Counting Nodes in a Binary Tree

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Questions and Answers

What is the purpose of the CountNodes function in the given code?

To count the number of nodes in the binary search tree (correct)
To retrieve an item from the binary search tree
To delete a node from the binary search tree
To insert a new item into the binary search tree

What happens when the Retrieve function is called with a NULL tree?

It returns an error
It sets the found variable to true
It crashes the program
It sets the found variable to false (correct)

How are new nodes inserted into a binary search tree?

As a sibling node
As a leaf node (correct)
As a root node
As a parent node

What is the purpose of the TreeType::LengthIs function?

To count the number of nodes in the binary search tree (A) Signup and view all the answers

What happens when the Retrieve function finds a matching item in the binary search tree?

It sets the found variable to true (C) Signup and view all the answers

How does the InsertItem function handle the insertion of a new node into the binary search tree?

It inserts the new node as a leaf node (A) Signup and view all the answers

What is the role of the tree parameter in the InsertItem function?

It is a pointer within the tree (A) Signup and view all the answers

What is the purpose of the recursive InsertItem function?

To insert a new item into the binary search tree (B) Signup and view all the answers

What is the purpose of the DeleteNode algorithm?

To delete a node from a binary search tree (C) Signup and view all the answers

What happens when the Left(tree) is NULL and Right(tree) is also NULL?

The node is set to NULL (B) Signup and view all the answers

What is the base case for the Delete recursive algorithm?

When the item's key matches the key in Info(tree) (A) Signup and view all the answers

What happens when the item is less than the key in Info(tree) in the Insert algorithm?

The item is inserted into the left subtree (D) Signup and view all the answers

What is the purpose of the GetPredecessor function in the DeleteNode algorithm?

To find the predecessor of a node (B) Signup and view all the answers

What is the result of calling Delete(tree->left, item) in the DeleteNode algorithm?

The item is deleted from the left subtree (D) Signup and view all the answers

What happens when the Right(tree) is NULL in the DeleteNode algorithm?

The node is set to its left child (C) Signup and view all the answers

What is the general case for the Delete recursive algorithm?

When the item is less than the key in Info(tree) (B) Signup and view all the answers

What is the purpose of the FindNode function in a binary search tree?

To find the insertion point for a new node (A) Signup and view all the answers

What happens if the parentPtr is NULL in the AttachNewNode function?

The new node is inserted as the root (B) Signup and view all the answers

In the InsertItem function, what happens if the item is less than the parent node's info?

The new node is inserted as the left child (D) Signup and view all the answers

What is the purpose of the DeleteItem function in a binary search tree?

To delete a node from the tree (C) Signup and view all the answers

What is the relationship between the nodePtr and parentPtr in the DeleteItem function?

parentPtr is the parent of nodePtr (C) Signup and view all the answers

In an array representation of a binary search tree, what is the index of the left child of a node at index i?

i * 2 + 1 (B) Signup and view all the answers

What is the purpose of the FindNode function in the InsertItem function?

To find the insertion point for a new node (B) Signup and view all the answers

In the InsertItem function, what happens if the item is not found in the tree?

The item is inserted as a new node (B) Signup and view all the answers

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Study Notes

Binary Search Tree Operations

The CountNodes function is a recursive function that counts the nodes in a binary search tree.
The RetrieveItem function searches for an item in the binary search tree and returns the item if found, along with a boolean indicating whether the item was found.
The InsertItem function inserts a new node into the binary search tree, maintaining the tree's properties.

Retrieval Operation

The Retrieve function is called with a TreeNode pointer, an ItemType reference, and a boolean reference.
If the tree is NULL, the function sets found to false.
If the item is less than the info in the current node, the function recursively calls itself on the left child.
If the item is greater than the info in the current node, the function recursively calls itself on the right child.
If the item is equal to the info in the current node, the function sets the item to the info and sets found to true.

Insert Operation

A new node is always inserted into its appropriate position in the tree as a leaf.
The Insert function is a recursive function that inserts a new node into the binary search tree.
If the tree is NULL, the function finds the insertion place and attaches a new node.
The FindNode function is used to find the insertion point.

Delete Operation

The DeleteItem function deletes an item from the binary search tree.
The function uses FindNode to find the node to be deleted and its parent.
If the node to be deleted is the root, the function calls DeleteNode on the root.
If the node to be deleted is a leaf node, the function simply deletes it.
If the node to be deleted has one child, the function replaces the node with its child.
If the node to be deleted has two children, the function finds the predecessor, copies its value, and deletes the predecessor.

DeleteNode Algorithm

If the left child is NULL and the right child is NULL, the function sets the tree to NULL.
If the left child is NULL, the function sets the tree to the right child.
If the right child is NULL, the function sets the tree to the left child.
If the node has two children, the function finds the predecessor, copies its value, and deletes the predecessor.

Array Representation

For any node tree.nodes[index], its left child is in tree.nodes[index*2 + 1] and its right child is in tree.nodes[index*2 + 2].
The parent of a node is in tree.nodes[(index – 1)/2].