Introduction to Tree Data Structures

Overview

• Trees are a type of data structure with wide applications in computer science.
• Previously discussed linear data structures: Array, Linked List, Stack, and Queue.
• Linear structures: Sequential data arrangement with a logical start and end.

Factors Influencing Data Structure Choice

• Data Type: Certain structures best fit specific data types.
• Operation Cost: Minimize frequent operation costs (e.g., binary search on a sorted array).
• Memory Consumption: Aim to reduce memory usage.
• Ease of Implementation: Consider simplicity, though not always ideal.

Tree Structure

• Trees represent hierarchical data (e.g., organizational charts).
• Tree as a Logical Model:
  • Collection of nodes linked to simulate hierarchy.
  • Non-linear, top node is the root.
  • Nodes contain data and references to children.

Vocabulary and Concepts

• Root: Topmost node, no parent.
• Children: Nodes linked from a parent.
• Parent: Node with links to children.
• Sibling: Nodes sharing a parent.
• Leaf Node: Node with no children.
• Internal Node: Node with at least one child.
• Ancestor/Descendant: A can be an ancestor of B if there is a path; B is descendant of A.
• Cousins/Uncle: Nodes sharing a grandparent; Uncle shares parent with a node's parent.

Properties of Trees

• Recursion: Trees can be defined recursively, with sub-trees.
• Edges: Tree with n nodes has n-1 edges.
• Depth and Height:
  • Depth: Number of edges from root to node.
  • Height: Number of edges from node to the deepest leaf.
  • Tree height is defined as the height of the root.

Types and Implementation

• Binary Tree: Each node has at most 2 children.
• Implementation:
  • Nodes with three fields: data, left child address, right child address (binary tree).
  • Defined using structures in programming languages like C/C++.

Applications of Trees

• Hierarchical Data: File systems.
• Data Organization: For quick search, insertion, and deletion (e.g., Binary Search Trees).
• Specific Trees:
  • Trie: Used for dynamic spell checking.
• Network Routing: Utilized in algorithms.

Conclusion

• Trees are versatile and used in various applications.
• Future lessons will cover Binary Search Trees and implementation details.