CSC 1061: Binary Search Tree

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Questions and Answers

What is the term for the number of edges from the root to a node in a binary tree?

Forest

Depth of a Node (correct)

Height of a Tree

Degree of a Node

Which statement accurately describes a Binary Search Tree?

A tree structure where each node has at most two children. (correct)

A tree that allows duplicate values in child nodes.

A linear structure that stores data sequentially.

A type of tree that does not require a root node.

Which of the following describes a 'leaf' in the context of tree data structures?

A node that does not contain any pointers to child nodes. (correct)

A node that is the highest point in the tree.

A node that connects two other nodes in the structure.

A node that has one or more child nodes.

In a tree, what is the collection of disjoint trees called?

Forest Signup and view all the answers

Which characteristic is true about the 'height' of a tree?

It is the highest number of edges from the root to any leaf. Signup and view all the answers

What does the method BinTree::isEmpty() return?

True if root is nullptr Signup and view all the answers

Which statement is correct regarding the addition of nodes to a non-empty binary tree?

A loop is preferred for its efficiency in traversing. Signup and view all the answers

When adding a new item to an empty tree, what is the first action taken?

Allocate memory for a new node. Signup and view all the answers

Which traversal method processes nodes in the order: left, process, right?

In Order Signup and view all the answers

What should be done if the cursor's left is not nullptr while traversing?

Set the cursor to the left child. Signup and view all the answers

Which of the following options is NOT a way to traverse a binary tree?

Radial Order Signup and view all the answers

What is the ideal method for adding items to a binary tree to ensure efficient traversal?

Using a loop Signup and view all the answers

What characterizes a binary tree?

It stores and retrieves data in a sorted order. Signup and view all the answers

Which statement accurately describes the role of the left pointer in a binary search tree?

It points to children with values less than or equal to the parent node. Signup and view all the answers

What is a leaf node in a binary tree?

A node that does not have any children. Signup and view all the answers

How is a BinNode class characterized in relation to memory allocation?

It has no allocation or deallocation of memory. Signup and view all the answers

What does the BinTree class include to effectively manage its nodes?

Pointers to maintain relationships between nodes. Signup and view all the answers

What is the initial state of a binary tree created using the default constructor?

The root pointer is set to nullptr. Signup and view all the answers

Which methodology is used to check if a binary tree is empty?

Comparing the root pointer to nullptr. Signup and view all the answers

In a binary search tree, where would 'Green' be placed if the items are inserted in the following order: Red, Yellow, Green, Orange, Blue, Violet?

To the right of 'Red'. Signup and view all the answers

Study Notes

Course: CSC 1061

Binary Search Tree (BST)

A BST is a non-linear data structure.
Unlike linear structures (arrays, linked lists, etc.), BSTs provide faster data access.
BSTs organize data hierarchically, with a root node at the top.
The relationship between nodes is parent/child. Each node has at most one parent and two children (left and right).

BST Terms

Root: The topmost node in the tree.
Edge: The link (pointer) connecting two nodes.
Leaf: A node with no children.
Depth of a Node: The number of edges from the root to the node.
Height of a Tree: The height of the root node or the depth of the deepest node.
Degree of a Node: The number of branches of that node.
Forest: A collection of disjoint trees.

BST Overview (Computer Science Perspective)

The root is at the top.
The relationship between a node and the node below it is parent/child relationship.
A node can only have one parent.
A tree is often used to represent a hierarchy.
A directory structure on a UNIX machine has a tree structure.
The root directory is the top.
The BST is useful for quickly storing and retrieving sorted data.

BST (Programiz)

A binary tree where each node contains data and pointers to at most two children (left and right).
In a BST, the left pointer is used to store nodes with values less than or equal to the parent node.
The right pointer stores children with values greater than the parent node.
A node with no children is called a leaf node.

Binary Tree Data Structure Class

A container of BinNode elements stored in the heap at runtime.
A BinNode pointer is allocated with each addition to the tree.
Memory is deallocated when a node is removed, ensuring the tree only uses the necessary memory.

BinNode (Element Class)

A helper class for BST.
Stores fundamental data and pointers of the current tree element (left and right children).
The structure of the element stored in the BST.
Encapsulates the data, left pointer (referencing left child), and right pointer (referencing right child).
Not dynamic: It does not allocate or deallocate memory.
Not a container: It cannot add, remove, or find elements within the tree.

BST: Creating the Tree

Initialize root to nullptr to signify an empty tree in the constructor.

BST: IsEmpty

Check if a tree is empty by comparing the root pointer to nullptr.
The root pointer can either have an address (empty) or is nullptr(not empty).

BST: Adding to an Empty Tree

Allocate a new BinNode for the item..
Set the root to the new node.

BST: Adding to a Non-Empty Tree

Traverse the tree to find the correct position for addition based on the comparison to the parent node.
Create a loop to add recursively to the subtree.

BST Traversals

Traversing a tree involves visiting every node.
Linear structures (e.g. arrays, linked lists) traverse in a single path.
Hierarchical structures (e.g., trees) can be traversed in multiple ways using recursive calls to enable traversal back through subtrees.
Inorder: Left, Process, Right
Preorder: Process, Left, Right
Postorder: Left, Right, Process
Backward Inorder: Right, Process, Left

BST Traversal: Design

A function to handle recursive calls for traversal, handling the potential nullptr cases.

BST Traversal: In-Order

Recursive function that performs an in-order traversal of a BST.
Prints the values in the tree in an ascending order.

BST Rule of 3

Copy Constructor: Makes a deep copy of the source tree on the heap.
Assignment Operator: Makes a deep copy of the source tree on the heap.
Destructor: Destroys all memory allocated for the tree on the heap.

BST: Deep Copy of Memory

Check for self-assignment.
Free existing memory
Initialize memory of the new tree as nullptr.
Traverse source tree using a recursive helper function to perform a deep copy of each node.
Copy each item in the source tree into the destination tree based on the traversal order and the comparison of data values.

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Description

This quiz covers the fundamental concepts of Binary Search Trees (BST) as outlined in the CSC 1061 course. It includes definitions of key terms such as root, edge, leaf, and more, providing a comprehensive overview of how BSTs function as non-linear data structures. Test your understanding of the hierarchical organization and relationships within a BST.