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これでわかるB-treeアルゴリズム / B-tree algorithm

これでわかるB-treeアルゴリズム / B-tree algorithm

・二分探索木 (binary search tree)
・AVL tree
・B-tree
・B+ tree

について順を追いながら説明。
流れを細かく書いたので、わかりやすいと思います。

ハトネコエ

December 06, 2018
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Transcript

  1. ͜ΕͰΘ͔Δ(?)

    B-tree ΞϧΰϦζϜ
    2018/12/06 ࣾ಺ษڧձ
    ϋτωίΤ

    View Slide

  2. ϋτωίΤ
    @nekonenene
    ࢲ͸ॳԻϛΫͰ͢
    ͝ଘ஌͋ͷํ

    View Slide

  3. • B໦ͱ΋ݺ͹ΕΔ

    • σʔλߏ଄ͷҰछͰ͋Δ໦ߏ଄ͷҰछ

    • ϧʔτ͔Βͷߴ͕͞Ұఆͷฏߧ໦ʢ΁͍͜͏͗ʣͷҰछ

    • Mongo DBͳͲͷσʔλϕʔεͷ΄͔ɺ

    WindowsͷϑΝΠϧγεςϜNTFS ΍

    MacͷϑΝΠϧγεςϜAPFS ͳͲͰ࢖ΘΕ͍ͯΔ
    B-tree

    View Slide

  4. • MySQLͷσʔλϕʔεΤϯδϯ InnoDB Ͱ͸ɺ

    ॱʑʹΞΫηε͢ΔੑೳΛ্͛ͨ B+ tree ͕࢖ΘΕ͍ͯΔ

    • Oracle Database ΍

    MacͷϑΝΠϧγεςϜͩͬͨHFS+ Ͱ͸

    B* tree ͕࢖ΘΕ͍ͯΔʢࠓճ͸ѻ͍·ͤΜʣ
    B-tree ѥछ

    View Slide

  5. Χϯλϯͳ΋ͷ͔Β

    ࢝Ί͍ͯ͜͏

    View Slide

  6. • ΋ͬͱ΋୯७ͳ໦ߏ଄

    • খ͍͞஋ΛࠨԼʹɺେ͖͍஋ΛӈԼʹ͚͍ͭͯ͘
    ೋ෼୳ࡧ໦

    View Slide

  7. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    ೋ෼୳ࡧ໦ɿྫ
    10
    5

    View Slide

  8. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    ೋ෼୳ࡧ໦ɿྫ
    10
    5
    ਌ϊʔυ
    ࢠϊʔυ

    View Slide

  9. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    ೋ෼୳ࡧ໦ɿྫ
    10
    5
    3
    2

    View Slide

  10. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    ೋ෼୳ࡧ໦ɿྫ
    10
    5
    3
    2
    8

    View Slide

  11. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    ೋ෼୳ࡧ໦ɿྫ
    10
    5
    3
    2
    8
    4

    View Slide

  12. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    ೋ෼୳ࡧ໦ɿྫ
    10
    5
    3
    2
    1
    8
    4

    View Slide

  13. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    ೋ෼୳ࡧ໦ɿྫ
    10
    5
    3
    2
    1
    8
    4 6

    View Slide

  14. • ໦ͷόϥϯε͕ۉ౳ʹ੔͍ͬͯΕ͹ɺ

    ཁૉ਺ n ʹରͯ͠୳ࡧʹ͔͔Δ࠷ѱܭࢉྔ͸ O (log n) ʹͰ͖Δ

    • ͭ·Γɺσʔλ͕૿͑ͯ΋ݕࡧͷ͕࣌ؒ૿͑ͳ͍
    ೋ෼୳ࡧ໦ͷར఺
    10
    5
    2 8
    16
    12 20
    ཁૉ਺ n
    ܭࢉྔ

    View Slide

  15. • ࠨԼͷਤͷΑ͏ͳภͬͨ໦ߏ଄ͷ࠷ѱͷ৔߹Λߟ͑Δ

    • ཁૉ਺͕ଟ͍΄ͲൺֱΛ͓͜ͳ͏ͷͰ࠷ѱܭࢉྔ͸ O (n)
    ೋ෼୳ࡧ໦ͷܽ఺
    ཁૉ਺ n
    ܭࢉྔ
    10
    5
    3
    2

    View Slide

  16. ͦΕͳΒ੔ͬͨ

    ໦ߏ଄ʹ͠Α͏ʂ

    View Slide

  17. • ߟҊऀͷ2ਓͷ໊લ͕༝དྷʢAdelson-Velskii and Landis' treeʣ

    • ࠨ෦෼໦ͷߴ͞ͱӈ෦෼໦ͷߴ͕͞1ΑΓେ͖͘ͳͬͨΒ

    ʮ໦ͷճసʯʹΑΓ࠶ߏ੒͠ɺฏߧΛอͭ
    AVL໦

    View Slide

  18. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    AVL໦ɿྫ
    10
    5

    View Slide

  19. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    AVL໦ɿྫ
    10
    5
    3
    ʮ10ʯ͔Βݟͯ

    ࠨ͸ߴ͞ 2

    ӈ͸ߴ͞ 0

    ʹͳͬͯ͠·͏
    ͦ͜Ͱɺ໦ͷճసʂ

    View Slide

  20. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    AVL໦ɿྫ
    10
    5
    3
    த৺ʹ͍ͨ

    ʮ5ʯΛ਌ʹͯ͠

    ଞΛࢠʹ͢Δ

    View Slide

  21. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    AVL໦ɿྫ
    10
    5
    3
    2

    View Slide

  22. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    AVL໦ɿྫ
    10
    5
    3
    2 8

    View Slide

  23. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    AVL໦ɿྫ
    10
    5
    3
    2 8
    4

    View Slide

  24. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    AVL໦ɿྫ
    10
    5
    3
    2 8
    4
    1

    View Slide

  25. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    AVL໦ɿྫ
    10
    5
    3
    2 8
    4
    1 ͭͳ͛ΒΕΔՕॴͷߴ͞ͷ͕ࠩ2

    ͜Ε͸໦ͷճస͕ى͜Δʁ
    ?
    ?

    View Slide

  26. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    AVL໦ɿྫ
    10
    5
    3
    2 8
    4
    1
    ʮ5ʯ͔Βݟͯ

    ࠨͷߴ͞ 3

    ӈͷߴ͞ 2
    ʮ3ʯ͔Βݟͯ

    ࠨͷߴ͞ 2

    ӈͷߴ͞ 1
    ࠨ෦෼໦ͱӈ෦෼໦ͷߴ͞ͷࠩΛ

    ݟΔͷͰɺ·ͩ଱͑·͢

    View Slide

  27. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    AVL໦ɿྫ
    10
    5
    3
    2 8
    4
    1 6
    ʮ10ʯ͔Βݟͯ

    ࠨͷߴ͞ 2

    ӈͷߴ͞ 0
    ໦ͷճసνϟϯεʂ

    View Slide

  28. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    AVL໦ɿྫ
    10
    5
    3
    2 8
    4
    1 6
    த৺ʹ͍Δ

    ʮ8ʯΛ਌ʹ͠ɺ

    ଞ2ͭ͸ࢠʹ

    View Slide

  29. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    AVL໦ɿྫ
    8
    5
    3
    2 6
    4
    1
    10
    ׬੒ʂ

    View Slide

  30. • ࠷ѱܭࢉྔ͕େ͖͘ͳΒͳ͍Α͏ɺ

    ໦ͷճసΛ༻͍ɺͰ͖Δ͚ͩภΓͷͳ͍໦Λ࡞͍ͬͯͬͨ

    • ͜ͷΑ͏ͳฏୱʹۙ෇͚Δ໦ߏ଄Λ

    ฏߧ໦ʢ΁͍͜͏͗ʣͱݺͿ
    AVL໦ ͓͞Β͍

    View Slide

  31. • ໦ͷߴ͕͞ߴ͘ͳΓ΍͍͢

    • ݁Ռɺσʔλྔ͕ͱͯ΋ଟ͍৔߹ɺݕࡧʹ͕͔͔࣌ؒΔ

    • → ͦ͜Ͱ B-tree ʂ
    AVL໦ͷܽ఺

    View Slide

  32. • ֤ϊʔυʹ࣋ͨͤΔ஋Λ1ͭͰͳ͘ෳ਺ʹ͠ɺ໦ͷߴ͞Λ཈͑Δ

    • ࠓ·Ͱͷϊʔυ͸஋XΑΓখ͍͔ͦ͞ΕҎ্͔ɺͷ

    2ຊͷࢬ͔͍࣋ͬͯ͠ͳ͔͕ͬͨɺB-treeͰ͸ΑΓଟ͘ͷࢬΛ࣋ͭ

    • ྫ͑͹ X ͱ Y ͷ 2 ͭͷ஋Λϊʔυʹ΋ͭͱܾΊͨ৔߹ɺ

    ஋Xະຬ / ஋XҎ্ͰYະຬ / ஋YҎ্

    ͷ3ຊͷࢬΛϊʔυ͸࠷େͰ࣋ͭʢΦʔμʔ3ʣ
    ͦ͜Ͱ B-tree

    View Slide

  33. • ϊʔυ͕࠷େͰ࣋ͭࢬͷ਺ʹԠͯ͡ɺ

    ʮΦʔμʔ m ͷB-treeʯͱ͍͏ݴ͍ํΛ͢Δ

    • Φʔμʔ͸ 3 ʙ 5 ͕Α͋͘ΔΒ͍͠

    • ࠓճ͸ɺΦʔμʔ 3 ͷ B-tree ʢͭ·Γϊʔυʹ2ͭͷ஋Λ࣋ͭʣ

    ʹ͍ͭͯྫΛݟ͍ͯ͘ɻ

    ࢠϊʔυΛ2ʙ3࣋ͭ͜ͱ͔Βɺ2-3 tree ͱ΋ݺ͹ΕΔ
    Φʔμʔ

    View Slide

  34. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    5 10 ϊʔυʹ2ͭͷ

    ஋Λ΋ͭ

    View Slide

  35. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    5 10 ϊʔυʹ

    3ͭ໨ͷ஋͕……
    3
    த৺ͷ஋͸਌ϊʔυʹҠಈʂ

    View Slide

  36. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    5
    10
    3

    View Slide

  37. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    5
    10
    2 3

    View Slide

  38. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    5
    8
    2 3 10

    View Slide

  39. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    5
    8
    2 3 10
    4

    View Slide

  40. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    5
    8
    2 3 10
    4
    த৺ͷ஋͸

    ਌ϊʔυʹҠಈʂ

    View Slide

  41. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    5
    8
    2 3 10
    4
    Զ͕਌ϊʔυͩʂ
    த৺ͷ஋͸

    ਌ϊʔυʹҠಈʂ

    View Slide

  42. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    3
    8
    2 10
    4
    5

    View Slide

  43. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    3
    8
    1 10
    4
    5
    2

    View Slide

  44. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    3
    6
    1 8
    4
    5
    2 10
    த৺ͷ஋͸

    ਌ϊʔυʹҠಈʂ

    View Slide

  45. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    3
    6
    1
    8
    4
    5
    2 10
    ͋Ε……͓अຐʁ

    View Slide

  46. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    3
    6
    1
    8
    4
    5
    2 10
    த৺ͷ஋͸

    ਌ϊʔυʹҠಈʂ

    View Slide

  47. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B-treeɿྫ
    3
    6
    1
    8
    4
    5
    2 10
    ߴ͞Ξοϓʂ
    ˍ׬੒ʂ

    View Slide

  48. • جຊͷΞϧΰϦζϜ͸ B-tree

    • ࠷Լ૚ͷϊʔυΛϙΠϯλͰͭͳ͗߹Θͤͨ͜ͱͰɺ

    খ͞ͳ஋͔Βେ͖ͳ஋΁ॱʑʹΞΫηε͍ͯ͘͠

    ͱ͍͏ڍಈͷύϑΥʔϚϯεΛ্͛Δ͜ͱʹ੒ޭ

    • ઌ΄Ͳಉ༷ɺΦʔμʔ 3 ʢϊʔυ͕࠷େͰ࣋ͭࢬ͕3ຊʣͷ

    B+ tree ʹ͍ͭͯݟ͍ͯ͘
    B+ tree

    View Slide

  49. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5 10

    View Slide

  50. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5 10 ϊʔυʹ

    3ͭ໨ͷ஋͕……
    3
    த৺ͷ஋͸਌ϊʔυʹҠಈʂ

    View Slide

  51. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5
    3 10
    ਌ϊʔυ΁Ҡಈͭͭ͠…
    ΋ͱͷ஋΋࢒͢ʂ

    View Slide

  52. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5
    3 10
    ࠷Լ૚ಉ࢜Λ

    ϙΠϯλͰͭͳ͙ʂ
    ͜Ε͕ B+ tree ͷ
    Ұ൪ͷಛ௃ʂ

    View Slide

  53. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5
    3 10

    View Slide

  54. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5
    2 10
    3

    View Slide

  55. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5
    2 8
    3 10
    த৺ͷ஋͸

    ਌ϊʔυʹҠಈʂ

    View Slide

  56. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5
    2 8
    3 10
    8
    ΋ͱͷ஋΋࢒͢

    View Slide

  57. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5
    2 8
    3 10
    8
    4
    த৺ͷ஋͸

    ਌ϊʔυʹҠಈʂ

    View Slide

  58. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5
    2 8
    3
    10
    8
    4
    3
    ΋ͱͷ஋΋࢒͢

    View Slide

  59. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5 8
    3
    10
    8
    4
    3
    3ͭʹͳͬͯ͠·ͬͨ……
    2

    View Slide

  60. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5 8
    3
    10
    8
    4
    3
    2
    த৺ͷ஋͸

    ਌ϊʔυʹҠಈʂ
    3ͭʹͳͬͯ͠·ͬͨ……

    View Slide

  61. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    3 8
    5
    Θ͔Γ΍͍͢Α͏

    ্෦෼͚ͩߟ͑Δ
    ৽͍͠ύύͩΑ
    ΋ͱͷ஋΋࢒͢

    View Slide

  62. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    3 8
    5
    Θ͔Γ΍͍͢Α͏

    ্෦෼͚ͩߟ͑Δ
    5ະຬ
    5Ҏ্

    View Slide

  63. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5 8
    3
    10
    8
    4
    3
    2
    ͳͷͰಉ༷ʹ……

    View Slide

  64. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5 8
    3
    10
    8
    4
    3
    2
    5
    ͜͏ͳΔʂ

    View Slide

  65. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5 8
    3
    10
    8
    4
    3
    2
    5
    ʢ஫ҙʣ
    ͜͏͸ͳΒͳ͍ Φʔμʔ 3 ͷ

    B໦Ͱ͸

    ࠷௿ 2 ͭͷ

    ࢠϊʔυΛ࣋ͭ

    View Slide

  66. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5 8
    3
    10
    8
    4
    3
    2
    5
    ࿩Λ໭ͯ࣍͠΁…

    View Slide

  67. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5 8
    3
    10
    8
    4
    3
    1
    5
    2

    View Slide

  68. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5 8
    3
    10
    8
    4
    3
    1
    5
    2 6

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  69. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5 8
    3
    10
    8
    4
    3
    1
    5
    2 6
    ׬੒ʂ

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  70. • ࠷Լ૚ͷϊʔυ͕ϙΠϯλͰͭͳ͕͍ͬͯΔͨΊɺ

    খ͞ͳ஋͔Βେ͖ͳ஋΁ॱʑʹΞΫηε͍͖͍ͯͨ͠৔߹ʹɺ

    ຖճݕࡧͷखؒΛڬ·ͳͯ͘ࡁΉ

    • ͳ͓ɺ͜ͷ࠷Լ૚ͷϊʔυΛ

    ʮϦʔϑϊʔυʢleaf nodesʣʯͱݴ͍·͢
    B+ tree ͓͞Β͍

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  71. • 10 → 5 → 3 → 2 → 8 → 4 → 1 → 6 ͷॱʹೖΕ͍͖ͯ·͢
    B+ treeɿྫ
    5
    5 8
    3
    10
    8
    4
    3
    1
    5
    2 6
    Ϧʔϑϊʔυ

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  72. • ΧϥϜʹΠϯσοΫεΛషΔ͜ͱͰɺ

    B+ tree ͷߏ଄͕࡞ΒΕɺॱʑʹͳ͍ͬͯΔͷͰ

    ൣғݕࡧ͕εϐʔυग़͠΍͍͢

    • ͳ͓ɺInno DB Ͱ͸ϦʔϑϊʔυؒͷϙΠϯλ͕

    Ұํ޲Ͱ͸ͳ͘૒ํ޲ʹͳ͍ͬͯΔ
    Inno DB ʹ͓͍ͯ
    5 8 10
    4
    3
    1 2 6

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  73. • AVL໦

    https://www.cs.usfca.edu/~galles/visualization/AVLtree.html

    • B-tree

    https://www.cs.usfca.edu/~galles/visualization/BTree.html

    • B+ tree

    https://www.cs.usfca.edu/~galles/visualization/BPlusTree.html

    • ͦͷଞ

    https://www.cs.usfca.edu/~galles/visualization/Algorithms.html
    ศརͳγϛϡϨʔλʔ

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