A binary search tree (BST) with a height of $n-1$ for $n$ nodes guarantees $O(log n)$ time complexity for search operations. True or False?
Understand the Problem
The question discusses the time complexity of search operations in a binary search tree (BST) with a specific height ($n-1$ for $n$ nodes). Specifically, we need to determine if a BST with a height of $n-1$ guarantees $O(\log\ n)$ time complexity for search operations. A binary search tree with a height of $n-1$ is essentially a linked list, since only one child exists for each node. Thus, the time complexity is $O(n)$.
Answer
False
False. A binary search tree (BST) with a height of n-1 for n nodes resembles a linked list, leading to O(n) time complexity for search operations in the worst case, not O(log n).
Answer for screen readers
False. A binary search tree (BST) with a height of n-1 for n nodes resembles a linked list, leading to O(n) time complexity for search operations in the worst case, not O(log n).
More Information
A binary search tree's efficiency is highly dependent on its structure. A balanced BST ensures O(log n) search time, while a skewed tree can degrade to O(n).
Tips
It is a common mistake to assume all binary search trees have O(log n) search time complexity. Remember to consider the tree's balance.
Sources
- Why lookup in a Binary Search Tree is O(log(n))? - Stack Overflow - stackoverflow.com
- Binary search tree - Wikipedia - en.wikipedia.org
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