Welcome, Explorer! Today, we will delve deeper into the fascinating world of tree-based data structures. Building upon our comprehensive understanding of these structures, we're ready to enhance our knowledge further. Today's lesson focuses on Binary and Non-Binary Trees: their basic structure, implementation, complexity analyses, and the core operations performed on them.
As a reminder, tree data structures possess an impressive versatility that allows them to tackle many complex problems. For instance, managing hierarchies of employees in a large organization or efficiently storing words in a spell-checking system — these real-world scenarios naturally form tree-like structures!
Starting with a brief overview, a tree in computer science is a non-linear data structure representing a hierarchical and connected arrangement of entities known as nodes. A binary tree is a specific type of tree data structure where each node has, at most, two children: one left child and one right child.
On the other hand, a non-binary tree, also known as a multi-way tree, can have more than two children per node.
Before we jump into tree implementation, let's familiarize ourselves with key concepts and facts about tree data structures essential for beginners learning about trees.
Terminology:
- Root: The topmost node in a tree.
- Edge: The connection between one node to another.
- Leaf: A node that doesn't have any children.
- Depth of a Node: The number of edges from the node to the tree's root node.
- Height of a Tree: The maximal depth of the tree nodes.
- Subtree: Any node and its descendants form a subtree of the original tree.
Tree properties:
