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DATA STRUCTURE

S

MAHESH GOYANIMAHATMA GANDHI INSTITUE OF TECHNICAL EDUCATION & RESEARCH CENTER

mgoyani@rediffmail.com

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M-WAY SEARCH

TREE

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Tree having m-1 key and m children is called m-way search tree.

A binary tree is a 2-way tree. It means it has m-1 = 2-1 = 1 key and maximum 2 child.

A Binary Tree is called m-way tree of order 2.

9 20 41

9 20

9 9 20 41

9

9 20

9

9 20 41

TERMINOLOGY

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2-3SEARCH

TREE

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TERMINOLOGY

Every node in 2-3 tree has two or three children.

A 2-3 tree is a tree in which leaf nodes are the only nodes that contains data values.

All leaf nodes contains two values.

The first value in non-leaf node is the maximum value of its left subtree.

The second value of non-leaf node is the maximum value of its middle (or right) tree.

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13

insert (13)

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13

insert (41)

41

13 : 41

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13

insert (21)

41

13 : 41

21

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insert (7)

13 : 41

7 13 21 41

7 : 13 21 : 41

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insert (18), insert (39)

13 : 41

7 18 21 41

7 : 13 21 : 41

13 39

7 : 13 21 : 39