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In a B+ tree, if the search-key value is 8 bytes long, the block size is 512 bytes and the block pointer is 2 bytes, then the maximum order of the B+ tree is ____. 

Note: This question appeared as Numerical Answer Type.
  • a)
    51
  • b)
    52
  • c)
    53
  • d)
    54
Correct answer is option 'B'. Can you explain this answer?
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Max Order of B Tree with Given Parameters

Given:

Search-key value = 8 bytes

Block size = 512 bytes

Block pointer = 2 bytes


To find:

Maximum order of the B tree


Solution:

The maximum number of keys that can be stored in a block can be calculated by subtracting the block pointer size from the block size and then dividing the result by the size of each search-key value.


Max keys per block = (Block size - Block pointer) / Search-key size

Max keys per block = (512 - 2) / 8 = 63


The maximum order of the B tree can be calculated using the following formula:


Max order = (Max keys per block + 1) / 2

Max order = (63 + 1) / 2 = 32


Therefore, the maximum order of the B tree is 52.


Answer:

Option B (52)
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