A tree is a nonlinear data structure with hierarchical relationships between its elements without having any cycle, it is basically a real life tree flipped upside down. No cycle means one node cannot have two references to it.
- Hierarchical Structure: Trees organize data in a parent-child relationship, forming a hierarchy.
- Nodes: Each element in a tree is called a node.
- Root Node: The topmost node is the root, with no parent.
- Child Nodes: Nodes connected below another node are its children. A node can have zero or more children.
- Leaf Nodes: Nodes with no children are called leaf nodes
Types of Trees:
- Binary Tree : Each node has at most two children (left and right).
- Binary Search Tree (BST): A special kind of binary tree where the value of each node is greater than all its left children and less than all its right children. This allows for efficient searching.
Applications
- File Systems: Organize files and directories in a hierarchical structure on your computer.
- Search Algorithms: Binary search trees enable efficient searching of sorted data.
- Parse Trees: Represent the structure of expressions or programs in computer science.
- Decision Trees: Used in machine learning to make predictions based on a series of questions.
- Social Networks: Represent relationships between people (friends, followers, etc.).
- Routing Protocols: Used in computer networks to determine the best path for data packets.
Pros/Cons
Advantages of Trees:
- Hierarchical Representation: Efficiently model hierarchical relationships between data items.
- Searching: Binary Search Trees allow for fast searching of sorted data.
- Dynamic Structure: Trees can grow and shrink as data is added or removed.
Disadvantages of Trees:
- Complexity for Some Operations: Inserting or deleting elements in certain tree structures can be complex.
- Memory Usage: Storing unused space in the tree can be inefficient compared to arrays for simple data.
For tree traversal methods, check Tree Traversal Theory.