Binary Search Tree Concepts Quiz

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Questions and Answers

What characterizes a complete tree?

Only the bottom level can have fewer nodes. (correct)

All nodes are filled at every level.

Every level, except the bottom, is fully populated. (correct)

Nodes are concentrated toward the right side.

What happens when the 19 node is added to the tree?

It will increase the diameter and do nothing else.

It becomes the right child of the 14 node.

It creates a new level and increases the height. (correct)

It does not affect the height of the tree.

Which method is NOT stated as part of the Binary Search Tree class?

Remove method

Search method (correct)

Add method

Traversal method

What does the 'add' method in a Binary Search Tree do?

Adds a binary node to the tree through recursion. Signup and view all the answers

Where does the 35 node attach itself in the tree?

As the left child of the 41 node. Signup and view all the answers

What impact does the addition of the 4 node have on the tree?

Increases the diameter of the tree. Signup and view all the answers

Which part of the BinarySearchTree class sets the initial state of the root?

The constructor. Signup and view all the answers

What is the final height of the tree after all nodes have been added?

5 Signup and view all the answers

What is the primary advantage of using a Binary Search Tree (BST) over a linked list for large data storage?

BST improves search, insert, and delete operations to logarithmic time complexity. Signup and view all the answers

In the given Binary Search Tree Node class, which type is suggested for the 'myValue' variable?

Comparable Signup and view all the answers

What does the worst-case time complexity of a Binary Search Tree depend on?

The balance of the tree. Signup and view all the answers

What does the following line of code within the toString method return when the left node is null? '", Left:"+(left==null?null:left.myValue)'

The string 'Left: null'. Signup and view all the answers

What is a potential downside of the Binary Search Tree in terms of its structure?

It can become unbalanced, leading to inefficient operations. Signup and view all the answers

Which property must be maintained when inserting new values into a Binary Search Tree?

Left child values must always be less than parent values. Signup and view all the answers

What does the conditional operator used in the toString method replace?

An if-else statement. Signup and view all the answers

Why is it encouraged to write a toString method in the Binary Search Tree Node class?

To provide a detailed representation of the node's value and its children. Signup and view all the answers

What is the first node printed during a preorder traversal of the described binary search tree?

7 Signup and view all the answers

Which child node is traversed immediately after the root node in a preorder traversal?

Left child Signup and view all the answers

What does the traversal do when it encounters a null node in the tree?

Return to the previous node without action Signup and view all the answers

In what order would the nodes be printed during the preorder traversal described?

7, 3, 4, 27, 11, 14, 12, 26, 19, 41, 35, 50 Signup and view all the answers

What is the significance of the recursive method in a preorder traversal?

It ensures that each node is processed before returning control Signup and view all the answers

What happens when the traversal attempts to process the left child of a node but finds it null?

It simply moves on to the right child Signup and view all the answers

During the preorder traversal, what occurs right after printing the value of a node?

The left child is processed next Signup and view all the answers

What structure is primarily utilized to manage the traversal in a preorder approach?

Stack Signup and view all the answers

What occurs first when executing the levelOrder function?

The root node is added to the queue. Signup and view all the answers

What happens if a node has a null left child during level order traversal?

Only the right child is added to the queue. Signup and view all the answers

How is the temp String variable constructed during the traversal?

Values are added with a space between them. Signup and view all the answers

What is the final outcome after the queue is empty in the level order procedure?

The trimmed temp String is returned. Signup and view all the answers

Which part of the queue does the 3 node represent when it is processed?

It is the left child of node 7. Signup and view all the answers

What does the toString method do in relation to traversal methods?

It chooses among the four traversal methods. Signup and view all the answers

What will happen if the queue contains only leaf nodes at some point during the traversal?

Leaf nodes will still be processed but not add any children. Signup and view all the answers

In the context of this procedure, what role does the queue serve?

It stores the nodes that need to be processed next. Signup and view all the answers

What does the remove method return when a target node is removed from a binary search tree?

The removed node that is unattached Signup and view all the answers

What initial check must the programmer perform before executing the remove method?

Check if the tree is empty Signup and view all the answers

What is indicated by a root node of degree 0 in the context of the remove method?

The node has no children Signup and view all the answers

If the root of the binary search tree has a right child and no left child, what happens during the removal process?

The new root becomes the right child of the old root Signup and view all the answers

What is the purpose of assigning a temporary binary node called 'temp' to root?

To always have a reference to the original root Signup and view all the answers

How should the programmer handle the removal of a node with degree 1 in the binary search tree?

Promote the child node to the root position Signup and view all the answers

What does the method call for 'remove helper method' signify in the remove process for nodes with two children?

Further processing is required to find a replacement node Signup and view all the answers

What condition must be checked to ensure that the root is being removed correctly during the removal process?

If the root value equals the target value Signup and view all the answers

What happens when the root node is the only node in the tree and is removed?

The tree becomes empty. Signup and view all the answers

Which statement correctly describes the purpose of the 'inorderSuccessor' in the code?

It stores the node which will replace the node being removed. Signup and view all the answers

What is the condition checked when the method determines if the root should be removed?

If the target value equals the root's value. Signup and view all the answers

In the event that the root has both children, which method is called to handle the removal?

The successor method. Signup and view all the answers

What type of node must be provided to the remove helper method along with the target value?

The binary node called startNode. Signup and view all the answers

What happens if the root node has no left child during a removal operation?

The right child becomes the new root. Signup and view all the answers

What is the significance of the 'remove' method calling itself recursively?

To handle scenarios where the current root is not the target. Signup and view all the answers

What is the result of the statement 'root = null;' in the remove method?

It disconnects the root from the tree. Signup and view all the answers

Study Notes

Binary Search Tree Notes

A Binary Search Tree (BST) is a data structure for organizing large datasets efficiently. It allows for faster insertion, deletion, and searching compared to linked lists, with a logarithmic time complexity (O(log n)) for most operations. Linked lists, in contrast, have a linear time complexity (O(n)).
A BST node contains an object value and two pointers: a left pointer and a right pointer. The left pointer points to nodes with values less than the current node, while the right pointer points to nodes with values greater than the current node.
For optimal performance, the value within a Binary Search Tree node should implement the Comparable interface. This allows for comparisons between different objects.
The worst-case scenario for a BST is a linear time constraint, O(n), which is the most inefficient case.
The toString() method for a BST node should return the node's value along with the values of its left and right children (null if a child is missing).
The BST stores data in a sorted order allowing for quick retrieval.

Terminology for Binary Trees

Root: The starting node of the BST; it has no parent.
Parent: A node with at least one child.
Child: A node pointed to by a parent node. Left children have values less than the parent, while right children have values greater.
Edge: The connection between a parent and a child.
Sibling: A child that shares the same parent.
Leaf: A node with no children (also called an outer or terminal node).
Internal Node: A node with at least one child (also called a parent or branch node).
Degree: The number of children a node has. In a binary tree, degrees can be 0, 1, or 2.
Level: The distance of a node from the root, measured in edges.
Height: The longest path from the root to a leaf, measured in edges.
Path: The sequence of nodes from one node to another, moving through parent-child relationships
Branch/Subtree: Any portion of a tree starting from any node.
Width(tree): The largest number of nodes on any of the levels of the tree.
Diameter of Tree: The longest path between any two leaf nodes in the tree.

Inserting into a BST

New values are compared to the root node. If the new value is less than the root, it goes down the left subtree. If it's greater, it goes down the right subtree. This process continues until an empty spot is found and the new value is placed.

Creating a BST

The first value is the root node.
Subsequent values are placed accordingly to their relationship to the existing values.

Traversal Methods

Preorder Traversal: Print the root, traverse the left subtree, and traverse the right subtree.
Inorder Traversal: Traverse the left subtree, print the root, and traverse the right subtree (returns sorted values).
Postorder Traversal: Traverse the left subtree, traverse the right subtree, and print the root.
Level-Order Traversal: Visit all nodes at a given level before moving to the next level. This traversal, unlike the recursive ones, uses a queue.

Deletion

Removing involves identifying the node to be removed and determining its degree (number of children).
- Degree 0 (Leaf): The parent's relevant pointer is set to null -Degree 1: The parent's pointer is adjusted to point to the child of the node being removed. Degree 2: The node is replaced by its inorder successor (the node with the largest value in the left subtree or smallest value in the right subtree).

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Description

Test your understanding of Binary Search Trees (BST) with this quiz. Explore questions on tree characteristics, methods, and advantages over other data structures. This quiz covers various aspects including node addition, tree height, and complexities.