What is the: a. maximum number of levels that a binary search tree with 100 node

Question

What is the:
a. maximum number of levels that a binary search tree with 100 nodes can have?
b. minimum number of levels that a binary search tree with 100 nodes can have?
c. maximum total number of nodes in a binary tree that has N levels? (Remember that the root is level 0.)
d. maximum number of nodes in the Nth level of a binary tree?
e. number of ancestors of a node in the Nth level of a binary search tree?
f. number of different binary trees that can be made from three nodes that contain the key values 1, 2, and 3?
g. number of different binary search trees that can be made from three nodes that contain the key values 1, 2, and 3?

Explanation / Answer

a) minimum number of levels that a binary search tree with 100 nodes can have? : log 2100
b. maximum number of levels that a binary search tree with 100 nodes can have? : 99
c. maximum total number of nodes in a binary tree that has N levels? (Remember that the root is level 0.) : 2n+1 - 1
d. maximum number of nodes in the Nth level of a binary tree? : 2N

e. number of ancestors of a node in the Nth level of a binary search tree?: N
f. number of different binary trees that can be made from three nodes that contain the key values 1, 2, and 3? : 2n - n
g) g. number of different binary search trees that can be made from three nodes that contain the key values 1, 2, and 3?  (2n)C(n)/(n+1) == Catalan number which is same as (2n)!/( (n!)*(n+1)! )

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