A $B^+$ - tree index is to be built on the Name attribute of the relation STUDENT. Assume that all the student names are of length $8$ bytes, disk blocks are of size $512$ bytes, and index pointers are of size $4$ bytes. Given the scenario, what would be the best choice of the degree (i.e. number of pointers per node) of the $B^+$ - tree?
In a $B^+$ tree we want en entire node content to be in a disk block. A node can contain up to $p$ pointers to child nodes and up to $p-1$ key values for a $B^+$ tree of order $p$. Here, key size is 8 bytes and pointer size is 4 bytes. Thus we can write
$8(p-1) + 4p \leq 512 \\ \implies 12p \leq 520 \\\implies p = 43.$
Ans : C
Here we have to calculate P(non-leaf) not P(leaf) bcz in order to calculate P(leaf) we require record pointer which is not given in the question.
P(leaf)= n(K+Rp) + Bp <= Block size
K= key field
Rp= Record pointer
Bp= Block pointer