Elementary algorithm - Speaker Deck

Slide 1

Slide 1 text

ษڧձ

Slide 2

Slide 2 text

ࣗݾ঺հ https://github.com/mochisuna • ؙా୓࿨ʢ·ΔͨͻΖ͔ͣʣ • Twitter: @mochi_suna • ओʹαʔόʔαΠυΤϯδχΞ • झຯɿϐΞϊɺϘυήɺΞΠίϯ࡞੒ʢΧούʣɺϓϨθϯ • ࣗಈԽେ޷͖ɻख࡞ۀ͖Β͍ • githubɿ @mochisuna

Slide 3

Slide 3 text

ٕज़໘

Slide 4

Slide 4 text

଴ͯ଴ͯ

Slide 5

Slide 5 text

ࠓ·Ͱͷൃද ↑લʑճ ↑લճ

Slide 6

Slide 6 text

ΤϯδχΞɾɾɾʁ

Slide 7

Slide 7 text

ͪΐͬͱਅ໘໨ͳ ಺༰ʹ͍ͨ͠

Slide 8

Slide 8 text

ੲͷઐ໳͔Β࣋ͬͯ͜Α͏ʂ

Slide 9

Slide 9 text

ΞϧΰϦζϜͷೖ໳ ɾɾɾͷೖ໳ ·Δͨ

Slide 10

Slide 10 text

࿩͢͜ͱ • ΞϧΰϦζϜɾɾɾʁ • ʮྑ͍ʯΞϧΰϦζϜ • ܭࢉྔ • ޮ཰Α͘໰୊Λղ͜͏ • ੈքதͰ࢖ΘΕΔΞϧΰϦζϜ

Slide 11

Slide 11 text

ΞϧΰϦζϜɾɾɾʁ

Slide 12

Slide 12 text

No content

Slide 13

Slide 13 text

ΞϧΰϦζϜʢAlgorithmʣ • ʮܭࢉՄೳʯͳ͜ͱΛܭࢉ͢Δɺܗࣜతͳखଓ͖ ͷ͜ͱɺ͋Δ͍͸ͦΕΛܗࣜతʹදݱͨ͠΋ͷ • ίϯϐϡʔλʹܭࢉͤ͞ΔͨΊͷʮܭࢉํ๏ʯ

Slide 14

Slide 14 text

ΞϧΰϦζϜʢAlgorithmʣ • ʮܭࢉՄೳʯͳ͜ͱΛܭࢉ͢Δɺܗࣜతͳखଓ͖ ͷ͜ͱɺ͋Δ͍͸ͦΕΛܗࣜతʹදݱͨ͠΋ͷ • ίϯϐϡʔλʹܭࢉͤ͞ΔͨΊͷʮܭࢉํ๏ʯ 🤔🤔🤔

Slide 15

Slide 15 text

ॱ൪ʹ۷ΓԼ͍͛ͯ͘

Slide 16

Slide 16 text

ͦ΋ͦ΋

Slide 17

Slide 17 text

ίϯϐϡʔλ͸͓όΧ͞Μ ʘͳΜͩͱʔʗ ʘ͹͔ʹ͢Μͳʔʗ

Slide 18

Slide 18 text

ίϯϐϡʔλ͸͔֬ʹ͍͢͝ • ௒͍͢͝ܭࢉೳྗ • Կԯ×Կԯͷܭࢉ͕ਖ਼͔֬ͭߴ଎ • ௒͍͢͝هԱྗ • ԿઍɺԿສͷ਺஋Λਖ਼֬ʹهԱͰ͖Δ ʘ͑ͬ΁Μʗ ʘͲ΍͊ʗ

Slide 19

Slide 19 text

Ͱ΋ίϯϐϡʔλ͸͓όΧ͞Μ • ࣗྗͰ͸ߟ͑ΒΕͳ͍ • ՝୊ΛղऍͰ͖ͳ͍ • ʮϓϩάϥϜ͸ࢥͬͨ௨Γʹಈ͔ͳ͍ɻʯ ʮॻ͍ͨ௨Γʹಈ͘ʯ ʘOh…ʗ ʘͦΕ͸܅ͨͪͷ࢓ࣄ͞ʗ

Slide 20

Slide 20 text

۩ମతͳྫͰߟ͍͑ͯ͜͏

Slide 21

Slide 21 text

໰୊ • Q͞Μ͸3೥ʹҰ౓ɺఆظతʹπΠʔτ͠·͢ɻ • Q͞Μ͸3ͷഒ਺ͷ೥ྸͷ࣌ʹඞͣ೥1ճ͚ͩπΠʔτ ͠ɺͦΕҎ֎ͷ೥ྸͷ࣌͸Ұ੾͠·ͤΜɻ • Ͱ͸ɺQ͞Μ͸ಛఆͷAࡀ͔ΒBࡀ·ͰͷؒʹԿճπ Πʔτ͢ΔͰ͠ΐ͏͔ʁ

Slide 22

Slide 22 text

͜ͷ··Ͱ͸ ίϯϐϡʔλͰ͸ ॲཧͰ͖ͳ͍ ʘʁʁʁʗ ʘʁʁʁʗ

Slide 23

Slide 23 text

PCͰॲཧͰ͖ΔΑ͏ʹ੔ཧ • ੔਺A,BΛఆٛ • A≦ i ≦B Λຬͨ͢੔਺ i ͷதͰ3ͷഒ਺͕͍ͭ͘ ͋Δ͔Λܭ্͠ͳ͍͞ ྫɿA=10ࡀ, B=25ࡀɹˠɹ5ճ πΠʔτ º º ̋ º º ̋ º º ̋ º º ̋ º º ̋ º ೥ྸ

Slide 24

Slide 24 text

ϓϩάϥϜʹམͱ͠ࠐΉ sum := 0 FOR i := A; i <= B; i++ IF i%3 == 0 sum++ END END print(sum)

Slide 25

Slide 25 text

͜͜·Ͱ΍ͬͯ ॳΊͯ໰୊͕ղ͚Δ ʘ͜ͷϓϩάϥϜͰ͍͍ͷʁʗ ʘ͜ΕΛܭࢉ͢Ε͹͍͍ͷͶʁʗ

Slide 26

Slide 26 text

ΞϧΰϦζϜ

Slide 27

Slide 27 text

ΞϧΰϦζϜ • ίϯϐϡʔλʹܭࢉͤ͞ΔͨΊͷʮܭࢉํ๏ʯ • ʮͲ͏ܭࢉͤ͞Δ͔ʯͷखॱ ʘܭࢉ͸ʗ ʘ೚ͤͯʂʗ

Slide 28

Slide 28 text

ݱ࣮ͷ໰୊Λ Ͳ͏΍ͬͯϓϩάϥϜʹ མͱ͠ࠐΉ͔

Slide 29

Slide 29 text

͜Ε͕େࣄ

Slide 30

Slide 30 text

ࠓճ͸ΞϧΰϦζϜͷྫ͔Β ͦͷੌ͞ͱԞਂ͞ʹ ͪΐͬͱͰ΋఻͍͑ͨ

Slide 31

Slide 31 text

͋Μ·೉͍͠ ༻ޠͱ͔֓೦͸ ࢖Θͳ͍Α͏ʹؤுΔ ʢP vs NP໰୊ͱ͔ʣ

Slide 32

Slide 32 text

ʮྑ͍ʯΞϧΰϦζϜ

Slide 33

Slide 33 text

ΞϧΰϦζϜʹʮղ͖ํʯ • ޮ཰ͷྑ͍ղ͖ํɾѱ͍ղ͖ํ͕͋Δ • ͪΐͬͱݟͯΈΑ͏ • https://www.toptal.com/developers/ sorting-algorithms

Slide 34

Slide 34 text

ॲཧޮ཰͕શવҧ͏

Slide 35

Slide 35 text

ޮ཰ͷʮྑ͍ʯ ΞϧΰϦζϜ͕ ༏Ε͍ͯΔ

Slide 36

Slide 36 text

No content

Slide 37

Slide 37 text

PCͷੑೳ͕ 10ഒɺ20ഒʹͳΕ͹ ؔ܎ͳ͍ΑͶʂ ʘͤ΍ͳʗ ʘͦΕͳʗ

Slide 38

Slide 38 text

࢒೦

Slide 39

Slide 39 text

۪௚ͳΞϧΰϦζϜͰ͸ PCͰ΋ղ͚ͳ͍໰୊͕͋Δ ʘ͑ͬʗ ʘ͑ͬʗ

Slide 40

Slide 40 text

८ճηʔϧεϚϯ໰୊

Slide 41

Slide 41 text

८ճηʔϧεϚϯ໰୊ • Ұ൪গͳ͍ҠಈίετͰɺશͯͷՈΛͪΐ͏Ͳ ̍ճ͚ͩ๚໰͠ձࣾʹ໭ͬͯ͘Δ໰୊ • NݸͷՈ͕͋Δ৔߹N!௨Γͷ૊Έ߹Θͤ

Slide 42

Slide 42 text

ϐϯͱ͜ͳ͍ɾɾɾɻ • N=̑ͷ৔߹ɿ120௨Γ • N=10ͷ৔߹ɿ3628800௨Γ • N=15ͷ৔߹ɿ1.3*1012௨Γ • N=20ͷ৔߹ɿ2.4*1018௨Γ • N=100ͷ৔߹ɾɾɾʁ

Slide 43

Slide 43 text

૊Έ߹Θͤരൃ • 1೥ؒ = 31536000ඵ ≒ 3.2*108ඵ • 1GHzʹඵؒ1.0 * 109ճͷԋࢉ • 3.2*108 × 1.0*109 = 3.2 * 1017

Slide 44

Slide 44 text

૊Έ߹Θͤരൃ • 1೥ؒ = 31536000ඵ ≒ 3.2*108ඵ • 1GHzʹඵؒ1.0 * 109ճͷԋࢉ • 3.2*108 × 1.0*109 = 3.2 * 1017 N=20ʢ2.4*1018ʣͰ͢Β 10೥ۙ͘ճͯ͠΋ղ͕ग़ͳ͍

Slide 45

Slide 45 text

ޮ཰ͷʮྑ͍ʯΞϧΰϦζϜ ͕ ٻΊΒΕ͍ͯΔ

Slide 46

Slide 46 text

ޮ཰ͷʮྑ͞ʯ ʮܭࢉྔʯ

Slide 47

Slide 47 text

ܭࢉྔ • ϓϩάϥϜͷ࣮ߦ։͔࢝Βऴྃ·Ͱʹ͔͔Δ ࣌ؒʢۭؒʣΛධՁ • େࡶ೺ʹͲͷ͘Β͍͕͔͔࣌ؒΔͷ͔ • ࣮༻Ͱ΋େࣄ • ೖྗͷݸ਺΍஋ͷൣғΛม਺ͱ͢Δ

Slide 48

Slide 48 text

ܭࢉྔͷྫɿ1ॏϧʔϓ sum := 0 FOR i := 0; i < N; i++ sum += i END ճ࣮ߦ /ճ࣮ߦ

Slide 49

Slide 49 text

ܭࢉྔͷྫɿ1ॏϧʔϓ • sum, i ͷએݴɾॳظԽɿ1ճ • “i < N”, “sum += i”, “i++”ɿ Nճ • ૯ܭࢉ਺ɿ3N + 3ճ sum := 0 FOR i := 0; i < N; i++ sum += i END ճ࣮ߦ /ճ࣮ߦ

Slide 50

Slide 50 text

ܭࢉྔͷྫɿ1ॏϧʔϓ • sum, i ͷએݴɾॳظԽɿ1ճ • “i < N”, “sum += i”, “i++”ɿ Nճ • ૯ܭࢉ਺ɿ3N + 3ճ • ܭࢉྔɿO(N) sum := 0 FOR i := 0; i < N; i++ sum += i END ճ࣮ߦ /ճ࣮ߦ Ұ൪Өڹͷڧ͍ ม਺ʹൺྫ

Slide 51

Slide 51 text

ܭࢉྔͷྫɿ2ॏϧʔϓ • sum, i ͷએݴɾॳظԽɿ1ճ • “i < M”, “i++”, jͷએݴɾॳظԽɿ Mճ • “j < N”, “sum += i * j”, “j++”ɿ M*Nճ sum := 0 FOR i := 0; i < M; i++ FOR j := 0; j < N; j++ sum += i * j ճ࣮ߦ /ճ࣮ߦ

Slide 52

Slide 52 text

ܭࢉྔͷྫɿ2ॏϧʔϓ • sum, i ͷએݴɾॳظԽɿ1ճ • “i < M”, “i++”, jͷએݴɾॳظԽɿ Mճ • “j < N”, “sum += i * j”, “j++”ɿ M*Nճ • ૯ܭࢉ਺ɿ3MN + 4M + 3ճ • ܭࢉྔɿO(MN) sum := 0 FOR i := 0; i < M; i++ FOR j := 0; j < N; j++ sum += i * j ճ࣮ߦ /ճ࣮ߦ Ұ൪Өڹͷڧ͍ ม਺ʹൺྫ

Slide 53

Slide 53 text

Өڹʹ͍ͭͯิ଍ • 3MN + 4M + 3ʹ͍ͭͯߟ͑Δ ./ ./ ./ . ./ ./.

Slide 54

Slide 54 text

ܭࢉྔͷෆ౳ࣜ n ͕े෼େ͖͍ͱҎԼ͕੒ཱ ෆ౳ࣜͷࠨลʹߦ͘΄Ͳߴ଎ log n < n < n < n2 < n3 < 2n < 3n < n!

Slide 55

Slide 55 text

ܭࢉྔͷൺֱ

Slide 56

Slide 56 text

ޮ཰Α͘໰୊Λղ͜͏

Slide 57

Slide 57 text

͸͡ΊͷҰาɿ୳ࡧ • ͋ΔσʔληοτAʹ͋Δ਺n͕͋Δ͔ʁ • A = [4,8,23,7,1,9] • n = 7

Slide 58

Slide 58 text

۪௚ͳ୳ࡧ • લ͔Βॱʹ୳ࡧ → n = 7ʹҰகͨ͠ΒTRUE O ˣ J "

Slide 59

Slide 59 text

۪௚ͳ୳ࡧ • લ͔Βॱʹ୳ࡧ → n = 7ʹҰகͨ͠ΒTRUE O º ˣ J "

Slide 60

Slide 60 text

۪௚ͳ୳ࡧ • લ͔Βॱʹ୳ࡧ → n = 7ʹҰகͨ͠ΒTRUE O º º ˣ J "

Slide 61

Slide 61 text

۪௚ͳ୳ࡧ • લ͔Βॱʹ୳ࡧ → n = 7ʹҰகͨ͠ΒTRUE O º º º ˣ J "

Slide 62

Slide 62 text

۪௚ͳ୳ࡧ • લ͔Βॱʹ୳ࡧ → n = 7ʹҰகͨ͠ΒTRUE O º º º ✅ J "

Slide 63

Slide 63 text

͜ͷ··ͩͱ • Nݸͷσʔληοτͷ৔߹ɿO(N)ճͷܭࢉྔ • ਺͕গͳ͚Ε͹ྑ͍͚Ͳແବ͕ଟ͍ O º º º º º º J "

Slide 64

Slide 64 text

Ͳ͏͠Α͏ʁ

Slide 65

Slide 65 text

• ॲཧ͢Δର৅ΛݮΒ͠ޮ཰Խ ·ͣ͸ιʔτ O J " ͔͜͜Βઌ͸ ॲཧෆཁ

Slide 66

Slide 66 text

• ॲཧ͢Δର৅ΛݮΒ͠ޮ཰Խ • ͨͩ͠ɺܭࢉྔ͸Լ͕Βͳ͍ ·ͣ͸ιʔτ O J " ͔͜͜Βઌ͸ ॲཧෆཁ

Slide 67

Slide 67 text

΋ͬͱޮ཰Խ

Slide 68

Slide 68 text

• தԝ஋͔Βܭࢉɿ(5+0)/2 = 2 ೋ෼୳ࡧ O ˣ J "

Slide 69

Slide 69 text

• தԝ஋͔Βܭࢉɿ(5+0)/2 = 2 • 3 < 7 ͳͷͰࠨͷۭؒΛݕࡧ ೋ෼୳ࡧ O ˣ J "

Slide 70

Slide 70 text

• தԝ஋͔Βܭࢉɿ(2+0)/2 = 1 ೋ෼୳ࡧ O ˣ º J "

Slide 71

Slide 71 text

• தԝ஋͔Βܭࢉɿ(2+0)/2 = 1 • 3 < 4 ͳͷͰࠨͷۭؒΛݕࡧ ೋ෼୳ࡧ O ˣ º J "

Slide 72

Slide 72 text

• தԝ஋͔Βܭࢉɿ(1+0)/2 = 0 • 3 > 1 ͳͷͰଘࡏ͠ͳ͍ ೋ෼୳ࡧ O ˣ º º J "

Slide 73

Slide 73 text

΋ͬͱڊେͳྫ A = [1,2,…100] , n = 9 1.ɹi=50, A[i]=51 → 9 < 51ͳͷͰ i = (50 + 0) / 2 2.ɹi=25, A[i]=26 → 9 < 26ͳͷͰ i = (25 + 0) / 2 3.ɹi=12, A[i]=13 → 9 < 13ͳͷͰ i = (12 + 0) / 2 4.ɹi= 6, A[i]= 7 → 9 > 7ͳͷͰ i = (12 + 6) / 2 5.ɹi= 9, A[i]=10 → 9 < 10ͳͷͰ i = ( 9 + 6) / 2 6.ɹi= 7, A[i]= 8 → 9 > 8ͳͷͰ i = ( 9 + 7) / 2 7.ɹi= 8, A[i]= 9 → 9 = 9ͳͷͰ TRUE

Slide 74

Slide 74 text

ೋ෼୳ࡧ • ৗʹ୳ࡧۭؒΛ൒෼ʹ͠ଓ͚Δ • ܭࢉྔɿO(log n) d d d d d d d × n=13 × ×

Slide 75

Slide 75 text

ಉ͡୳ࡧͰ΋ɾɾɾ • ΞϧΰϦζϜҰͭͰѹ౗తʹߴ଎ʹͳΔ • ߴ଎ͳΞϧΰϦζϜͷݚڀ͸ੈքతʹ͞Ε͍ͯΔ

Slide 76

Slide 76 text

͜͜·Ͱฉ͍ͯօ͞Μ ͜͏ࢥͬͨͰ͠ΐ͏

Slide 77

Slide 77 text

ʘผʹ਺ࣈ୳͠ͱ͔͠ͳ͍͠ʗ

Slide 78

Slide 78 text

ΞϧΰϦζϜͷੌ͞͸ ͦ͜͡Όͳ͍

Slide 79

Slide 79 text

ੈքதͰ࢖ΘΕΔ ΞϧΰϦζϜ

Slide 80

Slide 80 text

ྫɿϓϩάϥϛϯάݴޠ • ͦ΋ͦ΋Ͳ͏΍ͬͯղऍͯ͠Μͷʁ package main import "fmt" func main() { sum := 0 A, B := 10, 25 for i := A; i <= B; i++ { if i%3 == 0 { sum++ } } fmt.Println(sum) }

Slide 81

Slide 81 text

ྫɿϓϩάϥϛϯάݴޠ • ࣈ۟ղੳ/ߏจղੳ/AST a = 1 b = 2 if (b < 3) print(“hoge")

Slide 82

Slide 82 text

ྫɿϓϩάϥϛϯάݴޠ • ࣈ۟ղੳ/ߏจղੳ/AST a = 1 b = 2 if (b < 3) print(“hoge") B C JG C UIFO QSJOU lIPHF FMTF QSJOU B ࣈ۟ղੳ

Slide 83

Slide 83 text

ྫɿϓϩάϥϛϯάݴޠ • ࣈ۟ղੳ/ߏจղੳ/AST a = 1 b = 2 if (b < 3) print(“hoge") B C JG C UIFO QSJOU lIPHF FMTF QSJOU B CMPDL ม਺ B ԋࢉࢠ ؔ਺ JG Ҿ਺ lIPHFz ୅ೖ ม਺ C ୅ೖ ԋࢉࢠ ؔ਺ UIFO ࠨล C ӈล ؔ਺ QSJOU ԋࢉࢠ ࣈ۟ղੳ ߏ จ ղ ੳ

Slide 84

Slide 84 text

ྫɿϓϩάϥϛϯάݴޠ • ࣈ۟ղੳɺߏจղੳ/AST a = 1 b = 2 if (b < 3) print(“hoge") B C JG C UIFO QSJOU lIPHF FMTF QSJOU B CMPDL ม਺ B ԋࢉࢠ ؔ਺ JG Ҿ਺ lIPHFz ୅ೖ ม਺ C ୅ೖ ԋࢉࢠ ؔ਺ UIFO ࠨล C ӈล ؔ਺ QSJOU ԋࢉࢠ ࣈ۟ղੳ ߏ จ ղ ੳ ҙ ຯ ղ ੳ

Slide 85

Slide 85 text

ྫɿ஍ਤɾ࿏ઢܦ࿏ • GoogleMap • Yahoo࿏ઢͳͲ • ໎࿏

Slide 86

Slide 86 text

• ෯༏ઌ୳ࡧɿBFS / ਂ͞༏ઌ୳ࡧɿDFS • Dijikstra๏ / ϕϧϚϯɾϑΥʔυ๏ • ϫʔγϟϧɾϑϩΠυ๏ ࠷୹ܦ࿏໰୊ Start 3 6 8 12 10 3 2 1 0 5 7 4

Slide 87

Slide 87 text

• ෯༏ઌ୳ࡧɿBFS / ਂ͞༏ઌ୳ࡧɿDFS • Dijikstra๏ / ϕϧϚϯɾϑΥʔυ๏ • ϫʔγϟϧɾϑϩΠυ๏ ࠷୹ܦ࿏໰୊ Start 3 6 8 12 10 3 2 1 0 5 7 4 Start 3 6 8 12 10 3 2 1 0 5 7 4

Slide 88

Slide 88 text

ྫɿϚονϯάΞϓϦ

Slide 89

Slide 89 text

ϚονϯάΞϓϦ • ޷ײ౓͔ΒάϥϑΛఆٛ உ ঁ 2 4 5 5 1 3 6 2 3

Slide 90

Slide 90 text

ϚονϯάΞϓϦ • ༑޷౓͔ΒάϥϑΛఆٛ • ݩͷάϥϑʹෛͷॏΈͰ༗޲ลΛுΔ உ ঁ 2 4 5 5 1 3 6 2 3 உ ঁ -2 -4 -5 -1 -3 -6 -2 -3 4 5 -5

Slide 91

Slide 91 text

• ࠷େྲྀΞϧΰϦζϜ • ݩͷάϥϑͰ͸࠷େೋ෦Ϛονϯά ϚονϯάΞϓϦ -2 -5 -1 -2 -3 -5 உ ঁ -4 -3 -6 4 5 2 5 1 2 3 5 உ ঁ 4 3 6

Slide 92

Slide 92 text

ήʔϜ֤छ • ΠϯάϨε • ਞऔΓ • ಺෦൑ఆ

Slide 93

Slide 93 text

࠷େࡾ֯ܗ໰୊ • Nݸͷ௖఺Ͱ࡞ΕΔ࠷େͷࡾ֯ܗ͸ʁ

Slide 94

Slide 94 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1

Slide 95

Slide 95 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2

Slide 96

Slide 96 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2

Slide 97

Slide 97 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2

Slide 98

Slide 98 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2

Slide 99

Slide 99 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2

Slide 100

Slide 100 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3

Slide 101

Slide 101 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3

Slide 102

Slide 102 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4

Slide 103

Slide 103 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4

Slide 104

Slide 104 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4

Slide 105

Slide 105 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4

Slide 106

Slide 106 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4

Slide 107

Slide 107 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4

Slide 108

Slide 108 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4

Slide 109

Slide 109 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4

Slide 110

Slide 110 text

࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4

Slide 111

Slide 111 text

࠷େࡾ֯ܗ໰୊ • ࠷େࡾ֯ܗ͸ತแΛߏ੒͢Δ௖఺ʹଘࡏ

Slide 112

Slide 112 text

࠷େࡾ֯ܗ໰୊ • ͠Ό͘ͱΓ๏ • ֎ੵ

Slide 113

Slide 113 text

࠷େࡾ֯ܗ໰୊ • ͠Ό͘ͱΓ๏ • ֎ੵ

Slide 114

Slide 114 text

࠷େࡾ֯ܗ໰୊ • ͠Ό͘ͱΓ๏ • ֎ੵ

Slide 115

Slide 115 text

ଟ͘ͷ໰୊ղܾͰ ΞϧΰϦζϜʹʮؼணʯ ͞Ε͍ͯΔ

Slide 116

Slide 116 text

ΞϧΰϦζϜͷੌ͞ ೖྗ͕૝ఆ಺Ͱ͋Ε͹ • ͲΜͳέʔεͰ΋ • શ͘ಉ͡ϑϩʔͰ ղ͕ग़Δͱ͜Ζɻ

Slide 117

Slide 117 text

ΞϧΰϦζϜͷੌ͞ ೖྗ͕૝ఆ಺Ͱ͋Ε͹ • ͲΜͳέʔεͰ΋ • શ͘ಉ͡ϑϩʔͰ ղ͕ग़Δͱ͜Ζɻ ̍ͭͷϓϩάϥϜͰ ղܾͰ͖ͯ͠·͏

Slide 118

Slide 118 text

໰୊Λந৅Խ͢Δ͜ͱͰ ΞϧΰϦζϜ͸ ྗΛൃش͢Δ

Slide 119

Slide 119 text

ΞϧΰϦζϜʢ࠶ܝʣ • ίϯϐϡʔλʹܭࢉͤ͞ΔͨΊͷʮܭࢉํ๏ʯ • ʮͲ͏ܭࢉͤ͞Δ͔ʯͷखॱ ʘܭࢉ͸ʗ ʘ೚ͤͯʂʗ

Slide 120

Slide 120 text

Α͏ͦ͜ ೉͘͠΋ඒ͍͠ ΞϧΰϦζϜͷੈք΁

Slide 121

Slide 121 text

࣭ٙԠ౴ • ΞϧΰϦζϜɾɾɾʁ • ʮྑ͍ʯΞϧΰϦζϜ • ܭࢉྔ • ޮ཰Α͘໰୊Λղ͜͏ • ੈքதͰ࢖ΘΕΔΞϧΰϦζϜ