Tree Data Structure in C#

Introduction

Trees are hierarchical data structures widely used in computer science for representing hierarchical relationships between elements. They consist of nodes connected by edges, with one node designated as the root and every other node having a parent-child relationship. Trees find applications in various fields like computer science, data organization, and more.

• A tree is a hierarchical data structure consisting of nodes connected by edges.
• Unlike linear data structures (e.g., arrays, linked lists), trees have a branching structure.
• Key terminologies: root, parent, child, sibling, leaf, depth.
  

Objective

In this lesson, we'll explore the concept of trees, their terminology.

Topics Covered

1. Overview of Tree
2. Terminology
   

1. Overview of Tree

A tree is a collection of nodes where each node stores a value and has zero or more child nodes. The topmost node in a tree is called the root node. Nodes with no children are called leaf nodes. Trees are hierarchical structures, unlike linear structures like arrays and linked lists.

2. Terminology

• Node: An element in the tree that stores data and references to its child nodes.
• Root Node: The topmost node of a tree or the node which does not have any parent node is called the root node. {A} is the root node of the tree. A non-empty tree must contain exactly one root node and exactly one path from the root to all other nodes of the tree.
• Parent Node: A node that has child nodes, The node which is a predecessor of a node is called the parent node of that node. {B} is the parent node of {D, E}.
• Child Node: The node which is the immediate successor of a node is called the child node of that node. Examples: {D, E} are the child nodes of {B}.
• Leaf Node or External Node: The nodes which do not have any child nodes are called leaf nodes. {K, L, M, N, O, P, G} are the leaf nodes of the tree.
• Ancestor of a Node: Any predecessor nodes on the path of the root to that node are called Ancestors of that node. {A,B} are the ancestor nodes of the node {E}
• Depth/Level: The distance between a node and the root. The count of edges on the path from the root node to that node. The root node has level 0
• Height: The length of the longest path from a node to a leaf. The height of a tree is the height of its root node.
• Subtree: A tree rooted at a node.
• Descendant: descendants in a tree data structure are all the nodes that can be reached by following paths downward from a specific node, including its children, grandchildren, and further generations down the tree. {E,I,M,N} are the descendants of the node {B}.
  
• Sibling: Children of the same parent node are called siblings. {D,E} are called siblings.
• Internal node: A node with at least one child is called Internal Node.
• Neighbor of a Node: Parent or child nodes of that node are called neighbors of that node.

3.Conclusion

Trees are versatile data structures that find applications in various domains of computer science. Understanding the concepts of trees, their terminology, types, and traversal techniques is essential for solving complex problems and designing efficient algorithms. By implementing and working with trees in C#, you can enhance your skills in data organization and manipulation.