The maximum number of levels that a binary search tree with 3 nodes can have is 2.Group of answer choicesTrueFalse

Answer

The statement "The maximum number of levels that a binary search tree with 3 nodes can have is 2" is False.

Explanation

1. Understanding Levels in a Binary Search Tree:

   • A binary search tree (BST) can have nodes structured in such a way that each node has at most two children (left and right).
   • Levels are counted from the root node (level 0) down to the deepest node.

2. Maximum Levels with 3 Nodes:

   • To have the maximum number of levels, the nodes should be arranged such that each added node creates a new level.
   • Assuming a maximum height configuration:
     • One way to arrange 3 nodes is to have the first node as the root (level 0), the second node as a left or right child (level 1), and the third node as a child of either of those (level 2).
     • However, this arrangement still results in only 3 total levels (level 0, level 1, and level 2).

3. Conclusion:

   • The maximum number of levels in a binary search tree with 3 nodes can actually be 3, not 2.
   • Hence, the statement is False.

Final Answer

False