1. m-Way Search Trees A m-way Search tree of degree ‘m’ can have
at most m child nodes.
If a node has k child nodes, then the node can
have only (k-1) keys contained in the node.
For a node A0, (K1, A1), (K2, A2)…………….
..(Km-1, Am-1), all key value in the sub-tree
pointed to by Ai are less than the key Ki+1, and
all key values in the sub-tree pointed to by Am-1
are greater than Km-1.

2. Example 2 : 22 25
5 10 14 27

3. m-Way searching : Similar to Binary searching What about if d>2 ?
If search item s<k1 search the leftmost child.
If search item s>k(d-1), search the rightmost child
What about if d>2 ?
Find two keys k(i-1) and k(i) between which s falls,
and search the item in that node.

4. m-Way searching : Search for 8 Search for 12 22 25 5 10 3 4 6 8 14
5 10 14 27

5. What would an in-order traversal look like :22 25
5 10 14 27 3, 4, 5, 6, 8,
10,
11,
13,
14,
17,
18,
19,
20,
21,
22,
23,
24,
25, 27

6. Properties (2, 4) Tree It is a kind of m-way search tree.12
At most 4 children
All leaf are at same level 15 11 17

7. Insertion in m-way search tree :
STEPS :
Search the node where the key is to be inserted.
If the searched node is not full then insert the
key into that node.
If the searched node is full then open a new
child node and insert the key.

8. Insertion in m-way search tree :
Since 6<18
TO INSERT 6 X X
Since 6<7 & node
is not full 6 will
be inserted
at this
node. 7 12 80 92
141
262 X X X X X 8 12 77
148
151
172
186
272
286
350 X X X X X X X X X X X X X X

9. Insertion in m-way search tree :
To insert 6 X X 7 12 80 92
141
262 X X X X X 8 12 77
148
151
172
186
272
286
350 X X X X X X X X X X X X X X

10. Insertion in m-way search tree :
TO INSERT 6 X X 7 12 80 92
141
262 X X X X X 8 12 77
148
151
172
186
272
286
350 X X X X X X X X X X X X X X