Trees Data Structure

Types of Trees

General Tree

A tree with no constraints assigned to it comes under the general tree. It can have any number of nodes. Each node in a general tree can have any number of children. It is the superset of all the other kinds of trees. 

Fig 2. Example of General Tree

Directed Tree

A directed tree is a type of tree where directions are assigned on the edges. The Arrow sign is used to show the directions in a directed tree. The node with 0 in-degree is the root node of the given tree. The nodes with out-degree 0 are called the terminal or leaf nodes,, and the nodes with out-degree one or greater are called internal nodes.

Fig 3. Example of Directed Tree

Rooted Tree

A tree in which one node is present with zero in-degree is called the root node. Other than root nodes are either internal nodes or terminal nodes. The internal node is the node that has one or more children, and the terminal node is a node that has no child. 

Fig 4. Example of Rooted Tree 

Ordered Tree

In an ordered tree, all the nodes are ordered in some manner. It is a specification of a rooted tree in which nodes are in some order.

Fig 5. Example of Ordered Tree

Binary Tree

A binary tree consists of a single item called the root and two disjoint binary trees called the left subtree and right subtree

It is the type of tree in which each node can have 0,1 or 2 children; therefore, the maximum degree of any node is 2.

Fig 6. Example of Binary Tree

Binary Search Tree

It is an advancement in the binary tree which is ordered. In a binary search tree, the data item at the left child is smaller in value than the root node, and the data item at the right child is greater than the root node. In this, the left child and the right child should also be a binary search tree.

Fig 7. Example of Binary Search Tree

Also read - Data Structure MCQ

Applications of Tree Data Structure

Tree is a non-linear, hierarchical data structure consisting of nodes connected by edges. Unlike arrays and linked lists, trees allow for efficient searching, sorting, and dynamic updates, making them ideal for various real-world applications.

Applications

• File System
  Trees naturally represent hierarchical relationships, which makes them ideal for modeling file systems. Each directory is a node, with files and subfolders as child nodes, forming a tree-like structure for efficient navigation and storage.
• Searching Efficiency
  Trees like Binary Search Trees (BSTs) enable fast lookups with time complexity of O(log n) in balanced scenarios. They are widely used in search algorithms and search engines to improve query performance.
• Sorting
  Trees facilitate efficient sorting, especially through balanced binary search trees like AVL or Red-Black Trees. These structures maintain sorted data and allow in-order traversal to retrieve data in ascending order.
• Dynamic Data Handling
  Trees are well-suited for applications where data frequently changes. Their dynamic nature allows for efficient insertion and deletion without needing to reorganize the entire structure.
• Efficient Insertion and Deletion
  With efficient algorithms, trees allow fast updates, especially in self-balancing variants, making them ideal for real-time systems and databases.

Other Key Applications

• Binary Search Tree (BST):
  Used for maintaining sorted data with efficient search, insert, and delete operations.
• Heap:
  Supports priority queues used in scheduling and resource management.
• B-Tree / B+ Tree:
  Extensively used in database indexing and file systems for managing large blocks of data.
• Syntax Tree:
  Used by compilers and interpreters to parse and evaluate expressions in programming languages.
• K-D Tree:
  Organizes points in a K-dimensional space, used in computer graphics and spatial data.
• Trie (Prefix Tree):
  Efficient for implementing dictionaries, autocomplete, and IP routing with fast prefix searches.
• Suffix Tree:
  Helps in fast pattern matching and substring searches in text processing.
• Spanning Trees and Shortest Path Trees:
  Used in network design and routing algorithms to find optimal paths.
• Decision Trees:
  Widely used in machine learning and artificial intelligence for classification and regression problems.
• Other Uses:
  XML parsing, DNS servers, game development (e.g., chess strategies), and rule-based AI systems leverage tree structures for their efficiency and hierarchy.

Advantages and Disadvantages of Tree Data Structure

Trees are hierarchical, non-linear data structures that organize data through nodes connected by edges. They are crucial in modeling structured data and are commonly used in applications like file systems, compilers, and databases. However, it is essential to understand both their strengths and limitations when designing systems.

Advantages of Tree Data Structure

• Efficient Searching (O(log n))
  Self-balancing trees like AVL and Red-Black Trees provide logarithmic time complexity for search operations, making them faster than linear structures.
• Fast Insertion and Deletion
  Trees allow quick updates while maintaining order. Self-balancing variants keep operations efficient even with frequent changes.
• Hierarchical Representation
  Trees model parent-child relationships naturally, ideal for structured data like folders, decision paths, or inheritance hierarchies.
• Recursion-Friendly Structure
  Tree traversal (in-order, pre-order, post-order) is naturally implemented using recursion, making operations like search and print straightforward.
• Natural Organization of Data
  Tree structures closely resemble real-world scenarios like organizational charts or file hierarchies, enhancing clarity and manageability.
• Flexible Size
  Trees grow and shrink dynamically as data is inserted or deleted, unlike static arrays which require pre-defined sizes.

Disadvantages of Tree Data Structure

• Memory Overhead
  Trees require extra memory for storing pointers (left, right, or child links), which increases usage especially in large trees.
• Imbalanced Trees
  Without balancing, trees can become skewed (e.g., linked list-like), degrading performance from O(log n) to O(n).
• Implementation Complexity
  Compared to arrays or linked lists, trees are harder to implement and understand, especially self-balancing variants.
• Performance Limitation vs. Hashing
  In simple applications like key-value storage, hash tables offer faster O(1) lookup, insert, and delete operations.
• Algorithm Complexity
  Tree operations require a good grasp of recursive algorithms and data organization principles, posing a learning curve for beginners.

Frequently Asked Questions

1. What is the difference between a binary search tree and a binary tree?

A binary search tree is a specialization of binary trees in which the left child is smaller than the root node, and the right child is larger than the root node.

2. What is the degree of a node of a tree?

The count of the number of children of a node is defined as the degree of the node. In a binary tree, the maximum degree of a node is 2.

3. What is tree data structure?

A tree is a data structure in which the elements are not arranged in hierarchical order. It is an acyclic graph with nodes and edges.

4. What is a non-linear data structure?

In a Non-linear data structure, the elements are not arranged in a sequential manner. Trees and graphs are examples of non-linear data structures.

5. What is tree traversal?

Tree traversal is the process of visiting each node in a tree exactly once. There are three techniques, namely inorder, preorder, and postorder traversal.

Conclusion

In this article, we learned that a tree is a non-linear data structure in which elements are stored in an acyclic graph manner. We also discussed its properties and types.