The maximum height of a binary search tree is O(log n), where n is the number of nodes.Group of answer choicesTrueFalse

Answer Analysis

1. Understanding the Definition of Binary Search Tree (BST): A binary search tree is a binary tree in which for each node:

   • The left child's key is less than the node's key.
   • The right child's key is greater than the node's key.

2. Height of the BST:

   • The height of a binary search tree is defined as the number of edges on the longest path from the root to a leaf node.
   • In a balanced binary search tree, where the nodes are organized evenly, the height is logarithmic in relation to the number of nodes, expressed as $O(\log n)$. This is because each comparison reduces the search space by about half.

3. Unbalanced BST Cases:

   • However, in the case of an unbalanced binary search tree (e.g., inserting nodes in an already sorted order), the height could become linear, which is $O(n)$ instead of $O(\log n)$.

Conclusion

The statement "The maximum height of a binary search tree is $O(\log n)$" is False. In the worst-case scenario of an unbalanced BST, the height can be $O(n)$.

Final Answer

False