# Maximum number of node splitting operations of a B-tree

**Q. Algorithms: Consider a B-tree of order 4 and is built from scratch by 10 successive insertions. What would be the maximum number of node splitting operations that take place?***- Published on 24 Jun 15***a.** 6

**b.** 3

**c.** 4

**d.** 2

**ANSWER: 4**

A B-tree of order m contains n records and each contains b records on average then the tree will have about n/b leaves. If we split k nodes along the path from leaves then

k<=1+logm/2 [n/b]

here n=10,b=3,m=4 so

k<=1+log4/2 [n/b]

k<=1+log2 4

k<= 1+2

k<=3