Tree Data Structure Overview

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Questions and Answers

What is a tree?

A tree is an ABSTRACT Data type that stores elements hierarchically, representing a non-linear hierarchical relationship.

What is a node in a tree data structure?

A node is a fundamental part of the tree, containing data and possibly links to child nodes.

What is the difference between a parent node and a child node?

A parent node has one or more child nodes, while a child node descends from its parent node.

What is the height of a tree data structure?

The height of a tree is the distance from a node to the deepest leaf in its subtree. Signup and view all the answers

What is the degree of a tree?

The degree of a tree is the highest degree of a node among all the nodes in the tree. Signup and view all the answers

What is a binary tree?

A binary tree is an ordered tree where every node has at most two children, each labeled as either a left or right child. Signup and view all the answers

What is a proper binary tree?

A proper binary tree is a binary tree where every node has either 0 or 2 children. No node has only one child. Signup and view all the answers

What is an almost complete binary tree?

An almost complete binary tree is a binary tree where all levels are fully filled except possibly the last level, and the last level must be strictly filled from left to right. Signup and view all the answers

What is a balanced binary tree?

A balanced binary tree is a binary tree where the height of the left and right subtrees of any node differs by at most 1. Signup and view all the answers

What is the purpose of tree traversal?

Tree traversal is a systematic way of accessing or visiting all the positions of a tree. Signup and view all the answers

What is the purpose of depth-first traversal?

Depth-first traversal explores as deep as possible along one branch before exploring other branches. Signup and view all the answers

What is a binary search tree (BST)?

A binary search tree is a binary tree that follows the rule that all nodes in the left subtree are smaller than the root node, and all nodes in the right subtree are larger than the root node. Signup and view all the answers

How are nodes inserted into a binary search tree?

New nodes are inserted into a BST by comparing the value to be inserted with the current node. If the value is smaller, it's inserted into the left subtree; otherwise, it's inserted into the right subtree. Signup and view all the answers

What is a level-order traversal?

Level-order traversal is a breadth-first traversal technique where you visit all the nodes on the same level before moving to the next level. This is often called breadth-first search (BFS). Signup and view all the answers

Study Notes

Tree Data Structure

A tree is an abstract data type that stores elements hierarchically.
It's a non-linear hierarchical relationship between data elements called nodes.
Nodes have a parent-child relationship.
There is one unique path between any two nodes in a tree.
A tree with n nodes has n-1 edges.
A graph is a tree if and only if it is minimally connected.

Tree Data Structure Properties

Root: The topmost node in the tree; it has no parent.
Node: A fundamental part of the tree; it contains data and possibly links to child nodes.
Edge: Connections between two nodes.
Parent Node: A node with one or more child nodes.
Child Node: A node descending from a parent node.
Leaf Node (External Node): A node with no children.
Subtree: A tree consisting of a node and its descendants.
Depth: The distance (number of edges) from the root to a specific node.
Height: The distance from a node to the deepest leaf in its subtree.
Sibling: Nodes sharing the same parent.
Degree: The total number of children a node has.
Internal Node (Non-terminal Node): A node with at least one child; nodes other than leaf nodes.

Binary Tree

A binary tree is an ordered tree with:
- At most two children per node.
- Each child is labeled as left or right.
- A left child precedes a right child in the order of children of a node.

Types of Binary Trees

Proper/Full/Strictly Binary Tree: Every node has either 0 or 2 children. No node has only one child.
- All internal nodes have two children.
- All leaves are at the same level, or at the last two levels of the tree.
Almost Complete Binary Tree:
- All levels are completely filled, except possibly the last level.
- The last level is filled from left to right.
Skewed Binary Tree/Degenerate (or Pathological) Tree: All nodes except one have one child; the remaining node has no children.
Balanced Binary Tree: The height of the left and right subtrees of any node differ by at most 1.
- Ensures logarithmic height O(log n).
- Used to maintain efficient search, insert, and delete operations.

Tree Traversal

Depth-First Traversal: Visiting nodes in a depth-first manner.
- In-order: Left subtree, root, then right subtree.
- Pre-order: Root, left subtree, right subtree.
- Post-order: Left subtree, right subtree, then root.
Breadth-First Traversal: Visiting nodes level by level, beginning from the root.

Binary Search Tree (BST)

A specialized binary tree where each node contains:
- Only smaller values in its left subtree
- Only larger values in its right subtree.

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Description

This quiz covers the fundamental concepts of tree data structures, including their definitions, properties, and hierarchical relationships. Discover the roles of nodes, edges, and unique paths that characterize trees as an abstract data type. Test your knowledge on key terms and structures involved in tree data representation.