Ordered Trees and Binary Search Trees Quiz

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Questions and Answers

What is an ordered tree in the context of a directed tree?

A tree where an ordering of the nodes at each level is prescribed

Define a binary search tree.

A binary tree where each node's key satisfies certain conditions

What conditions must a key in a binary search tree satisfy in relation to the root and its subtrees?

Left subtree keys are less than the root key. 2. Root key is less than right subtree keys.

What is a height balanced binary tree or an AVL Tree?

A tree where each node is either left heavy, right heavy, or balanced in terms of subtree path lengths Signup and view all the answers

Explain the Preorder traversal technique of a binary tree.

Nodes are processed in the order: root, left subtree, right subtree Signup and view all the answers

Explain the Inorder traversal technique of a binary tree.

Nodes are processed in the order: left subtree, root, right subtree Signup and view all the answers

Explain the Postorder traversal technique of a binary tree.

Nodes are processed in the order: left subtree, right subtree, root Signup and view all the answers

Define a full binary tree.

A tree where every node has either 0 or 2 children and the number of nodes at level i is 2^(i-1). Signup and view all the answers

What is a strictly binary tree?

A tree in which every non-leaf node has exactly two children. Signup and view all the answers

How is the height of a tree defined?

The height of a tree is the length of the path from the root to the deepest node in the tree. Signup and view all the answers

Explain what a positional m-ary tree is.

A tree where the m children of any node are assumed to have m distinct positions. Signup and view all the answers

Define a forest in the context of trees.

A set of disjoint trees obtained by deleting the root and its connecting edges. Signup and view all the answers

What is an m-ary tree?

A tree in which the out degree of every node is less than or equal to m. Signup and view all the answers

What is the purpose of constructing a B tree?

To efficiently store and search for data in a sorted manner. Signup and view all the answers

Explain the process of inserting data '5' into the B tree.

Insert '5' into the leaf node containing 1, 2, and then split the node into 1, 2 and 5. Signup and view all the answers

What happens during an overflow in a B tree?

When a node in the B tree has too many keys, it is split into two nodes. Signup and view all the answers

Describe the key characteristics of a 2-3 tree.

A 2-3 tree has all data at the leaves, orders data from minimum to maximum, and is a balanced tree. Signup and view all the answers

What is the primary advantage of using a B tree over a binary search tree?

B trees are optimized for disk access and can have a higher fanout factor, reducing disk I/O operations. Signup and view all the answers

How does a B tree support efficient range queries?

B trees allow for faster range queries by traversing fewer levels in the tree compared to binary search trees. Signup and view all the answers

Study Notes

Tree Data Structures

An ordered tree is a directed tree where an ordering of the nodes at each level is prescribed.
Siblings are nodes that share the same parent node.

Binary Search Tree

A binary search tree is a binary tree in which each node possesses a key that satisfies the following conditions:
All keys (if any) in the left subtree of the root precede the key in the root.
The key in the root precedes all keys (if any) in the right subtree.
The left and right subtrees of the root are again search trees.

AVL Tree (Height Balanced Binary Tree)

A tree is called AVL (height balance binary tree) if each node possesses one of the following properties:
A node is called left heavy if the longest path in its left subtree is one longer than the longest path in its right subtree.
A node is called right heavy if the longest path in the right subtree is one longer than the path in its left subtree.
A node is called balanced if the longest path in both the right and left subtrees are equal.

Traversal Techniques

There are three ways of traversing a binary tree: Preorder, Inorder, and Postorder traversal.

B-Tree of Order 5

A B-tree of order 5 can be constructed for the given data: 1, 6, 7, 2, 11, 5, 10, 13, 12, 20, 16, 24, 3, 4, 18, 19, 14, 25.

2-3 Tree

A 2-3 tree is a type of data structure with the following properties:
All data appears at the leaves.
Data elements are ordered from left (minimum) to right (maximum).

Other Tree Concepts

A forest is a set of disjoint trees obtained by deleting the root and its edges connecting the nodes at level 1.
A strictly binary tree (sometimes proper binary tree or 2-tree or full binary tree) is a tree in which every node other than the leaves has two children.
A complete binary tree is a tree in which every node other than the leaves has two children, and all leaf nodes are at the same level.
The height of a tree is the length of the path from the root to the deepest node in the tree.
A positional m-ary tree is an m-ary tree in which the m children of any node are assumed to have m distinct positions.
A full or complete m-ary tree is a tree in which the out degree of each and every node is exactly equal to m or 0, and the number of nodes at level i is m(i-1).
An m-ary tree is a tree in which the out degree of every node is less than or equal to m.

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Description

Test your knowledge on ordered trees and binary search trees. Learn about the characteristics and properties of ordered trees and binary search trees in this quiz based on topics from Prof. Pradyumansinh Jadeja's Data Structure course.