What is the maximum number of keys that a B+ -tree of order 3 and of height 3 have?
Question
What is the maximum number of keys that a B+ -tree of order 3 and of height 3 have?
Solution
The maximum number of keys that a B+ tree of order 3 and height 3 can have is calculated as follows:
- A B+ tree of order 'm' can have a maximum of 'm-1' keys in each node.
- The root node can have a maximum of 'm-1' keys.
- Each level below the root can have a maximum of 'm' nodes.
- Therefore, a B+ tree of height 'h' can have a maximum of (m^(h-1))*(m-1) keys.
Substituting the given values, m=3 and h=3, we get:
- The root node can have a maximum of 3-1 = 2 keys.
- Each level below the root can have a maximum of 3 nodes.
- Therefore, a B+ tree of height 3 can have a maximum of (3^(3-1))*(3-1) = (3^2)2 = 92 = 18 keys.
So, a B+ tree of order 3 and height 3 can have a maximum of 18 keys.
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