GATE CS 2015 Set 3 — Question 39
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Databases → Indexing & File Organization → B+ Tree Numericals
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Question
Consider a B+ tree in which the search key is 12 bytes long, block size is 1024 bytes, record pointer is 10 bytes long and block pointer is 8 bytes long. The maximum number of keys that can be accommodated in each non-leaf node of the tree is ___________.
Correct answer
50 to 50
Solution
In a B+ tree, non-leaf nodes (internal nodes) contain only block pointers and search keys. They do not contain record pointers (which are only in leaf nodes). Let be the order of the B+ tree (maximum number of block pointers in a node).
A node with block pointers will have keys.The size of a block pointer is bytes.
The size of a search key is bytes.
The block size is bytes.The inequality for the size of a non-leaf node is:Since must be an integer, the maximum order is .
The maximum number of keys in a non-leaf node is .
A node with block pointers will have keys.The size of a block pointer is bytes.
The size of a search key is bytes.
The block size is bytes.The inequality for the size of a non-leaf node is:Since must be an integer, the maximum order is .
The maximum number of keys in a non-leaf node is .
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