How Tree Is Represented in Data Structure?
In data structure, a tree is a hierarchical structure that represents relationships between elements. It is widely used in various applications such as file systems, database systems, and network routing algorithms. In this article, we will explore how a tree is represented in data structure.
Before diving into the representation of a tree, let’s first understand some basic terminology:
- Node: Each element in a tree is called a node.
- Root: The topmost node of the tree is called the root node.
- Parent and Child: A node that is connected to another node below it is called its parent, while the connected nodes below are called its children.
- Sibling: Nodes that have the same parent are called siblings.
- Leaf: Nodes that do not have any children are called leaf nodes or external nodes.
The Tree Representation
In data structure, there are two common ways to represent a tree: using an array and using linked structures (pointers).
A tree can be represented using an array by assigning each element of the array to a specific node in the tree. The elements of the array represent the values of the nodes, while their indices represent their positions within the tree.
This representation requires additional space for nodes that do not exist in the actual tree. For example, if we have a binary tree with only three levels but we use an array representation for four levels (to maintain complete binary tree properties), the last level will have dummy nodes.
Linked Structure Representation
The linked structure representation uses pointers to connect nodes. Each node contains a value and one or more pointers to its child nodes. The root node is accessible through a pointer called the root pointer.
In this representation, each node has a dynamic memory allocation, which allows for efficient memory usage. However, it requires additional memory space for storing the pointers.
Common Tree Traversal Algorithms
Tree traversal algorithms are used to visit each node in a tree. There are three commonly used algorithms:
- Preorder Traversal: In this algorithm, the root node is visited first, followed by its left subtree and then its right subtree.
- Inorder Traversal: In this algorithm, the left subtree is visited first, followed by the root node and then the right subtree.
- Postorder Traversal: In this algorithm, the left subtree is visited first, followed by the right subtree and then the root node.
A tree is an important data structure used for representing hierarchical relationships between elements. It can be represented using either an array or linked structures depending on specific requirements. Additionally, tree traversal algorithms allow us to visit each node in a tree in a specific order.
Understanding how trees are represented in data structures is crucial for building efficient algorithms and solving various problems effectively.