Question

. If 2,000 elements are inserted into a binary search tree using the traditional, naïve algorithm what is the height of the tree (give the actual number, not the order) in:

1. The worst case

2. The best case

(Please explain not just answer)

Answer 1

The maximum number of edges from the root to any leaf node provides the height of the tree.

Total number of elements or nodes = 2000

Worst Case:

Height of the tree = n - 1 = 2000 - 1 = 1999

Explanation:

If the tree structure is a left-skewed binary tree. In the left-skewed binary tree, each and every node has one child only and this child is the left child.  The height of a left-skewed binary tree is maximum.

Best Case:

Height of the tree = log₂(n) = Floor (log₂(2000)) = Floor (l0.97) = 10

Explanation:

If each and every node in a binary tree has two children starting from the root node to the leaf node. This tree is a full binary tree or a complete binary tree. It has a minimum height.