔɽ ըૉʢϐΫηϧʣ "σδλϧԽ
ըૉ • ը૾ͷେ͖͞ըૉʢ૯ըૉʣͰදݱ͞ΕΔɽ • ը૾ͷըૉॎͷըૉYԣͷըૉͰܭࢉͰ͖Δɽ • ըૉ = ॎͷըૉ×ԣͷըૉ •
ԼਤͷըૉɼॎԣͦΕͧΕըૉͳͷͰ • 8×8 = 64ըૉ ըૉ ըૉ
ը૾ͷࢄԽ
ը૾ • ը૾ॴͱͦͷॴͷ৭ͷ̎ͭͷྔͰද͞ΕΔɽ ৭ " ॴ 𝑥 𝑦
ը૾ͷσδλϧԽ • ը૾Λσδλϧʹม͢ΔͨΊʹࢄԽ͢Δඞཁ͕͋Δɽ • ը૾ͷॴͱ৭ͷೱ୶ΛࢄԽ͢Δ͜ͱͰɼը૾ΛࢄԽ͢Δɽ • ॴͷࢄԽΛඪຊԽʢαϯϓϦϯάʣͱ͍͏ɽ • ৭ͷೱ୶ʢըૉʣͷࢄԽΛྔࢠԽͱ͍͏ɽ •
ίϯϐϡʔλͰऔΓѻ͏ʹࢄԽͨ͠Λ̎ਐʹม͢Δඞཁ ͕͋Δɽ • ͜ͷ࡞ۀΛූ߸Խͱ͍͏ɽ ৭ " ॴ 𝑥 𝑦
ը૾ͷσδλϧԽͷྲྀΕ αϯϓϦϯά ྔࢠԽ ූ߸Խ
ྔࢠԽ " ৭ͷೱ୶ࢄԽ͞ΕΔ ৭ͷೱ୶·ͩ࿈ଓ ॴ৭̎ਐʹͳΔ
ඪຊԽ αϯϓϦϯά • ը૾ΛࢄతͳྖҬʹׂ͢Δʢը૾ΛϐΫηϧͰ۠Δʣ͜ͱΛ ඪຊԽʢαϯϓϦϯάʣͱ͍͏ɽ • ͜ͷஈ֊Ͱ৭ͷೱ୶ʢըૉʣ࿈ଓͷͷ··Ͱ͋Δɽ ඪຊԽ ඪຊԽ͞ΕΔͱɼॴ͕ࢄԽ͞Ε ΔɽͦͷͨΊɼࢄԽ͞Εͨॴͷ
ըૉ͔͠ແ͍ɽͦͷͨΊɼਤͰ ըૉ͕ͱͯ͠දݱ͞Ε͍ͯΔɽ ৭ͷೱ୶Λද͢Λ ըૉͱݴ͏ɽ
ྔࢠԽ • ඪຊԽ͞Εͨը૾ɼϐΫηϧ͝ͱʹ৭ͷೱ୶ʢըૉʣΛࢄ ʹม͞ΕΔɽ • ըૉΛࢄ͢Δ͜ͱΛྔࢠԽͱ͍͏ɽ ྔࢠԽ ըૉࢄԽ͞ΕΔɽͷ࢛ࣺޒ ೖ؆୯ͳࢄԽͷํ๏Ͱ͋Δɽ࢛ ࣺޒೖ͢Δͱɼͱ͍ͬͨ
ʹؙΊΒΕΔɽͦͷͨΊɼͳ ΊΒ͔ͳมԽΛ͍ͯͨ͠ͷมԽ ͕֊ஈঢ়ͷมԽʹͳΔɽ Ґஔ ըૉ Ґஔ ըૉ ྔࢠԽ
άϨʔεέʔϧը૾
άϨʔεέʔϧը૾ͱ৭ • άϨʔεέʔϧը૾ • ޫͷ໌҉ʢೱ୶ʣͷΈදݱͰ͖Δը૾ɽ • ໌҉ΛࢄͰද͢ɽ • ըૉʹ͖ͭ৭ʢ໌҉ʣΛද͢Λ̍ͭ࣋ͭɽ •
ըૉͱݺͿɽ • දݱͰ͖Δ৭ͷ͖ݸ͋Δɽ • ӈਤͷྫͰന͔Βࠇ·Ͱͷ৭Λɼ2! = 8৭Ͱ৭Λදݱ͍ͯ͠Δɽ ֊ௐάϨʔεέʔϧ ׂʢࢄԽʣ ඞͣ̎͠ͷ͖ݸͰ͋Δඞཁͳ͍ɽ ͔͠͠ɼͷ͖ίϯϐϡʔλͱ૬ੑ ͕ྑ͍ͷͰ̎ͷ͖ݸʹ͍ͯ͠Δɽίϯ ϐϡʔλͰΛਐͰදݱ͠ͳ͚Ε ͳΒͳ͍ɽਐͰදݱͰ͖Δͷ ͷܻͰ͋Δɽͭ·ΓɼըૉΛ ਐͰදݱ͢Δͱɼͷ͖छྨͷ৭Λ දݱͰ͖Δ͜ͱʹͳΔɽ
άϨʔεέʔϧը૾ͱ৭ • άϨʔεέʔϧը૾ • දݱͰ͖Δ৭ͷΛ֊ௐͱݺͿɽ • ৭දͤΔ߹ɼ֊ௐ • ৭දͤΔ߹ɼ֊ௐ •
֊ௐϏοτɾόΠτͰදͤΔɽ͜Ε৭ͷྔࢠԽϏοτͰ͋Δɽ • ֊ௐ2!֊ௐˠϏοτ • ֊ௐ2"֊ௐˠϏοτόΠτ ֊ௐάϨʔεέʔϧ ׂʹ֊ௐˠϏοτ ྟচֶߨ࠲ҩ༻ใॲཧֶ ͳƘ< E Ǒ× Ƥ c 2j "p : gfl p : hfl 2jG Ȱ ȵ˵aJ0a]K p : ifm ਐ ࣮ࡍྔࢠԽϏοτΛܾΊ͔ͯΒ֊ௐ͕ܾ·Δɽ ྫ͑ྔࢠԽϏοτ͕Ϗοτͷ߹ɼܻͷਐ ͰըૉΛද͔͢Βɼͷݸͷ৭Λද͢͜ͱ͕Ͱ͖ Δɽ͢ͳΘͪɼܻͷਐʢϏοτʣͰ֊ௐͷ৭ ͕දͤΔ͜ͱʹͳΔɽ
άϨʔεέʔϧը૾ͱըૉ ֊ௐͷͱ͖നΛɼࠇΛʹׂΓͯΔ͜ͱ͕ଟ͍ɽ
άϨʔεέʔϧը૾ͱσʔλྔ • άϨʔεέʔϧը૾ͷσʔλྔ࣍ͷࣜͰද͞ΕΔɽ • ը૾ͷσʔλྔʹըૉ Yըૉ͋ͨΓͷσʔλྔ • ըૉ͋ͨΓͷσʔλྔ֊ௐΛϏοτͰදͨ͠ͷʢྔࢠԽϏ οτʣʹͳΔɽ •
ྫ͑ɼ֊ௐͷͱ͖ɼͭͷ৭ΛਐͰද͞ͳ͚ΕͳΒͳ͍ɽ • छྨͷਐΛ࡞ΔͨΊʹɼগͳ͘ͱਐܻͰͳ͚ΕͳΒͳ ͍ɽ • Αͬͯɼ֊ௐͷ৭Λදݱ͢ΔʹϏοτͷσʔλྔ͕ඞཁͰ͋Δɽ • ͜Εɼ֊ௐΛͷOͰදͨ͠ͱ͖ͷOͱ͍͠ʢ֊ௐ2!֊ௐˠϏο τʣɽ • Լਤ͕৭ʢ֊ௐʣͰද͞ΕΔάϨʔεέʔϧը૾ͳΒ • 8×8×3 = 192Ϗοτ = 24όΠτ ըૉ ըૉ͋ͨΓͷσʔλྔʢ֊ௐΛϏοτͰදͨ͠ͷʣ
ԋश • ըૉ͕YͷϞϊΫϩը૾Λஈ֊ͷೱͰදࣔ͢Δ ͨΊʹඞཁͳσʔλྔΛ͑Αɽͨͩ͠ɼѹॖ͍ͯ͠ͳ͍ͱ͢Δ ʢୈճࠃՈࢼݧվʣ ըૉΛܭࢉ͢Δɽ ըૉ͋ͨΓͷσʔλྔΛܭࢉ͢Δɽ ըૉͱըૉ͋ͨΓͷσʔλྔΛ͔͚Δɽ
ԋश • ըૉ͕YͷϞϊΫϩը૾Λஈ֊ͷೱͰදࣔ͢Δ ͨΊʹඞཁͳσʔλྔΛ͑Αɽͨͩ͠ɼѹॖ͍ͯ͠ͳ͍ͱ͢Δ ʢୈճࠃՈࢼݧվʣ ըૉΛܭࢉ͢Δɽ Yըૉ ըૉ͋ͨΓͷσʔλྔΛܭࢉ͢Δɽ
128 = 2"͔ͩΒ֊ௐͷ৭Λදݱ͢ΔͨΊʹϏοτඞཁͰ͋Δɽ ըૉͱըૉ͋ͨΓͷσʔλྔΛ͔͚Δɽ YϏοτ .Ϗοτ LόΠτ
ԋश • നࠇࣸਅΛºըૉɼ֊ௐͷೱ୶ը૾ͱͯ͠ɼίϯ ϐϡʔλͷϝϞϦʹอଘ͍ͨ͠ɽѹॖͳͲͷॲཧΛߦΘͳ͍߹ɼ গͳ͘ͱԿL#ʢΩϩόΠτʣͷϝϞϦ༰ྔ͕ඞཁ͔ɽͨͩ͠ɼ L##ͱ͢Δɽ ୈճ.&छ ըૉΛܭࢉ͢Δɽ ըૉ͋ͨΓͷσʔλྔΛܭࢉ͢Δɽ ըૉͱըૉ͋ͨΓͷσʔλྔΛ͔͚Δɽ
ԋश • നࠇࣸਅΛºըૉɼ֊ௐͷೱ୶ը૾ͱͯ͠ɼίϯ ϐϡʔλͷϝϞϦʹอଘ͍ͨ͠ɽѹॖͳͲͷॲཧΛߦΘͳ͍߹ɼ গͳ͘ͱԿ,#ʢΩϩόΠτʣͷϝϞϦ༰ྔ͕ඞཁ͔ɽͨͩ͠ɼ ,##ͱ͢Δɽ ୈճ.&छ ըૉΛܭࢉ͢Δɽ
૯ըૉ1024×1024ըૉͰ͋Δɽ͜͜Ͱֻ͚ࢉͷ··ʹ͓ͯ͘͠ɽ ըૉ͋ͨΓͷσʔλྔΛܭࢉ͢Δɽ 256 = 2#ͳͷͰɼ֊ௐͷ৭Λදݱ͢ΔͨΊʹϏοτඞཁͰ͋Δɽ ըૉͱըૉ͋ͨΓͷσʔλྔΛ͔͚Δɽ 1024×1024×8CJU= 1024×1024#= 1024,#
3(#Χϥʔը૾ͱ৭
ޫͷࡾݪ৭ • ̏छྨͷ৭Λ༷ࠞͥͯʑͳ৭ʢޫʣΛͭ͘ΔʢՃ๏ࠞ৭ʣɽ • ਓɼɼ੨ͷޫΛଊ͑ΔηϯαΛ࣋ͭͨΊɼɼɼ੨ͷޫΛ ࠞͥΕਓ͕ײ͡Δ৭Λͭ͘Δ͜ͱ͕Ͱ͖Δɽ • ͜ͷͨΊɼɼɼ੨ޫͷࡾݪ৭ͱݺΕΔɽ • ·ͨɼɼɼ੨Λ༻͍৭Λͭ͘Δํ๏Λ
ͦΕΒͷ಄จࣈ͔Β3(#ΧϥʔͱݺͿɽ
ڭཆɿന͍ޫͱ • Մࢹޫઢͷͯ͢ͷΛۉʹؚΉޫന͘ݟ͑Δɽ • ͜ΕΛ౿·͑Δͱɼന৭ͷޫଘࡏ͠ͳ͍ɽ • సͯ͡ɼ͍ൣғͷपͷฒΛಉఔʹؚΉϊΠζͷ͜ͱΛന৭ ࡶԻʢXIJUFOPJTFʣͱ͍͏ɽ
Χϥʔը૾ͷߏ 3(# ըૉΛ֦େ ʢ࣮ࡍʹσΟεϓϨΠ Λ֦େ͢Δͱ̍ըૉʹ ͖ͭ̏৭ݟ͑Δʣ 3ɼ(ɼ#ͦΕͧΕͷًΛද͢ը૾͕͋Δɽ ͦΕΒΛಉ࣌ʹදࣔ͢ΔͱΧϥʔը૾ʹͳΔɽ ࣮ࡍͷσΟεϓϨΠͰըૉ͝ͱʹ 3(#ͦΕͧΕʹޫΔϥΠτ͕ຒΊࠐ
·Ε͓ͯΓɼ3(#ͦΕͧΕʹରԠ͢ Δը૾Λಉ࣌ʹද͍ࣔͯ͠Δɽ ࣮ࡍͷΈͬͱෳࡶɽ
3(#Χϥʔը૾ͱ৭ • ɼɼ੨ʢ3(#ʣͷΈ߹ΘͤͰ৭Λදݱ͢Δɽ • 3 ( #ͦΕͧΕͷೱ୶ΛͰද͢ɽ • ֤৭ͷදݱͰ͖Δೱ୶ͷΛ֊ௐͱݺͿɽ •
3(#֤৭ͭͷೱ୶Ͱද͢ʢஈ֊Ͱද͢ʣͱ͖ɼ3(#ͦΕͧΕ֊ௐͰද ݱ͞Ε͍ͯΔͱ͍͏ɽ • Ұ෦ͷྫ֎Λআ͖ɼදݱͰ͖Δ৭ ֤৭ͷ֊ௐ ?ݸ͋Δɽ • 3(#ͦΕͧΕ֊ௐͰද͢߹ɼදݱͰ͖Δ৭ɼ • 8!৭ • 3(#ͦΕͧΕ֊ௐͰද͢߹ɼදݱͰ͖Δ৭ɼ • 256!ສ৭ 3(# ըૉΛ֦େ ʢ࣮ࡍʹσΟεϓϨΠ Λ֦େ͢Δͱ̍ըૉʹ ͖ͭ̏৭ݟ͑Δʣ
3(#Χϥʔը૾ͱ৭ • දݱͰ͖Δ৭ϏοτɾόΠτͰදͤΔɽ • ͜Ε৭ͷྔࢠԽϏοτͰ͋Δɽ • 8! = 2! !
= 2$৭ˠϏοτ • 256! = 2# ! = 2%&৭ˠϏοτόΠτ • ৭༷ʑͳݴ͍ํ͕Ͱ͖Δɽ • 3(#ͦΕͧΕ৭ʢ֊ௐʣ • 3(#ͦΕͧΕϏοτ • ϏοτΧϥʔ • ৭3(# 3(# ըૉΛ֦େ ʢ࣮ࡍʹσΟεϓϨΠ Λ֦େ͢Δͱ̍ըૉʹ ͖ͭ̏৭ݟ͑Δʣ
3(#Χϥʔը૾ͱσʔλྔ • 3(#Χϥʔը૾ͷσʔλྔ • ը૾ͷσʔλྔʹըૉ Yըૉ͋ͨΓͷσʔλྔ • ըૉ͋ͨΓͷσʔλྔ3(#֤৭ͷ֊ௐΛϏοτͰදͨ͠ͷʢྔࢠ ԽϏοτʣͷ૯ͳͷͰ •
ը૾ͷσʔλྔʢϏοτʣʹըૉ Y3(#֤৭ͷྔࢠԽϏοτͷ૯ • 3(#֤৭ͷྔࢠԽϏοτ͕ಉ͡ͳΒ • ը૾ͷσʔλྔʢϏοτʣʹըૉ Y3(#֤৭ͷྔࢠԽϏοτ Y • ӈਤ͕৭Ͱද͞ΕΔը૾ͳΒ • YYϏοτόΠτ ըૉ ըૉ͋ͨΓͷσʔλྔʢ֊ ௐΛϏοτͰදͨ͠ͷʣ 512 = 2! → 9Ϗοτ
ԋश • 3(#֤৭ΛCJUͰྔࢠԽͨ͠ॎըૉɼԣըૉͷը૾ͷ σʔλྔΛCZUFͰ͑Αɽͨͩ͠ɼը૾ͷѹॖϔομใͷ Ճͳ͍ͷͱ͢ΔɽʢୈճࠃՈࢼݧվʣ ըૉΛܭࢉ͢Δɽ ̍ըૉ͋ͨΓͷσʔλྔΛܭࢉ͢Δɽ
ըૉͱ̍ըૉ͋ͨΓͷσʔλྔΛ͔͚Δɽ
ԋश • 3(#֤৭ΛCJUͰྔࢠԽͨ͠ॎըૉɼԣըૉͷը૾ͷ σʔλྔΛCZUFͰ͑Αɽͨͩ͠ɼը૾ͷѹॖϔομใͷ Ճͳ͍ͷͱ͢ΔɽʢୈճࠃՈࢼݧվʣ ըૉΛܭࢉ͢Δɽ ૯ըૉYըૉͰ͋Δɽ ̍ըૉ͋ͨΓͷσʔλྔΛܭࢉ͢Δɽ
ըૉʹඞཁͳσʔλྔϏοτYϏοτόΠτͰ͋Δɽ ըૉͱ̍ըૉ͋ͨΓͷσʔλྔΛ͔͚Δɽ YόΠτόΠτ .όΠτ
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ԋश • σʔλѹॖʹ͍ͭͯޡ͍ͬͯΔͷͲΕ͔ɽʢୈճྟচֶٕ ࢜ࠃՈࢼݧʣ ඇՄٯతͳॲཧσʔλѹॖͰ͋Δɽ ओͳతهԱ༰ྔͷઅͰ͋Δɽ ѹॖ͞Εͨը૾ݪը૾ΑΓߴਫ਼ࡉͰ͋Δɽ
Ի৴߸ΛѹॖͰ͖Δɽ ಈըσʔλΛѹॖͰ͖Δɽ
ԋश • σʔλѹॖʹ͍ͭͯޡ͍ͬͯΔͷͲΕ͔ɽʢୈճྟচֶٕ ࢜ࠃՈࢼݧʣ ඇՄٯతͳॲཧσʔλѹॖͰ͋Δɽ ओͳతهԱ༰ྔͷઅͰ͋Δɽ ѹॖ͞Εͨը૾ݪը૾ΑΓߴਫ਼ࡉͰ͋Δɽ
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