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Questions and Answers
Which type of binary search tree automatically keeps its height small?
Which type of binary search tree automatically keeps its height small?
What is the defined height for height-balanced binary trees in terms of the number of items?
What is the defined height for height-balanced binary trees in terms of the number of items?
Which type of self-balancing tree is not guaranteed to have a logarithmic height in the number of items?
Which type of self-balancing tree is not guaranteed to have a logarithmic height in the number of items?
For a binary tree with height $h$, what is the maximum number of nodes it can contain?
For a binary tree with height $h$, what is the maximum number of nodes it can contain?
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What abstract data structures can self-balancing binary search trees provide efficient implementations for?
What abstract data structures can self-balancing binary search trees provide efficient implementations for?
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What is the minimum height of a binary tree with n nodes?
What is the minimum height of a binary tree with n nodes?
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What happens when items are inserted in sorted key order in a binary search tree?
What happens when items are inserted in sorted key order in a binary search tree?
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What is a disadvantage of self-balancing BSTs compared to hash tables?
What is a disadvantage of self-balancing BSTs compared to hash tables?
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What is the time complexity for lookup, insertion, and removal in a self-balancing BST containing n items?
What is the time complexity for lookup, insertion, and removal in a self-balancing BST containing n items?
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What can be achieved by extending self-balancing BSTs to efficiently record additional information or perform new operations?
What can be achieved by extending self-balancing BSTs to efficiently record additional information or perform new operations?
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What is the defined height for height-balanced binary trees in terms of the number of items?
What is the defined height for height-balanced binary trees in terms of the number of items?
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What abstract data structures can self-balancing binary search trees provide efficient implementations for?
What abstract data structures can self-balancing binary search trees provide efficient implementations for?
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What is the maximum number of nodes a binary tree with height $h$ can contain?
What is the maximum number of nodes a binary tree with height $h$ can contain?
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Which type of self-balancing tree is not guaranteed to have a logarithmic height in the number of items?
Which type of self-balancing tree is not guaranteed to have a logarithmic height in the number of items?
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What is the time complexity for lookup, insertion, and removal in a self-balancing BST containing $n$ items?
What is the time complexity for lookup, insertion, and removal in a self-balancing BST containing $n$ items?
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What is the minimum height of a binary tree with 1,000,000 nodes?
What is the minimum height of a binary tree with 1,000,000 nodes?
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What is the additional space requirement for maintaining a BST with minimum height?
What is the additional space requirement for maintaining a BST with minimum height?
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What is the time complexity for ordered enumeration of all items in a self-balancing BST containing $n$ items?
What is the time complexity for ordered enumeration of all items in a self-balancing BST containing $n$ items?
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What is a disadvantage of self-balancing BSTs compared to hash tables?
What is a disadvantage of self-balancing BSTs compared to hash tables?
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What is the guaranteed factor of the optimal height for an AVL tree?
What is the guaranteed factor of the optimal height for an AVL tree?
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What is the time complexity for lookup, insertion, and removal in a self-balancing BST containing $n$ items?
What is the time complexity for lookup, insertion, and removal in a self-balancing BST containing $n$ items?
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What is the minimum height of a binary tree with 1,000,000 nodes?
What is the minimum height of a binary tree with 1,000,000 nodes?
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What is the guaranteed factor of the optimal height for an AVL tree?
What is the guaranteed factor of the optimal height for an AVL tree?
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What abstract data structures can self-balancing binary search trees provide efficient implementations for?
What abstract data structures can self-balancing binary search trees provide efficient implementations for?
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What happens when items are inserted in sorted key order in a binary search tree?
What happens when items are inserted in sorted key order in a binary search tree?
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Which type of self-balancing tree is not guaranteed to have a logarithmic height in the number of items?
Which type of self-balancing tree is not guaranteed to have a logarithmic height in the number of items?
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What is the maximum number of nodes a binary tree with height $h$ can contain?
What is the maximum number of nodes a binary tree with height $h$ can contain?
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What is the time complexity for lookup, insertion, and removal in a self-balancing BST containing $n$ items?
What is the time complexity for lookup, insertion, and removal in a self-balancing BST containing $n$ items?
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What abstract data structures can self-balancing binary search trees provide efficient implementations for?
What abstract data structures can self-balancing binary search trees provide efficient implementations for?
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What is a disadvantage of self-balancing BSTs compared to hash tables?
What is a disadvantage of self-balancing BSTs compared to hash tables?
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Study Notes
Binary Search Trees
- A self-balancing binary search tree automatically keeps its height small.
- The defined height for height-balanced binary trees is O(log n), where n is the number of items.
Height-Balanced Binary Trees
- The minimum height of a binary tree with n nodes is O(log n).
- A binary tree with height h can contain a maximum of 2^h - 1 nodes.
Self-Balancing Trees
- AVL trees are an example of a self-balancing tree that guarantees a logarithmic height in the number of items.
- Splay trees are an example of a self-balancing tree that is not guaranteed to have a logarithmic height in the number of items.
Abstract Data Structures
- Self-balancing binary search trees can provide efficient implementations for abstract data structures such as sets, multisets, and ordered dictionaries.
Insertion and Deletion
- When items are inserted in sorted key order in a binary search tree, the tree can become unbalanced.
- The time complexity for lookup, insertion, and removal in a self-balancing BST containing n items is O(log n).
Disadvantages and Extensions
- A disadvantage of self-balancing BSTs compared to hash tables is that they can be slower and more complex to implement.
- By extending self-balancing BSTs, it is possible to efficiently record additional information or perform new operations, such as range queries or nearest neighbor searches.
Additional Space Requirement
- The additional space requirement for maintaining a BST with minimum height is O(n).
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Description
Test your knowledge of self-balancing binary search trees with this quiz. Explore the various types of BSTs that automatically maintain balanced height, ensuring efficient insertions and deletions.