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Which of the following statements about AVL trees is true?
- a)AVL trees are a type of balanced binary search tree.
- b)AVL trees have an unbounded height.
- c)AVL trees guarantee O(1) search time in the worst case.
- d)AVL trees only support insertion and deletion at the root.
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which of the following statements about AVL trees is true?a)AVL trees ...
AVL trees are a type of balanced binary search tree that ensures the height of the tree remains logarithmic.
Most Upvoted Answer
Which of the following statements about AVL trees is true?a)AVL trees ...
AVL trees:
AVL trees are a type of balanced binary search tree that ensures the height of the tree remains balanced. AVL trees were named after their inventors, Adelson-Velsky and Landis.
Statement analysis:
Let's analyze each statement to determine which one is true:
a) AVL trees are a type of balanced binary search tree:
This statement is true. AVL trees are a self-balancing binary search tree, meaning that the heights of the left and right subtrees of every node differ by at most 1. This balance property is maintained during insertion and deletion operations.
b) AVL trees have an unbounded height:
This statement is false. AVL trees have a bounded height due to their self-balancing nature. The height of an AVL tree is guaranteed to be O(log n), where n is the number of nodes in the tree. This ensures efficient search, insertion, and deletion operations.
c) AVL trees guarantee O(1) search time in the worst case:
This statement is false. The search time in an AVL tree is not guaranteed to be O(1) in the worst case. While the height of the tree is balanced, the search time is still dependent on the height of the tree, which is O(log n) in the worst case.
d) AVL trees only support insertion and deletion at the root:
This statement is false. AVL trees support insertion and deletion operations at any node, not just the root. When a node is inserted or deleted, the tree automatically adjusts its structure to maintain balance.
Conclusion:
Based on the analysis, the correct statement is a) AVL trees are a type of balanced binary search tree. AVL trees are a self-balancing binary search tree that ensures the heights of the left and right subtrees differ by at most 1, making them an efficient data structure for searching, insertion, and deletion operations.
AVL trees are a type of balanced binary search tree that ensures the height of the tree remains balanced. AVL trees were named after their inventors, Adelson-Velsky and Landis.
Statement analysis:
Let's analyze each statement to determine which one is true:
a) AVL trees are a type of balanced binary search tree:
This statement is true. AVL trees are a self-balancing binary search tree, meaning that the heights of the left and right subtrees of every node differ by at most 1. This balance property is maintained during insertion and deletion operations.
b) AVL trees have an unbounded height:
This statement is false. AVL trees have a bounded height due to their self-balancing nature. The height of an AVL tree is guaranteed to be O(log n), where n is the number of nodes in the tree. This ensures efficient search, insertion, and deletion operations.
c) AVL trees guarantee O(1) search time in the worst case:
This statement is false. The search time in an AVL tree is not guaranteed to be O(1) in the worst case. While the height of the tree is balanced, the search time is still dependent on the height of the tree, which is O(log n) in the worst case.
d) AVL trees only support insertion and deletion at the root:
This statement is false. AVL trees support insertion and deletion operations at any node, not just the root. When a node is inserted or deleted, the tree automatically adjusts its structure to maintain balance.
Conclusion:
Based on the analysis, the correct statement is a) AVL trees are a type of balanced binary search tree. AVL trees are a self-balancing binary search tree that ensures the heights of the left and right subtrees differ by at most 1, making them an efficient data structure for searching, insertion, and deletion operations.
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Which of the following statements about AVL trees is true?a)AVL trees are a type of balanced binary search tree.b)AVL trees have an unbounded height.c)AVL trees guarantee O(1) search time in the worst case.d)AVL trees only support insertion and deletion at the root.Correct answer is option 'A'. Can you explain this answer?
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Which of the following statements about AVL trees is true?a)AVL trees are a type of balanced binary search tree.b)AVL trees have an unbounded height.c)AVL trees guarantee O(1) search time in the worst case.d)AVL trees only support insertion and deletion at the root.Correct answer is option 'A'. 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 statements about AVL trees is true?a)AVL trees are a type of balanced binary search tree.b)AVL trees have an unbounded height.c)AVL trees guarantee O(1) search time in the worst case.d)AVL trees only support insertion and deletion at the root.Correct answer is option 'A'. 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 statements about AVL trees is true?a)AVL trees are a type of balanced binary search tree.b)AVL trees have an unbounded height.c)AVL trees guarantee O(1) search time in the worst case.d)AVL trees only support insertion and deletion at the root.Correct answer is option 'A'. Can you explain this answer?.
Which of the following statements about AVL trees is true?a)AVL trees are a type of balanced binary search tree.b)AVL trees have an unbounded height.c)AVL trees guarantee O(1) search time in the worst case.d)AVL trees only support insertion and deletion at the root.Correct answer is option 'A'. 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 statements about AVL trees is true?a)AVL trees are a type of balanced binary search tree.b)AVL trees have an unbounded height.c)AVL trees guarantee O(1) search time in the worst case.d)AVL trees only support insertion and deletion at the root.Correct answer is option 'A'. 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 statements about AVL trees is true?a)AVL trees are a type of balanced binary search tree.b)AVL trees have an unbounded height.c)AVL trees guarantee O(1) search time in the worst case.d)AVL trees only support insertion and deletion at the root.Correct answer is option 'A'. Can you explain this answer?.
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Which of the following statements about AVL trees is true?a)AVL trees are a type of balanced binary search tree.b)AVL trees have an unbounded height.c)AVL trees guarantee O(1) search time in the worst case.d)AVL trees only support insertion and deletion at the root.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Which of the following statements about AVL trees is true?a)AVL trees are a type of balanced binary search tree.b)AVL trees have an unbounded height.c)AVL trees guarantee O(1) search time in the worst case.d)AVL trees only support insertion and deletion at the root.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Which of the following statements about AVL trees is true?a)AVL trees are a type of balanced binary search tree.b)AVL trees have an unbounded height.c)AVL trees guarantee O(1) search time in the worst case.d)AVL trees only support insertion and deletion at the root.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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