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Tree is a non-linear data structure. It consists of nodes and edges. A tree represents data in a hierarchical organization. It is a special type of connected graph without any cycle or circuit.

Tree Terminologies:

• Node: Node is the main component of a tree that stores the data along with the links to other nodes.
• Edge: Edge( also called branch) connects two nodes of a tree. A node can have more than one edge.
• Parent: Parent node is a predecessor to any other node. In simple words, it is a node in the tree that has branches to other nodes.
• Child: The node which is connected below to another node is called a child of that node. All nodes except the root node are child nodes.
• Root: The first node of the tree which originates it is called the root of the tree. A tree can have only one root.
• Leaf node(External node): Nodes with no child are called leaf nodes or external nodes.
• Internal node(Non-Leaf node): Nodes with at least one child is called an internal node or non-leaf nodes.
• Siblings: Nodes having the same parent are called siblings.
• Cousins: The nodes belonging to the same level with different parent nodes.
• Degree: Degree of a node is defined as the number of children of that node. The degree of the tree is the highest degree of a node among all the nodes.
• Path: The nodes in the tree has to be reachable from other nodes through a unique sequence of edges called path. The number of edges in a path is called the length of the path.
• Level of a node: The level of a node is defined as the number of edges in the unique path between the root and the node.
• Subtree: A tree formed by a node and all of its descendants in the tree is called a subtree.

TREE

Applications of Tree:

• File Systems: The file system of a computer is often represented as a tree. Each folder or directory is a node in the tree, and files are the leaves.
• XML Parsing: Trees are used to parse and process XML documents. An XML document can be thought of as a tree, with elements as nodes and attributes as properties of the nodes.
• Database Indexing: Many databases use trees to index their data. The B-tree and its variations are commonly used for this purpose.
• Compiler Design: The syntax of programming languages is often defined using a tree structure called a parse tree. This is used by compilers to understand the structure of the code and generate machine code from it.
• Artificial Intelligence: Decision trees are often used in artificial intelligence to make decisions based on a series of criteria.

Real-Time Applications of Tree :

• Databases use tree data structure for indexing.
• Tree data structure is used in file directory management.
• DNS uses tree data structure.
• Trees are used in several games like moves in chess.
• Decision-based algorithms in machine learning uses tree algorithms.

• Efficient searching: Trees are particularly efficient for searching and retrieving data. The time complexity of searching in a tree is typically O(log n), which means that it is very fast even for very large data sets.
• Flexible size: Trees can grow or shrink dynamically depending on the number of nodes that are added or removed. This makes them particularly useful for applications where the data size may change over time.
• Easy to traverse: Traversing a tree is a simple operation, and it can be done in several different ways depending on the requirements of the application. This makes it easy to retrieve and process data from a tree structure.
• Easy to maintain: Trees are easy to maintain because they enforce a strict hierarchy and relationship between nodes. This makes it easy to add, remove, or modify nodes without affecting the rest of the tree structure.
• Natural organization: Trees have a natural hierarchical organization that can be used to represent many types of relationships. This makes them particularly useful for representing things like file systems, organizational structures, and taxonomies.
• Fast insertion and deletion: Inserting and deleting nodes in a tree can be done in O(log n) time, which means that it is very fast even for very large trees.