Self-Balancing Binary Search Tree Quiz
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Questions and Answers

Which type of binary search tree automatically keeps its height small?

  • Self-balancing binary search tree (correct)
  • AVL tree
  • Red–black tree
  • Splay tree

    • What is the defined height for height-balanced binary trees in terms of the number of items?

  • $O(n^2)$
  • $O(\log n)$ (correct)
  • $O(1)$
  • $O(n)$

    • Which type of self-balancing tree is not guaranteed to have a logarithmic height in the number of items?

  • Treap
  • AVL tree
  • Red–black tree
  • Splay tree (correct)

    • For a binary tree with height $h$, what is the maximum number of nodes it can contain?

    <p>$2^{h+1}-1$</p> Signup and view all the answers

    What abstract data structures can self-balancing binary search trees provide efficient implementations for?

    <p>Mutable ordered lists, associative arrays, priority queues, and sets</p> Signup and view all the answers

    What is the minimum height of a binary tree with n nodes?

    <p>$\lfloor \log _{2}n\rfloor$</p> Signup and view all the answers

    What happens when items are inserted in sorted key order in a binary search tree?

    <p>The tree degenerates into a linked list with n nodes</p> Signup and view all the answers

    What is a disadvantage of self-balancing BSTs compared to hash tables?

    <p>They have worse worst-case lookup performance</p> Signup and view all the answers

    What is the time complexity for lookup, insertion, and removal in a self-balancing BST containing n items?

    <p>$O(\log n)$</p> Signup and view all the answers

    What can be achieved by extending self-balancing BSTs to efficiently record additional information or perform new operations?

    <p>Count the number of nodes in a certain key range in $O(\log n)$ time</p> Signup and view all the answers

    What is the defined height for height-balanced binary trees in terms of the number of items?

    <p>$O(\log n)$</p> Signup and view all the answers

    What abstract data structures can self-balancing binary search trees provide efficient implementations for?

    <p>Mutable ordered lists, priority queues, and sets</p> Signup and view all the answers

    What is the maximum number of nodes a binary tree with height $h$ can contain?

    <p>$2^{h+1}-1$</p> Signup and view all the answers

    Which type of self-balancing tree is not guaranteed to have a logarithmic height in the number of items?

    <p>Splay trees</p> Signup and view all the answers

    What is the time complexity for lookup, insertion, and removal in a self-balancing BST containing $n$ items?

    <p>$O(\log n)$</p> Signup and view all the answers

    What is the minimum height of a binary tree with 1,000,000 nodes?

    <p>$19$</p> Signup and view all the answers

    What is the additional space requirement for maintaining a BST with minimum height?

    <p>It tends to outweigh the decrease in search time</p> Signup and view all the answers

    What is the time complexity for ordered enumeration of all items in a self-balancing BST containing $n$ items?

    <p>$O(n)$</p> Signup and view all the answers

    What is a disadvantage of self-balancing BSTs compared to hash tables?

    <p>Worse average-case performance for lookup algorithms</p> Signup and view all the answers

    What is the guaranteed factor of the optimal height for an AVL tree?

    <p>1.44</p> Signup and view all the answers

    What is the time complexity for lookup, insertion, and removal in a self-balancing BST containing $n$ items?

    <p>$O(\log n)$</p> Signup and view all the answers

    What is the minimum height of a binary tree with 1,000,000 nodes?

    <p>19</p> Signup and view all the answers

    What is the guaranteed factor of the optimal height for an AVL tree?

    <p>1.44</p> Signup and view all the answers

    What abstract data structures can self-balancing binary search trees provide efficient implementations for?

    <p>Ordered lists and associative arrays</p> Signup and view all the answers

    What happens when items are inserted in sorted key order in a binary search tree?

    <p>The tree degenerates into a linked list with $n$ nodes</p> Signup and view all the answers

    Which type of self-balancing tree is not guaranteed to have a logarithmic height in the number of items?

    <p>Splay trees</p> Signup and view all the answers

    What is the maximum number of nodes a binary tree with height $h$ can contain?

    <p>$2^{h+1} - 1$</p> Signup and view all the answers

    What is the time complexity for lookup, insertion, and removal in a self-balancing BST containing $n$ items?

    <p>$O(\log n)$</p> Signup and view all the answers

    What abstract data structures can self-balancing binary search trees provide efficient implementations for?

    <p>All of the above</p> Signup and view all the answers

    What is a disadvantage of self-balancing BSTs compared to hash tables?

    <p>Higher time complexity for lookup</p> Signup and view all the answers

    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.

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