Chapter 12 - Multiway Trees

8/6/2019 Chapter 12 - Multiway Trees

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Chapter 12

Lexicographic Search Trees: Tries

Multiway Trees

B-Tree, B*-Tree, B+-Tree

Red-Black Trees (BST and B-Tree)

2-d Tree, k-d Tree

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Basic Concepts

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Trees

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Trees and Orchard

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Lexicographic Search Tree

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Multiway Trees

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M-Way Search Tree

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B-Tree

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B-Tree Insertion

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B-Tree Insertion

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B-Tree

B_Node

count

data

branch

End B_Node

B_Tree

root

End B_Tree

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Methods and Functions

SearchTree recursiveSearchTree(calls)

SearchNode

Insert recursiveInsert

splitNode

push_in


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B-Tree SeachTree

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SearchTree (reftarget )

1. return recursiveSearchTree(root, target)

End SearchTree


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B-Tree SeachTree

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recursiveSearchTree (val subroot ,

reftarget )

1. result = not_present

2. if(subroot is not NULL)

1. result = SearhNode (subroot, target, position)2. if(result = not_present)

1. result = recursiveSearchTree ( subroot->branchposition, target)

3. else

1. target = subroot->dataposition

3. return result

End recursiveSearchTree


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B-Tree SeachTree

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SearchNode (val subroot ,

val target ,

refposition )

1. position = 02. loop (position < subroot->count) AND (target>subroot->dataposition)

1. position = position + 1 // Sequential Search

3. if(position < subroot->count) AND (target = subroot->dataposition)

1. return success

4. else

1. return not_present

End SearchNode


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Methods and Functions

SearchTree recursiveSearchTree(calls)

SearchNode

Insert recursiveInsert

splitNode

push_in


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B-Tree Insertion

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Insert (val newData )

(local variable: median , rightBranch ,newroot , result )

Return duplicate_error, success

1. result = recursiveInsert (root, newData, median, rightBranch)

2. if (result = overflow)1. Allocate newroot

2. newroot->count = 1

3. newroot->data0 = median

4. newroot->branch0 = root5. newroot->branch1 = rightBranch

6. root = newroot

7. result = success

3. return resultEnd Insert


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Split Node

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B-Tree Insertion

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recursiveInsert (val subroot ,

val newData ,

refmedian ,

refrightBranch )

Return overflow, duplicate_error, success

1. if(subroot = NULL)

1. median = newData

2. rightbranch = NULL

3. result = overflow

2. else

recursiveInsert (val subroot


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recursiveInsert (val subroot ,

val newData ,

refmedian ,

refrightBranch ) (cont.)

2. // else, local variables: extraEntry, extraBranch

1. if(SearchNode (subroot, newData, position) = success)

1. result = duplicate_error

2. else

1. result = recursiveInsert (subroot->branchposition, newData,extraEntry, extraBranch)

2. if(result = overflow)

1. if(subroot->count < order-1)

1. result = success

2. push_in (subroot, extraEntry, extraBranch, position)

2. else

1. splitNode (subroot, extraEntry, extraBranch, position,

rightBrach, median)

3. return result

End recursiveInsert


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Push In

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B-Tree

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push_in (val subroot ,

val entry ,val rightBranch ,

val position )

1. i = subroot->count

2. loop ( i > position)

1. subroot->datai = subroot->datai - 12. subroot->branchi + 1 = subroot->branchi3. i = i + 1

3. subroot->data position= entry

4. subroot->branch position + 1= rightBranch

5. subroot->count = -subroot->count + 1

End push_in


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B-Tree

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splitNode (val subroot ,

val extraEntry ,val extraBranch ,

val position ,

refrightHalf,

refmedian )


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B-Tree Insertion

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B-Tree Insertion

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B-Tree Deletion

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B-Tree Deletion

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B-Tree Deletion

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k d T


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k-d Trees

2-d Tree

k-d Tree

Chapter 12 - Multiway Trees

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