### Answer: True

A binary search tree (BST) is a data structure that maintains its elements in a sorted manner, allowing for efficient search, insertion, and deletion operations. In a balanced binary search tree, the maximum height is indeed $ O(\log n) $, where $ n $ is the number of nodes. This is because each level of the tree contains approximately double the number of nodes of the previous level, leading to a logarithmic relationship between the number of nodes and the height of the tree.

However, it's important to note that if the binary search tree is unbalanced (e.g., if nodes are inserted in sorted order), the height can become linear, $ O(n) $. But in the context of a balanced binary search tree, which maintains its height using techniques like AVL or Red-Black trees, the statement is true.

Question

### Answer: True

A binary search tree (BST) is a data structure that maintains its elements in a sorted manner, allowing for efficient search, insertion, and deletion operations. In a balanced binary search tree, the maximum height is indeed $ O(\log n) $, where $ n $ is the number of nodes. This is because each level of the tree contains approximately double the number of nodes of the previous level, leading to a logarithmic relationship between the number of nodes and the height of the tree.

However, it's important to note that if the binary search tree is unbalanced (e.g., if nodes are inserted in sorted order), the height can become linear, $ O(n) $. But in the context of a balanced binary search tree, which maintains its height using techniques like AVL or Red-Black trees, the statement is true.

Knowee AI · Accepted Answer

### Answer: True

A binary search tree (BST) is a data structure that maintains its elements in a sorted manner, allowing for efficient search, insertion, and deletion operations. In a balanced binary search tree, the maximum height is indeed $ O(\log n) $, where $ n $ is the number of nodes. This is because each level of the tree contains approximately double the number of nodes of the previous level, leading to a logarithmic relationship between the number of nodes and the height of the tree.

However, it's important to note that if the binary search tree is unbalanced (e.g., if nodes are inserted in sorted order), the height can become linear, $ O(n) $. But in the context of a balanced binary search tree, which maintains its height using techniques like AVL or Red-Black trees, the statement is true.

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

Question

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

Solution

Answer: True

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