Operation of Multiway search tree

1. Multi-Way Search Tree
CSE 203
Data Structures2
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2. Multi-way Search Tree
22
5 10 25
3 4 6 8 14 2723 24
11 13 17

3. Multi-way Search Tree
• Any node v, in a multi-way search tree is a d-
node if v has d children.
• Properties:
– Each internal node is a d-node, where d  2
– Each internal node of T stores a collection of item in
the form (k, x).
– Each d-node v of T, with children v1, …, vd, stores (d-
1) items (k1, x1), … , (kd-1, xd-1) where k1…kd-1
– For each item (k, x) stored at a node in the sub-tree
of v rooted at vi, i=1,…, d, we have that ki-1 k ki

4. Multi-way Search Tree
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5 10 25
3 4 6 8 14 2723 24
11 13 17
v
v1 v2 v3
k2k1

5. • Proposition: A multi-way search tree with n
items has n+1 external nodes.
Multi-way Search Tree
Justification Try Yourself

6. SEARCHING
Multi-way Search Tree

7. Multi-way Search Tree
(Searching)
22
5 10 25
3 4 6 8 14 2723 24
11 13 17
Search for 12
Compare with the root
Compare with the node
Compare with the node
Compare with the node
External
Node!!!!
Not Found

8. • Space Requirement: O(n)
• Search Time: O(hdmax) or O(h lg dmax)
Multi-way Search Tree

9. Thank You