Java Software Structures Chapter 11

Questions and Answers

What is a binary search tree?

A binary search tree is a binary tree with the added property that the left child is less than the parent, which is less than or equal to the right child.

Where do we get our definition of a binary search tree?

The definition of a binary search tree is an extension of the definition of a binary tree.

What references does a BinaryTreeNode object maintain?

Each BinaryTreeNode object maintains a reference to the element stored at that node, as well as references to each of the node's children.

What must happen when an element in a binary search tree is removed?

In removing an element from a binary search tree, another node must be promoted to replace the node being removed. Signup and view all the answers

Where are the minimum and maximum elements in a binary search tree?

The leftmost node in a binary search tree will contain the minimum element, whereas the rightmost node will contain the maximum element. Signup and view all the answers

What is one use of a tree?

One of the uses of trees is to provide efficient implementations of other collections. Signup and view all the answers

What could happen if a binary search tree is not balanced?

If a binary search tree is not balanced, it may be less efficient than a linear structure. Signup and view all the answers

What is the height of the right subtree minus the height of the left subtree called?

The height of the right subtree minus the height of the left subtree is called the balance factor of a node. Signup and view all the answers

What are the ways a tree or subtree can become unbalanced?

There are only two ways in which a tree, or any subtree of a tree, can become unbalanced: through the insertion of a node and through the deletion of a node. Signup and view all the answers

Is the balance restriction on red/black trees more strict than the balance restriction on AVL trees?

False Signup and view all the answers

What is a binary search tree?

A binary tree with an added ordering property Signup and view all the answers

What is the term used to describe a node in a tree being moved up to replace a parent node?

Promoted Signup and view all the answers

What is a degenerate tree?

A degenerate tree is a tree that does not branch. Signup and view all the answers

What is a right rotation?

A single rotation strategy for rebalancing a tree when the long path is in the left subtree of the left child of the root. Signup and view all the answers

What is a left rotation?

A single rotation strategy for rebalancing a tree when the long path is in the right subtree of the right child of the root. Signup and view all the answers

What is a right-left rotation?

A double rotation strategy for rebalancing a tree when the long path is in the left subtree of the right child of the root. Signup and view all the answers

What is a left-right rotation?

A double rotation strategy for rebalancing a tree when the long path is in the right subtree of the left child of the root. Signup and view all the answers

What are AVL trees?

A strategy for keeping a binary search tree balanced that makes use of the balance factor of each node. Signup and view all the answers

What is the balance factor?

A property of a node that is computed by subtracting the height of the left subtree from the height of the right subtree. Signup and view all the answers

What are red/black trees?

A strategy for keeping a binary search tree balanced that makes use of a color (either red or black) associated with each node. Signup and view all the answers

What is the difference between a binary tree and a binary search tree?

A binary search tree has the added ordering property that the left child of any node is less than the node, and the node is less than or equal to its right child. Signup and view all the answers

Why are we able to specify addElement and removeElement operations for a binary search tree but not for a binary tree?

With the added ordering property of a binary search tree, we are now able to define what the state of the tree should look like after these operations. Signup and view all the answers

Study Notes

Binary Search Trees Overview

A binary search tree (BST) allows for efficient searching and sorting by structuring the tree such that the left child is less than the parent, and the parent is less than or equal to the right child.
The definition of a BST builds on the foundational concept of a binary tree, emphasizing the ordering property.

BinaryTreeNode Structure

Each BinaryTreeNode maintains references to the element it stores and its left and right children.

Node Removal in BSTs

When removing an element from a BST, it’s necessary to promote another node to replace the removed node, maintaining the tree's properties.

Locating Extremes

The minimum element in a BST is found at the leftmost node, while the maximum element is at the rightmost node.

Tree Efficiency and Balance

Trees are widely used to implement efficient data structures for collections.
An unbalanced BST can degrade performance, making operations less efficient than those in linear structures.

Balance Factor and Tree Balance

The balance factor of a node is calculated by subtracting the height of the left subtree from the height of the right subtree; a balance factor outside the range of -1 to 1 indicates an unbalanced tree.
A tree can become unbalanced primarily through the insertion or deletion of nodes.

Tree Balancing Techniques

Red/black trees and AVL trees are strategies used to keep BSTs balanced, though red/black trees have a less strict balancing requirement than AVL trees.
In both trees, the find operation complexity is O(log n).

Types of Rotations for Rebalancing

Right rotation is employed when the long path is within the left subtree of the left child.
Left rotation is applied when the long path is in the right subtree of the right child.
Right-left rotation is a double rotation strategy for balancing involving the left child of the right subtree.
Left-right rotation is a double rotation strategy for balancing involving the right child of the left subtree.

AVL and Red/Black Trees

AVL trees maintain balance using the balance factor of each node, ensuring the tree remains balanced after operations.
Red/black trees utilize a color property for balance, assigning either red or black to each node to facilitate rebalancing.

Conceptual Differences

A key distinction between binary trees and binary search trees is the ordering of node values, which is crucial for the operations of addElement and removeElement in a BST, not available in a general binary tree structure.

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Explore flashcards for Chapter 11 on Binary Search Trees in Java Software Structures. This quiz covers key concepts and definitions related to binary search trees, emphasizing their structure and properties. Perfect for reinforcing your understanding of this fundamental data structure.