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Which of the following is not a property of a binary search tree (BST)?
- a)The left subtree of a node contains only nodes with values less than the node's value.
- b)The right subtree of a node contains only nodes with values greater than the node's value.
- c)There are no duplicate values in the BST.
- d)The height of the BST is always O(n), where n is the number of nodes.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Which of the following is not a property of a binary search tree (BST)...
The height of a binary search tree can vary depending on the order of insertion, and it is not necessarily always O(n). It can be O(logn) in a balanced BST.
Most Upvoted Answer
Which of the following is not a property of a binary search tree (BST)...
Explanation:
In a binary search tree (BST), the left subtree of a node contains only nodes with values less than the node's value, and the right subtree contains only nodes with values greater than the node's value. There are no duplicate values in a BST. However, the height of a BST is not always O(n), where n is the number of nodes.
Height of a BST:
The height of a BST is the maximum number of edges in any path from the root to a leaf node. It represents the length of the longest path in the tree. The height of a BST can vary depending on the order in which elements are inserted.
Explanation of Option D:
The height of a BST is not always guaranteed to be O(n). It depends on the order in which elements are inserted into the tree. In the worst-case scenario, where the elements are inserted in a sorted or nearly sorted order, the height of the BST can be O(n), which means the tree essentially becomes a linked list.
To understand this better, let's consider an example:
Suppose we have a BST with n nodes, and the elements are inserted in ascending order (1, 2, 3, 4, ..., n) into the tree. In this case, the BST will essentially become a linked list with a height of n-1, which is not O(n).
On the other hand, if the elements are inserted in a balanced manner, maintaining the properties of a BST, the height of the tree can be significantly smaller than n, resulting in a more efficient search.
Conclusion:
To summarize, while the left-subtree, right-subtree, and no-duplicate properties are fundamental to a binary search tree, the height of a BST is not always O(n). The height can vary depending on the order of element insertion, and in the worst-case scenario, it can be O(n) when the tree becomes a linked list.
In a binary search tree (BST), the left subtree of a node contains only nodes with values less than the node's value, and the right subtree contains only nodes with values greater than the node's value. There are no duplicate values in a BST. However, the height of a BST is not always O(n), where n is the number of nodes.
Height of a BST:
The height of a BST is the maximum number of edges in any path from the root to a leaf node. It represents the length of the longest path in the tree. The height of a BST can vary depending on the order in which elements are inserted.
Explanation of Option D:
The height of a BST is not always guaranteed to be O(n). It depends on the order in which elements are inserted into the tree. In the worst-case scenario, where the elements are inserted in a sorted or nearly sorted order, the height of the BST can be O(n), which means the tree essentially becomes a linked list.
To understand this better, let's consider an example:
Suppose we have a BST with n nodes, and the elements are inserted in ascending order (1, 2, 3, 4, ..., n) into the tree. In this case, the BST will essentially become a linked list with a height of n-1, which is not O(n).
On the other hand, if the elements are inserted in a balanced manner, maintaining the properties of a BST, the height of the tree can be significantly smaller than n, resulting in a more efficient search.
Conclusion:
To summarize, while the left-subtree, right-subtree, and no-duplicate properties are fundamental to a binary search tree, the height of a BST is not always O(n). The height can vary depending on the order of element insertion, and in the worst-case scenario, it can be O(n) when the tree becomes a linked list.
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Which of the following is not a property of a binary search tree (BST)?a)The left subtree of a node contains only nodes with values less than the nodes value.b)The right subtree of a node contains only nodes with values greater than the nodes value.c)There are no duplicate values in the BST.d)The height of the BST is always O(n), where n is the number of nodes.Correct answer is option 'D'. Can you explain this answer?
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Which of the following is not a property of a binary search tree (BST)?a)The left subtree of a node contains only nodes with values less than the nodes value.b)The right subtree of a node contains only nodes with values greater than the nodes value.c)There are no duplicate values in the BST.d)The height of the BST is always O(n), where n is the number of nodes.Correct answer is option 'D'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about Which of the following is not a property of a binary search tree (BST)?a)The left subtree of a node contains only nodes with values less than the nodes value.b)The right subtree of a node contains only nodes with values greater than the nodes value.c)There are no duplicate values in the BST.d)The height of the BST is always O(n), where n is the number of nodes.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is not a property of a binary search tree (BST)?a)The left subtree of a node contains only nodes with values less than the nodes value.b)The right subtree of a node contains only nodes with values greater than the nodes value.c)There are no duplicate values in the BST.d)The height of the BST is always O(n), where n is the number of nodes.Correct answer is option 'D'. Can you explain this answer?.
Which of the following is not a property of a binary search tree (BST)?a)The left subtree of a node contains only nodes with values less than the nodes value.b)The right subtree of a node contains only nodes with values greater than the nodes value.c)There are no duplicate values in the BST.d)The height of the BST is always O(n), where n is the number of nodes.Correct answer is option 'D'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about Which of the following is not a property of a binary search tree (BST)?a)The left subtree of a node contains only nodes with values less than the nodes value.b)The right subtree of a node contains only nodes with values greater than the nodes value.c)There are no duplicate values in the BST.d)The height of the BST is always O(n), where n is the number of nodes.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is not a property of a binary search tree (BST)?a)The left subtree of a node contains only nodes with values less than the nodes value.b)The right subtree of a node contains only nodes with values greater than the nodes value.c)There are no duplicate values in the BST.d)The height of the BST is always O(n), where n is the number of nodes.Correct answer is option 'D'. Can you explain this answer?.
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