Recursive Data Structures

1
Chapter 3.4

• Recursive Data Structures
• Part 3
• Storing Trees on Disk

2
Trees on Disk

• To save a tree between uses
• e.g. An AVL dictionary used for spelling
• Saving pointer values is useless
• Tree has to be
• Written in preorder on a sequential file
• Rebuild with a straight building program
• Because central memory isn't large enough
• Beware of virtual memory
• Use multiway BTrees

3
Storing a Tree on diskWrite in PreOrder on
sequential file
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root (left subtree) (right subtree) hdbacfegljikn
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskUse ordinary binary
tree building
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Restoring a Tree from diskWhy not AVL tree
building ???
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Storing a Tree on diskWhy not use InOrder or
PostOrder ?
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InOrder (left subtree) root (right
subtree) abcdefghijklmno
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Restoring a Tree from disk Why not use InOrder
???
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Restoring a Tree from disk Why not use InOrder
???
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Restoring a Tree from disk Why not use InOrder
???
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Trees on Disk

• To save a tree between uses
• e.g. An AVL dictionary used for spelling
• Saving pointer values is useless
• Tree has to be
• Written in preorder on a sequential file
• Rebuild with a straight building program
• Because central memory isn't large enough
• Beware of virtual memory
• Use multiway BTrees

45
BTrees

• Objectives
• Build well balanced trees
• take properties of disk into account
• space inexpensive
• access time very long
• data transfers by entire sectors or tracks
• Minimize number of disk accesses
• one node of the tree sector or track
• leave spare space to minimize rebalancing

46
BTrees

• Definitions
• A node contains k ordered data items
• n is a system dependant constant such that a
  sector or a track of the disk can hold 2n data
  items and 2n1 pointers
• In the root 0 lt k lt 2n
• In all other nodes n lt k lt 2n
• A node has 0 or k1 successors
• All nodes with 0 successors are at the same level

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Multiway Trees
a
b
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BTree Growth

XX
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BTrees
Example n 2.
Insertion 25
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BTrees
Insertion 25, 36
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BTrees
Insertion 25, 36, 15
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BTrees
Insertion 25, 36, 15, 31
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BTrees
Insertion 25, 36, 15, 31, 18
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BTrees
Insertion 25, 36, 15, 18, 31, 43
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BTrees
Insertion 25, 36, 15, 18, 31, 43, 51
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BTrees
Insertion 25, 36, 15, 18, 31, 43, 51, 66
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BTrees
Insertion 25, 36, 15, 18, 31, 43, 51, 66, 42
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BTrees
Insertion 25, 36, 15, 18, 31, 43, 51, 66, 42, 75
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BTrees
Insertion 25, 36, 15, 18, 31, 43, 51, 66, 42,
75, 81
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BTrees
Insertion 25, 36, 15, 18, 31, 43, 51, 66, 42,
75, 81
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BTrees
Removal 75
15
18
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66
75
81
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BTrees
Removed 75
15
18
51
66
81

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BTrees
Removal 15
15
18
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BTrees
Removal 15
18

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BTrees
Removed 15
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66
BTrees
Removal 43
31
43


18
25
67
BTrees
Removal 43
31
42


18
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36



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BTrees
Removed 43
42



18
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