In computer science, a tree data structure is a widely used data structure that represents a hierarchical structure. It is named “tree” because it resembles a tree in nature, with a root node at the top and branches extending downwards. Each node in a tree can have zero or more child nodes, except for the root node which has no parent.
The Basic Structure
A tree is made up of nodes and edges. Each node in the tree contains some data and may have links to its child nodes.
The first node in the hierarchy is called the root node. From the root node, there can be multiple levels of child nodes, forming branches that make up the overall structure of the tree.
Let’s take an example of a simple binary tree:
A / \ B C / \ D E
In this example, node A is the root node. It has two child nodes: B and C. Node B does not have any child nodes, while C has two child nodes: D and E.
Before delving deeper into the structure of a tree, let’s understand some key terminologies:
- Node: A fundamental building block of a tree that contains data and links to other nodes.
- Root Node: The topmost node in a tree that has no parent.
- Child Node: A node directly connected to another node when moving away from the root.
- Parent Node: The inverse relationship of a child node; a parent node is connected to its child node(s).
- Leaf Node: A node that does not have any child nodes.
- Sibling Nodes: Nodes that share the same parent.
Types of Trees
Trees can be classified into various types based on their properties and characteristics. Some common types of trees include:
- Binary Tree: A tree in which each node has at most two children.
- Binary Search Tree (BST): A binary tree in which the left child is always lesser than the parent, and the right child is always greater.
- N-ary Tree: A tree in which each node can have a maximum of N children.
- Balanced Tree: A tree in which the height difference between the left and right subtree of any node is not greater than a certain value.
To navigate and access the elements of a tree, various traversal algorithms are used. These algorithms define an order in which nodes are visited. Some common traversal methods include:
- Inorder Traversal: Visit nodes in Left-Root-Right order.
- Preorder Traversal: Visit nodes in Root-Left-Right order.
- Postorder Traversal: Visit nodes in Left-Right-Root order.
- Breadth-First Traversal (Level Order): Visit nodes level by level, starting from the root.
The structure of a tree data structure is fundamental for organizing and representing hierarchical data. Understanding the basic structure, terminologies, and types of trees allows us to analyze and solve problems efficiently using tree-based algorithms. Traversal algorithms further help in accessing and manipulating tree elements.
Now that you have a good grasp of the structure of a tree, you can start exploring various tree-based algorithms and their applications in computer science!