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The smallest number of keys that will force a B-Tree of order 3 to have a height of 3 are _______

Consider that the root node is at height 0.

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Since, order = 3

Therefore, minimum keys at root, internal node or leaf = 1

And, node pointers = 2

For height = 3,

The number of keys at height 0 is = 1 // root node

The number of keys at height 1 is = 2

Number of keys at height 2 = 4

Number of keys at height 3 = 8

 

Therefore, total keys = 8 + 4 + 2 + 1 = 15

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