Elementary algorithm

Transcript

1. ษڧձ
2. ࣗݾ঺հ https://github.com/mochisuna • ؙా୓࿨ʢ·ΔͨͻΖ͔ͣʣ • Twitter: @mochi_suna • ओʹαʔόʔαΠυΤϯδχΞ • झຯɿϐΞϊɺϘυήɺΞΠίϯ࡞੒ʢΧούʣɺϓϨθϯ • ࣗಈԽେ޷͖ɻख࡞ۀ͖Β͍ • githubɿ @mochisuna
3. ٕज़໘
4. ଴ͯ଴ͯ
5. ࠓ·Ͱͷൃද ↑લʑճ ↑લճ
6. ΤϯδχΞɾɾɾʁ
7. ͪΐͬͱਅ໘໨ͳ ಺༰ʹ͍ͨ͠
8. ੲͷઐ໳͔Β࣋ͬͯ͜Α͏ʂ
9. ΞϧΰϦζϜͷೖ໳ ɾɾɾͷೖ໳ ·Δͨ
10. ࿩͢͜ͱ • ΞϧΰϦζϜɾɾɾʁ • ʮྑ͍ʯΞϧΰϦζϜ • ܭࢉྔ • ޮ཰Α͘໰୊Λղ͜͏ • ੈքதͰ࢖ΘΕΔΞϧΰϦζϜ
11. ΞϧΰϦζϜɾɾɾʁ
13. ΞϧΰϦζϜʢAlgorithmʣ • ʮܭࢉՄೳʯͳ͜ͱΛܭࢉ͢Δɺܗࣜతͳखଓ͖ ͷ͜ͱɺ͋Δ͍͸ͦΕΛܗࣜతʹදݱͨ͠΋ͷ • ίϯϐϡʔλʹܭࢉͤ͞ΔͨΊͷʮܭࢉํ๏ʯ
14. ΞϧΰϦζϜʢAlgorithmʣ • ʮܭࢉՄೳʯͳ͜ͱΛܭࢉ͢Δɺܗࣜతͳखଓ͖ ͷ͜ͱɺ͋Δ͍͸ͦΕΛܗࣜతʹදݱͨ͠΋ͷ • ίϯϐϡʔλʹܭࢉͤ͞ΔͨΊͷʮܭࢉํ๏ʯ 🤔🤔🤔
15. ॱ൪ʹ۷ΓԼ͍͛ͯ͘
16. ͦ΋ͦ΋
17. ίϯϐϡʔλ͸͓όΧ͞Μ ʘͳΜͩͱʔʗ ʘ͹͔ʹ͢Μͳʔʗ
18. ίϯϐϡʔλ͸͔֬ʹ͍͢͝ • ௒͍͢͝ܭࢉೳྗ • Կԯ×Կԯͷܭࢉ͕ਖ਼͔֬ͭߴ଎ • ௒͍͢͝هԱྗ • ԿઍɺԿສͷ਺஋Λਖ਼֬ʹهԱͰ͖Δ ʘ͑ͬ΁Μʗ ʘͲ΍͊ʗ
19. Ͱ΋ίϯϐϡʔλ͸͓όΧ͞Μ • ࣗྗͰ͸ߟ͑ΒΕͳ͍ • ՝୊ΛղऍͰ͖ͳ͍ • ʮϓϩάϥϜ͸ࢥͬͨ௨Γʹಈ͔ͳ͍ɻʯ ʮॻ͍ͨ௨Γʹಈ͘ʯ ʘOh…ʗ ʘͦΕ͸܅ͨͪͷ࢓ࣄ͞ʗ
20. ۩ମతͳྫͰߟ͍͑ͯ͜͏
21. ໰୊ • Q͞Μ͸3೥ʹҰ౓ɺఆظతʹπΠʔτ͠·͢ɻ • Q͞Μ͸3ͷഒ਺ͷ೥ྸͷ࣌ʹඞͣ೥1ճ͚ͩπΠʔτ ͠ɺͦΕҎ֎ͷ೥ྸͷ࣌͸Ұ੾͠·ͤΜɻ • Ͱ͸ɺQ͞Μ͸ಛఆͷAࡀ͔ΒBࡀ·ͰͷؒʹԿճπ Πʔτ͢ΔͰ͠ΐ͏͔ʁ
22. ͜ͷ··Ͱ͸ ίϯϐϡʔλͰ͸ ॲཧͰ͖ͳ͍ ʘʁʁʁʗ ʘʁʁʁʗ
23. 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 ೥ྸ 
24. ϓϩάϥϜʹམͱ͠ࠐΉ sum := 0 FOR i := A; i <= B; i++ IF i%3 == 0 sum++ END END print(sum)
25. ͜͜·Ͱ΍ͬͯ ॳΊͯ໰୊͕ղ͚Δ ʘ͜ͷϓϩάϥϜͰ͍͍ͷʁʗ ʘ͜ΕΛܭࢉ͢Ε͹͍͍ͷͶʁʗ
26. ΞϧΰϦζϜ
27. ΞϧΰϦζϜ • ίϯϐϡʔλʹܭࢉͤ͞ΔͨΊͷʮܭࢉํ๏ʯ • ʮͲ͏ܭࢉͤ͞Δ͔ʯͷखॱ ʘܭࢉ͸ʗ ʘ೚ͤͯʂʗ
28. ݱ࣮ͷ໰୊Λ Ͳ͏΍ͬͯϓϩάϥϜʹ མͱ͠ࠐΉ͔
29. ͜Ε͕େࣄ
30. ࠓճ͸ΞϧΰϦζϜͷྫ͔Β ͦͷੌ͞ͱԞਂ͞ʹ ͪΐͬͱͰ΋఻͍͑ͨ
31. ͋Μ·೉͍͠ ༻ޠͱ͔֓೦͸ ࢖Θͳ͍Α͏ʹؤுΔ ʢP vs NP໰୊ͱ͔ʣ
32. ʮྑ͍ʯΞϧΰϦζϜ
33. ΞϧΰϦζϜʹʮղ͖ํʯ • ޮ཰ͷྑ͍ղ͖ํɾѱ͍ղ͖ํ͕͋Δ • ͪΐͬͱݟͯΈΑ͏ • https://www.toptal.com/developers/ sorting-algorithms
34. ॲཧޮ཰͕શવҧ͏
35. ޮ཰ͷʮྑ͍ʯ ΞϧΰϦζϜ͕ ༏Ε͍ͯΔ
37. PCͷੑೳ͕ 10ഒɺ20ഒʹͳΕ͹ ؔ܎ͳ͍ΑͶʂ ʘͤ΍ͳʗ ʘͦΕͳʗ
38. ࢒೦
39. ۪௚ͳΞϧΰϦζϜͰ͸ PCͰ΋ղ͚ͳ͍໰୊͕͋Δ ʘ͑ͬʗ ʘ͑ͬʗ
40. ८ճηʔϧεϚϯ໰୊
41. ८ճηʔϧεϚϯ໰୊ • Ұ൪গͳ͍ҠಈίετͰɺશͯͷՈΛͪΐ͏Ͳ ̍ճ͚ͩ๚໰͠ձࣾʹ໭ͬͯ͘Δ໰୊ • NݸͷՈ͕͋Δ৔߹N!௨Γͷ૊Έ߹Θͤ
42. ϐϯͱ͜ͳ͍ɾɾɾɻ • N=̑ͷ৔߹ɿ120௨Γ • N=10ͷ৔߹ɿ3628800௨Γ • N=15ͷ৔߹ɿ1.3*1012௨Γ • N=20ͷ৔߹ɿ2.4*1018௨Γ • N=100ͷ৔߹ɾɾɾʁ
43. ૊Έ߹Θͤരൃ • 1೥ؒ = 31536000ඵ ≒ 3.2*108ඵ • 1GHzʹඵؒ1.0 * 109ճͷԋࢉ • 3.2*108 × 1.0*109 = 3.2 * 1017
44. ૊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
45. ޮ཰ͷʮྑ͍ʯΞϧΰϦζϜ ͕ ٻΊΒΕ͍ͯΔ
46. ޮ཰ͷʮྑ͞ʯ ʮܭࢉྔʯ
47. ܭࢉྔ • ϓϩάϥϜͷ࣮ߦ։͔࢝Βऴྃ·Ͱʹ͔͔Δ ࣌ؒʢۭؒʣΛධՁ • େࡶ೺ʹͲͷ͘Β͍͕͔͔࣌ؒΔͷ͔ • ࣮༻Ͱ΋େࣄ • ೖྗͷݸ਺΍஋ͷൣғΛม਺ͱ͢Δ
48. ܭࢉྔͷྫɿ1ॏϧʔϓ sum := 0 FOR i := 0; i < N; i++ sum += i END ճ࣮ߦ /ճ࣮ߦ
49. 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
50. 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
51. 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
52. 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
53. Өڹʹ͍ͭͯิ଍ • 3MN + 4M + 3ʹ͍ͭͯߟ͑Δ ./ ./ ./     .    ./    ./ .    
54. ܭࢉྔͷෆ౳ࣜ n ͕े෼େ͖͍ͱҎԼ͕੒ཱ ෆ౳ࣜͷࠨลʹߦ͘΄Ͳߴ଎ log n < n < n < n2 < n3 < 2n < 3n < n!
55. ܭࢉྔͷൺֱ
56. ޮ཰Α͘໰୊Λղ͜͏
57. ͸͡ΊͷҰาɿ୳ࡧ • ͋ΔσʔληοτAʹ͋Δ਺n͕͋Δ͔ʁ • A = [4,8,23,7,1,9] • n = 7
58. ۪௚ͳ୳ࡧ • લ͔Βॱʹ୳ࡧ → n = 7ʹҰகͨ͠ΒTRUE O ˣ J       "      
59. ۪௚ͳ୳ࡧ • લ͔Βॱʹ୳ࡧ → n = 7ʹҰகͨ͠ΒTRUE O º ˣ J       "      
60. ۪௚ͳ୳ࡧ • લ͔Βॱʹ୳ࡧ → n = 7ʹҰகͨ͠ΒTRUE O º º ˣ J       "      
61. ۪௚ͳ୳ࡧ • લ͔Βॱʹ୳ࡧ → n = 7ʹҰகͨ͠ΒTRUE O º º º ˣ J       "      
62. ۪௚ͳ୳ࡧ • લ͔Βॱʹ୳ࡧ → n = 7ʹҰகͨ͠ΒTRUE O º º º ✅ J       "      
63. ͜ͷ··ͩͱ • Nݸͷσʔληοτͷ৔߹ɿO(N)ճͷܭࢉྔ • ਺͕গͳ͚Ε͹ྑ͍͚Ͳແବ͕ଟ͍ O º º º º º º J       "      
64. Ͳ͏͠Α͏ʁ
65. • ॲཧ͢Δର৅ΛݮΒ͠ޮ཰Խ ·ͣ͸ιʔτ O J       "       ͔͜͜Βઌ͸
    ॲཧෆཁ
66. • ॲཧ͢Δର৅ΛݮΒ͠ޮ཰Խ • ͨͩ͠ɺܭࢉྔ͸Լ͕Βͳ͍ ·ͣ͸ιʔτ O J       "       ͔͜͜Βઌ͸
    ॲཧෆཁ
67. ΋ͬͱޮ཰Խ
68. • தԝ஋͔Βܭࢉɿ(5+0)/2 = 2 ೋ෼୳ࡧ O ˣ J       "      
69. • தԝ஋͔Βܭࢉɿ(5+0)/2 = 2 • 3 < 7 ͳͷͰࠨͷۭؒΛݕࡧ ೋ෼୳ࡧ O ˣ J       "      
70. • தԝ஋͔Βܭࢉɿ(2+0)/2 = 1 ೋ෼୳ࡧ O ˣ º J       "      
71. • தԝ஋͔Βܭࢉɿ(2+0)/2 = 1 • 3 < 4 ͳͷͰࠨͷۭؒΛݕࡧ ೋ෼୳ࡧ O ˣ º J       "      
72. • தԝ஋͔Βܭࢉɿ(1+0)/2 = 0 • 3 > 1 ͳͷͰଘࡏ͠ͳ͍ ೋ෼୳ࡧ O ˣ º º J       "      
73. ΋ͬ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
74. ೋ෼୳ࡧ • ৗʹ୳ࡧۭؒΛ൒෼ʹ͠ଓ͚Δ • ܭࢉྔɿO(log n) 
    d
     d d d d d d × n=13 × ×
75. ಉ͡୳ࡧͰ΋ɾɾɾ • ΞϧΰϦζϜҰͭͰѹ౗తʹߴ଎ʹͳΔ • ߴ଎ͳΞϧΰϦζϜͷݚڀ͸ੈքతʹ͞Ε͍ͯΔ
76. ͜͜·Ͱฉ͍ͯօ͞Μ ͜͏ࢥͬͨͰ͠ΐ͏
77. ʘผʹ਺ࣈ୳͠ͱ͔͠ͳ͍͠ʗ
78. ΞϧΰϦζϜͷੌ͞͸ ͦ͜͡Όͳ͍
79. ੈքதͰ࢖ΘΕΔ ΞϧΰϦζϜ
80. ྫ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) }
81. ྫɿϓϩάϥϛϯάݴޠ • ࣈ۟ղੳ/ߏจղੳ/AST a = 1 b = 2 if (b < 3) print(“hoge")
82. ྫɿϓϩάϥϛϯάݴޠ • ࣈ۟ղੳ/ߏจղੳ/AST a = 1 b = 2 if (b < 3) print(“hoge") B   C   JG  C  UIFO QSJOU lIPHF FMTF QSJOU B ࣈ۟ղੳ
83. ྫ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
84. ྫ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
85. ྫɿ஍ਤɾ࿏ઢܦ࿏ • GoogleMap • Yahoo࿏ઢͳͲ • ໎࿏
86. • ෯༏ઌ୳ࡧɿBFS / ਂ͞༏ઌ୳ࡧɿDFS • Dijikstra๏ / ϕϧϚϯɾϑΥʔυ๏ • ϫʔγϟϧɾϑϩΠυ๏ ࠷୹ܦ࿏໰୊  Start 3 6 8 12 10 3 2 1 0 5 7 4
87. • 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
88. ྫɿϚονϯάΞϓϦ
89. ϚονϯάΞϓϦ • ޷ײ౓͔ΒάϥϑΛఆٛ       உ ঁ 2 4 5 5 1 3 6 2 3
90. 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
91. • ࠷େྲྀ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
92. ήʔϜ֤छ • ΠϯάϨε • ਞऔΓ • ಺෦൑ఆ
93. ࠷େࡾ֯ܗ໰୊ • Nݸͷ௖఺Ͱ࡞ΕΔ࠷େͷࡾ֯ܗ͸ʁ
94. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1
95. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2
96. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2
97. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2
98. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2
99. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2
100. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3
101. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3
102. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4
103. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4
104. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4
105. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4
106. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4
107. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4
108. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4
109. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4
110. ࠷େࡾ֯ܗ໰୊ • ತ๏ • ෼ׂ౗ஔ๏ 1 2 3 4
111. ࠷େࡾ֯ܗ໰୊ • ࠷େࡾ֯ܗ͸ತแΛߏ੒͢Δ௖఺ʹଘࡏ
112. ࠷େࡾ֯ܗ໰୊ • ͠Ό͘ͱΓ๏ • ֎ੵ
113. ࠷େࡾ֯ܗ໰୊ • ͠Ό͘ͱΓ๏ • ֎ੵ
114. ࠷େࡾ֯ܗ໰୊ • ͠Ό͘ͱΓ๏ • ֎ੵ
115. ଟ͘ͷ໰୊ղܾͰ ΞϧΰϦζϜʹʮؼணʯ ͞Ε͍ͯΔ
116. ΞϧΰϦζϜͷੌ͞ ೖྗ͕૝ఆ಺Ͱ͋Ε͹ • ͲΜͳέʔεͰ΋ • શ͘ಉ͡ϑϩʔͰ ղ͕ग़Δͱ͜Ζɻ
117. ΞϧΰϦζϜͷੌ͞ ೖྗ͕૝ఆ಺Ͱ͋Ε͹ • ͲΜͳέʔεͰ΋ • શ͘ಉ͡ϑϩʔͰ ղ͕ग़Δͱ͜Ζɻ ̍ͭͷϓϩάϥϜͰ ղܾͰ͖ͯ͠·͏
118. ໰୊Λந৅Խ͢Δ͜ͱͰ ΞϧΰϦζϜ͸ ྗΛൃش͢Δ
119. ΞϧΰϦζϜʢ࠶ܝʣ • ίϯϐϡʔλʹܭࢉͤ͞ΔͨΊͷʮܭࢉํ๏ʯ • ʮͲ͏ܭࢉͤ͞Δ͔ʯͷखॱ ʘܭࢉ͸ʗ ʘ೚ͤͯʂʗ
120. Α͏ͦ͜ ೉͘͠΋ඒ͍͠ ΞϧΰϦζϜͷੈք΁
121. ࣭ٙԠ౴ • ΞϧΰϦζϜɾɾɾʁ • ʮྑ͍ʯΞϧΰϦζϜ • ܭࢉྔ • ޮ཰Α͘໰୊Λղ͜͏ • ੈքதͰ࢖ΘΕΔΞϧΰϦζϜ