In a database file structure, the search key field is 9 bytes long, the block…

Given:

• Search key size = 9 bytes

• Block pointer size = 6 bytes

• Block size = 512 bytes

For a non-leaf (internal) node with m pointers, the node stores m block pointers and m−1 keys. Therefore the space constraint is:

m × 6 + (m − 1) × 9 ≤ 512

Solve the inequality:

• m×6 + (m−1)×9 ≤ 512 ⇒ 6m + 9m − 9 ≤ 512 ⇒ 15m − 9 ≤ 512

• 15m ≤ 521 ⇒ m ≤ 521/15 ≈ 34.733…

• m must be an integer, so the largest possible order is 34.

Answer: 34